Adrian A. Correndo 03/24/2022
This code was prepared as a tutorial for potential users of the Modified
Arcsine-log Calibration Curve (modALCC) detailed in Correndo et
al. (2017).
Instructions for users
-
Load your dataframe with soil test value (STV) and relative yield (RY) data.
-
Specify the following arguments into the function -modALCC()-:
(i). data (optional),
(ii). soil test value STV and relative yield RY,
(iii). target of relative yield (e.g. 90%),
(iv). desired confidence level (e.g. 0.95 for 1 - alpha(0.05)). Used
for the estimation of critical soil test value (CSTV) lower and upper
limits.
-
Run and check results in a data.frame.
-
Check residuals plot, and warnings related to potential leverage points.
-
Adjust curve plots as desired.
Please, refer any question to Adrian Correndo,
correndo@agro.uba.ar - correndo@ksu.edu.
Note: RY should be expressed relative to a maximum in order to
obtain values bounded at %100. Otherwise, arcsine transformation doesn’t
work. If RY values > 100% are found, the function will cap them up to
100% and will display a warning about this.
References
*Correndo, A.A., Salvagiotti, F., García, F.O. and Gutiérrez-Boem, F.H.,
2017. A modification of the arcsine–log calibration curve for analysing
soil test value–relative yield relationships. Crop and Pasture Science,
68(3), pp.297-304. https://doi.org/10.1071/CP16444 *
# Install if needed
# install.packages("easypackages")
# install.packages("devtools")
library(easypackages) # Helps to load packages and install & load them if they are not installed yet.
library(devtools)
packages("readxl") # Open xlsx files
packages("tidyverse", "ggpmisc") # Data wrangling and plots
packages("smatr") # SMA regression analysis for reference
packages("agridat") # For cotton example dataset# Example 1 dataset
data_1 = data.frame("RY" = c(65,80,85,88,90,94,93,96,97,95,98,100,99,99,100),
"STV" = c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15))
# Example 2 dataframe. Imported from csv file
# It can be easily replaced with your own csv file
data_2 = read.csv(file = "data_test.csv")
# Example 3 dataframe. Imported from xlsx file
data_3 = readxl::read_xlsx(path ="data_3.xlsx", sheet = 1)
# Create nested structure as example of multiple datasets
data.all = bind_rows(data_1, data_2, data_3, .id = "id") %>%
tidyr::nest(data = c("STV", "RY"))modALCC <- function(data=NULL, RY, STV, target, confidence){
# Add a function to cap if there are RY values > 100
ry <- rlang::eval_tidy(data = data, rlang::quo(ifelse({{RY}} > 100, 100, as.double({{RY}})) ))
n <- length(ry) # Sample size
df <- n - 2 # Degrees of freedom
prob <- 1-((1-confidence)/2) # Probability for t-dist
tvalue <- qt(p=prob, df = df) # Student-t value
arc_RY <- asin(sqrt(ry/100)) - asin(sqrt(target/100)) # RY transformation (centered to target)
ln_STV <- rlang::eval_tidy(data = data, rlang::quo(log({{STV}}) ) ) # STV natural log transformation
r <- cor(ln_STV, arc_RY, method = "pearson") # Pearson correlation (r)
p_value <- cor.test(ln_STV,arc_RY, method = "pearson")$p.value # p-value of r
slope <- sd(ln_STV)/sd(arc_RY) # SMA slope for ln_STV ~ arc_RY
intercept <- mean(ln_STV) - (mean(arc_RY)*slope) # Intercept
SMA_line <- intercept + slope * arc_RY # Fitted ln_STV for observed RY
CSTV <- exp(intercept) # Critical STV for specified RY-target and confidence (1-alpha)
MSE <- sum((SMA_line-ln_STV)^2)/df # Mean Square Error of ln_STV
SSx <- sum((mean(arc_RY)-arc_RY)^2) # Sum of Squares of arc_RY
SE_int <- sqrt(MSE*((1/n)+ ((mean(arc_RY)^2)/SSx))) # Standard Error intercept
CSTV_lower <- exp(intercept - (tvalue * SE_int)) # Lower limit of CSTV
CSTV_upper <- exp(intercept + (tvalue * SE_int)) # Upper limit of CSTV
new_RY <- seq(min(ry),100, by=0.2) # New RY vector up to %100 to fit curve
new_arc_RY <- asin(sqrt(new_RY/100)) - asin(sqrt(target/100)) # Transforming new_RY vector
fitted_Line <- intercept + slope * new_arc_RY # Fitted ln_STV for curve plot
fitted_STV <- exp(fitted_Line) # Fitted ln_STV for new_RY
residuals <- ln_STV - SMA_line # Residuals of SMA Regression
fitted_axis <- ln_STV + slope * arc_RY # Fitted axis to check SMA residuals
target <- target # Target RY to show on summary
confidence <- confidence # Confidence level to show on summary
# Critical STV for RY = 90 & 100
arc_ry_100 <- asin(sqrt(ry/100)) - asin(sqrt(1))
cstv.100 <- exp(mean(ln_STV) - (mean(arc_ry_100)*(sd(ln_STV)/sd(arc_ry_100))))
arc_ry_90 <- asin(sqrt(ry/100)) - asin(sqrt(90/100))
cstv.90 <- exp(mean(ln_STV) - (mean(arc_ry_90)*(sd(ln_STV)/sd(arc_ry_90))))
# Count cases with STV > x2 cstv90 and STV > cstv100
n.90x2 <- rlang::eval_tidy(data=data, rlang::quo(length(which({{STV}} > (2*cstv.90))) ) )
n.100 <- rlang::eval_tidy(data=data, rlang::quo(length(which({{STV}} > cstv.100)) ) )
# Outcome
results <- as.data.frame(list("n" = n, "r" = r, "target" = target,"CSTV" = CSTV,
"LL" = CSTV_lower,"UL" = CSTV_upper,"confidence" = confidence,"p_value" = p_value,
"CSTV90" = cstv.90, "n.90x2" = n.90x2,"CSTV100" = cstv.100,"n.100" = n.100)) %>%
bind_cols(., as.data.frame(list("RY.fitted" = new_RY, "STV.fitted" = fitted_STV))%>% tidyr::nest(Curve = c("RY.fitted", "STV.fitted"))) %>%
bind_cols(., as.data.frame(list("ln_STV" = ln_STV, "arc_RY" = arc_RY, "SMA_line" = SMA_line,"residuals" = residuals,"fitted_axis" = fitted_axis)) %>% tidyr::nest(SMA = c("ln_STV", "arc_RY", "SMA_line","residuals", "fitted_axis") ) )
# WARNINGS
rlang::eval_tidy(data = data, rlang::quo(if (max({{RY}}) > 100) {
warning("One or more original RY values exceeded 100%. All RY values greater
than 100% have been capped to 100%.", call. = FALSE) } ) )
if (results$n.100 > 0) {warning(paste0(n.100," STV points exceeded the CSTV for 100%.
Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
re-run the modALCC(), and check results."), call. = FALSE) }
if (results$n.90x2 > 0) {warning(paste0(n.90x2," STV points exceeded two-times (2x)
the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
removing extreme points, re-run the modALCC(), and check results."), call. = FALSE) }
return(results) }# RY target = 90%, confidence level = 0.95, replace with your desired values
# Data 1
# Using dataframe
fit_example_1 = modALCC(data = data_1, RY = RY, STV = STV, target=90, confidence = 0.95)## Warning: 7 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
# Alternative using the vectors
#fit_example_1 = ALCC(RY = data_1$RY,STV = data_1$STV, target=90,confidence = 0.95)
fit_example_1## n r target CSTV LL UL confidence p_value
## 1 15 0.9682908 90 4.478476 3.947041 5.081463 0.95 3.296044e-09
## CSTV90 n.90x2 CSTV100 n.100
## 1 4.478476 7 19.15054 0
## Curve
## 1 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 1.097927, 1.108379, 1.118944, 1.129625, 1.140423, 1.151339, 1.162376, 1.173535, 1.184817, 1.196225, 1.207760, 1.219425, 1.231221, 1.243150, 1.255214, 1.267415, 1.279755, 1.292236, 1.304860, 1.317630, 1.330548, 1.343616, 1.356836, 1.370210, 1.383742, 1.397433, 1.411286, 1.425303, 1.439488, 1.453842, 1.468369, 1.483071, 1.497951, 1.513012, 1.528257, 1.543689, 1.559311, 1.575127, 1.591138, 1.607350, 1.623765, 1.640386, 1.657217, 1.674262, 1.691525, 1.709008, 1.726717, 1.744655, 1.762826, 1.781234, 1.799883, 1.818779, 1.837924, 1.857325, 1.876985, 1.896910, 1.917103, 1.937572, 1.958319, 1.979352, 2.000675, 2.022293, 2.044214, 2.066441, 2.088983, 2.111844, 2.135031, 2.158551, 2.182410, 2.206616, 2.231175, 2.256095, 2.281384, 2.307048, 2.333097, 2.359537, 2.386379, 2.413629, 2.441298, 2.469395, 2.497929, 2.526910, 2.556347, 2.586252, 2.616636, 2.647508, 2.678882, 2.710768, 2.743179, 2.776127, 2.809626, 2.843690, 2.878331, 2.913565, 2.949407, 2.985872, 3.022976, 3.060736, 3.099169, 3.138294, 3.178128, 3.218691, 3.260004, 3.302086, 3.344960, 3.388649, 3.433176, 3.478564, 3.524841, 3.572032, 3.620165, 3.669269, 3.719374, 3.770512, 3.822716, 3.876020, 3.930460, 3.986075, 4.042904, 4.100988, 4.160372, 4.221100, 4.283223, 4.346790, 4.411856, 4.478476, 4.546710, 4.616622, 4.688278, 4.761749, 4.837110, 4.914440, 4.993823, 5.075351, 5.159117, 5.245225, 5.333784, 5.424910, 5.518728, 5.615374, 5.714992, 5.817737, 5.923779, 6.033299, 6.146495, 6.263582, 6.384794, 6.510388, 6.640644, 6.775870, 6.916408, 7.062634, 7.214969, 7.373879, 7.539891, 7.713596, 7.895664, 8.086860, 8.288063, 8.500287, 8.724716, 8.962742, 9.216022, 9.486552, 9.776766, 10.089688, 10.429142, 10.800084, 11.209119, 11.665380, 12.182103, 12.779738, 13.492946, 14.389790, 15.647308, 19.150544
## SMA
## 1 0.00000000, 0.69314718, 1.09861229, 1.38629436, 1.60943791, 1.79175947, 1.94591015, 2.07944154, 2.19722458, 2.30258509, 2.39789527, 2.48490665, 2.56494936, 2.63905733, 2.70805020, -0.31130128, -0.14189705, -0.07594886, -0.03199105, 0.00000000, 0.07428349, 0.05398723, 0.12039263, 0.14766754, 0.09623715, 0.17985350, 0.32175055, 0.22158313, 0.22158313, 0.32175055, 0.09342397, 0.85846552, 1.15629226, 1.35480886, 1.49928272, 1.83475226, 1.74309289, 2.04298443, 2.16615987, 1.93389654, 2.31151393, 2.95233114, 2.49996793, 2.49996793, 2.95233114, -0.09342397, -0.16531834, -0.05767997, 0.03148550, 0.11015519, -0.04299279, 0.20281726, 0.03645711, 0.03106471, 0.36868855, 0.08638134, -0.46742449, 0.06498143, 0.13908940, -0.24428093, -1.40585875, 0.05232998, 0.75562183, 1.24182049, 1.60943791, 2.12722900, 2.18972031, 2.62314325, 2.86410172, 2.73719891, 3.21012648, 3.93795506, 3.56563456, 3.63974254, 4.16109861
# Data 2
fit_example_2 = modALCC(data = data_2, RY = RY, STV = STV, target=90, confidence = 0.95)## Warning: 9 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 22 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
fit_example_2## n r target CSTV LL UL confidence p_value
## 1 137 0.7164928 90 23.25457 21.57156 25.06888 0.95 7.314913e-23
## CSTV90 n.90x2 CSTV100 n.100
## 1 23.25457 22 53.10299 9
## Curve
## 1 12.000000, 12.200000, 12.400000, 12.600000, 12.800000, 13.000000, 13.200000, 13.400000, 13.600000, 13.800000, 14.000000, 14.200000, 14.400000, 14.600000, 14.800000, 15.000000, 15.200000, 15.400000, 15.600000, 15.800000, 16.000000, 16.200000, 16.400000, 16.600000, 16.800000, 17.000000, 17.200000, 17.400000, 17.600000, 17.800000, 18.000000, 18.200000, 18.400000, 18.600000, 18.800000, 19.000000, 19.200000, 19.400000, 19.600000, 19.800000, 20.000000, 20.200000, 20.400000, 20.600000, 20.800000, 21.000000, 21.200000, 21.400000, 21.600000, 21.800000, 22.000000, 22.200000, 22.400000, 22.600000, 22.800000, 23.000000, 23.200000, 23.400000, 23.600000, 23.800000, 24.000000, 24.200000, 24.400000, 24.600000, 24.800000, 25.000000, 25.200000, 25.400000, 25.600000, 25.800000, 26.000000, 26.200000, 26.400000, 26.600000, 26.800000, 27.000000, 27.200000, 27.400000, 27.600000, 27.800000, 28.000000, 28.200000, 28.400000, 28.600000, 28.800000, 29.000000, 29.200000, 29.400000, 29.600000, 29.800000, 30.000000, 30.200000, 30.400000, 30.600000, 30.800000, 31.000000, 31.200000, 31.400000, 31.600000, 31.800000, 32.000000, 32.200000, 32.400000, 32.600000, 32.800000, 33.000000, 33.200000, 33.400000, 33.600000, 33.800000, 34.000000, 34.200000, 34.400000, 34.600000, 34.800000, 35.000000, 35.200000, 35.400000, 35.600000, 35.800000, 36.000000, 36.200000, 36.400000, 36.600000, 36.800000, 37.000000, 37.200000, 37.400000, 37.600000, 37.800000, 38.000000, 38.200000, 38.400000, 38.600000, 38.800000, 39.000000, 39.200000, 39.400000, 39.600000, 39.800000, 40.000000, 40.200000, 40.400000, 40.600000, 40.800000, 41.000000, 41.200000, 41.400000, 41.600000, 41.800000, 42.000000, 42.200000, 42.400000, 42.600000, 42.800000, 43.000000, 43.200000, 43.400000, 43.600000, 43.800000, 44.000000, 44.200000, 44.400000, 44.600000, 44.800000, 45.000000, 45.200000, 45.400000, 45.600000, 45.800000, 46.000000, 46.200000, 46.400000, 46.600000, 46.800000, 47.000000, 47.200000, 47.400000, 47.600000, 47.800000, 48.000000, 48.200000, 48.400000, 48.600000, 48.800000, 49.000000, 49.200000, 49.400000, 49.600000, 49.800000, 50.000000, 50.200000, 50.400000, 50.600000, 50.800000, 51.000000, 51.200000, 51.400000, 51.600000, 51.800000, 52.000000, 52.200000, 52.400000, 52.600000, 52.800000, 53.000000, 53.200000, 53.400000, 53.600000, 53.800000, 54.000000, 54.200000, 54.400000, 54.600000, 54.800000, 55.000000, 55.200000, 55.400000, 55.600000, 55.800000, 56.000000, 56.200000, 56.400000, 56.600000, 56.800000, 57.000000, 57.200000, 57.400000, 57.600000, 57.800000, 58.000000, 58.200000, 58.400000, 58.600000, 58.800000, 59.000000, 59.200000, 59.400000, 59.600000, 59.800000, 60.000000, 60.200000, 60.400000, 60.600000, 60.800000, 61.000000, 61.200000, 61.400000, 61.600000, 61.800000, 62.000000, 62.200000, 62.400000, 62.600000, 62.800000, 63.000000, 63.200000, 63.400000, 63.600000, 63.800000, 64.000000, 64.200000, 64.400000, 64.600000, 64.800000, 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 2.336883, 2.355345, 2.373822, 2.392314, 2.410824, 2.429353, 2.447902, 2.466472, 2.485066, 2.503683, 2.522326, 2.540994, 2.559691, 2.578416, 2.597171, 2.615957, 2.634775, 2.653625, 2.672510, 2.691430, 2.710385, 2.729377, 2.748407, 2.767476, 2.786584, 2.805733, 2.824922, 2.844155, 2.863430, 2.882748, 2.902112, 2.921521, 2.940976, 2.960478, 2.980028, 2.999627, 3.019275, 3.038973, 3.058722, 3.078522, 3.098374, 3.118280, 3.138239, 3.158253, 3.178322, 3.198446, 3.218628, 3.238866, 3.259162, 3.279517, 3.299931, 3.320405, 3.340940, 3.361536, 3.382194, 3.402915, 3.423698, 3.444546, 3.465459, 3.486436, 3.507480, 3.528590, 3.549767, 3.571012, 3.592326, 3.613709, 3.635161, 3.656685, 3.678279, 3.699945, 3.721683, 3.743495, 3.765380, 3.787340, 3.809375, 3.831485, 3.853672, 3.875936, 3.898277, 3.920697, 3.943195, 3.965774, 3.988432, 4.011172, 4.033993, 4.056896, 4.079883, 4.102953, 4.126107, 4.149347, 4.172672, 4.196083, 4.219582, 4.243168, 4.266843, 4.290606, 4.314460, 4.338404, 4.362439, 4.386567, 4.410787, 4.435100, 4.459507, 4.484009, 4.508607, 4.533301, 4.558092, 4.582980, 4.607967, 4.633054, 4.658240, 4.683527, 4.708916, 4.734406, 4.760000, 4.785698, 4.811500, 4.837408, 4.863422, 4.889542, 4.915771, 4.942108, 4.968555, 4.995111, 5.021779, 5.048559, 5.075451, 5.102457, 5.129578, 5.156813, 5.184165, 5.211634, 5.239220, 5.266926, 5.294751, 5.322696, 5.350763, 5.378953, 5.407266, 5.435703, 5.464265, 5.492953, 5.521768, 5.550712, 5.579784, 5.608986, 5.638319, 5.667784, 5.697382, 5.727114, 5.756981, 5.786984, 5.817124, 5.847402, 5.877819, 5.908377, 5.939075, 5.969916, 6.000901, 6.032030, 6.063304, 6.094726, 6.126295, 6.158014, 6.189883, 6.221903, 6.254076, 6.286402, 6.318884, 6.351522, 6.384317, 6.417271, 6.450385, 6.483660, 6.517098, 6.550699, 6.584466, 6.618399, 6.652499, 6.686769, 6.721209, 6.755821, 6.790607, 6.825566, 6.860702, 6.896016, 6.931508, 6.967181, 7.003035, 7.039073, 7.075296, 7.111705, 7.148302, 7.185089, 7.222066, 7.259237, 7.296601, 7.334162, 7.371920, 7.409878, 7.448036, 7.486397, 7.524963, 7.563734, 7.602714, 7.641903, 7.681304, 7.720918, 7.760747, 7.800794, 7.841059, 7.881546, 7.922255, 7.963189, 8.004350, 8.045739, 8.087360, 8.129213, 8.171302, 8.213628, 8.256193, 8.298999, 8.342049, 8.385345, 8.428890, 8.472684, 8.516732, 8.561034, 8.605594, 8.650414, 8.695497, 8.740844, 8.786458, 8.832342, 8.878499, 8.924930, 8.971640, 9.018629, 9.065902, 9.113461, 9.161308, 9.209446, 9.257879, 9.306609, 9.355639, 9.404972, 9.454611, 9.504560, 9.554821, 9.605397, 9.656292, 9.707509, 9.759051, 9.810922, 9.863125, 9.915663, 9.968541, 10.021761, 10.075327, 10.129242, 10.183511, 10.238138, 10.293126, 10.348478, 10.404200, 10.460295, 10.516766, 10.573619, 10.630857, 10.688485, 10.746507, 10.804928, 10.863751, 10.922982, 10.982625, 11.042685, 11.103166, 11.164074, 11.225413, 11.287189, 11.349407, 11.412071, 11.475188, 11.538762, 11.602799, 11.667304, 11.732284, 11.797744, 11.863690, 11.930128, 11.997064, 12.064504, 12.132455, 12.200922, 12.269914, 12.339435, 12.409494, 12.480096, 12.551250, 12.622962, 12.695240, 12.768091, 12.841522, 12.915543, 12.990159, 13.065381, 13.141215, 13.217670, 13.294756, 13.372480, 13.450851, 13.529880, 13.609574, 13.689945, 13.771001, 13.852752, 13.935209, 14.018381, 14.102280, 14.186917, 14.272302, 14.358448, 14.445364, 14.533064, 14.621560, 14.710863, 14.800987, 14.891945, 14.983749, 15.076415, 15.169955, 15.264384, 15.359717, 15.455968, 15.553154, 15.651289, 15.750391, 15.850475, 15.951559, 16.053661, 16.156798, 16.260989, 16.366253, 16.472609, 16.580077, 16.688679, 16.798434, 16.909365, 17.021495, 17.134845, 17.249441, 17.365306, 17.482466, 17.600946, 17.720773, 17.841975, 17.964580, 18.088618, 18.214118, 18.341112, 18.469631, 18.599711, 18.731384, 18.864686, 18.999655, 19.136328, 19.274745, 19.414946, 19.556974, 19.700873, 19.846689, 19.994468, 20.144260, 20.296115, 20.450087, 20.606231, 20.764604, 20.925266, 21.088278, 21.253707, 21.421618, 21.592084, 21.765177, 21.940974, 22.119557, 22.301010, 22.485420, 22.672882, 22.863491, 23.057350, 23.254567, 23.455255, 23.659532, 23.867524, 24.079364, 24.295192, 24.515156, 24.739412, 24.968128, 25.201479, 25.439655, 25.682855, 25.931293, 26.185196, 26.444810, 26.710396, 26.982235, 27.260631, 27.545908, 27.838422, 28.138553, 28.446718, 28.763369, 29.089000, 29.424154, 29.769426, 30.125473, 30.493024, 30.872890, 31.265974, 31.673293, 32.095997, 32.535388, 32.992958, 33.470424, 33.969784, 34.493376, 35.043972, 35.624899, 36.240199, 36.894871, 37.595217, 38.349366, 39.168111, 40.066313, 41.065417, 42.198418, 43.520998, 45.142004, 47.343203, 53.102988
## SMA
## 1 1.386294361, 1.609437912, 1.791759469, 1.791759469, 1.945910149, 1.945910149, 2.197224577, 2.197224577, 2.302585093, 2.302585093, 2.302585093, 2.302585093, 2.397895273, 2.397895273, 2.484906650, 2.564949357, 2.564949357, 2.564949357, 2.564949357, 2.564949357, 2.639057330, 2.639057330, 2.639057330, 2.639057330, 2.639057330, 2.708050201, 2.708050201, 2.708050201, 2.708050201, 2.708050201, 2.772588722, 2.772588722, 2.772588722, 2.772588722, 2.772588722, 2.833213344, 2.833213344, 2.833213344, 2.833213344, 2.890371758, 2.890371758, 2.890371758, 2.890371758, 2.944438979, 2.944438979, 2.944438979, 2.944438979, 2.995732274, 2.995732274, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.135494216, 3.135494216, 3.135494216, 3.178053830, 3.178053830, 3.178053830, 3.218875825, 3.218875825, 3.218875825, 3.218875825, 3.258096538, 3.258096538, 3.295836866, 3.295836866, 3.295836866, 3.295836866, 3.332204510, 3.332204510, 3.332204510, 3.367295830, 3.401197382, 3.401197382, 3.433987204, 3.433987204, 3.526360525, 3.555348061, 3.555348061, 3.555348061, 3.583518938, 3.583518938, 3.583518938, 3.610917913, 3.610917913, 3.610917913, 3.610917913, 3.637586160, 3.637586160, 3.663561646, 3.663561646, 3.713572067, 3.713572067, 3.713572067, 3.713572067, 3.737669618, 3.737669618, 3.737669618, 3.737669618, 3.737669618, 3.761200116, 3.784189634, 3.784189634, 3.806662490, 3.806662490, 3.828641396, 3.850147602, 3.850147602, 3.871201011, 3.871201011, 3.891820298, 3.912023005, 3.912023005, 3.912023005, 3.912023005, 3.912023005, 3.931825633, 3.931825633, 3.951243719, 3.988984047, 3.988984047, 3.988984047, 3.988984047, 4.007333185, 4.007333185, 4.007333185, 4.025351691, 4.025351691, -0.895304167, -0.473648276, -0.246924949, -0.413563898, -0.061746450, -0.311301282, -0.016314700, -0.103238229, -0.154283264, -0.141897055, -0.141897055, -0.075948861, -0.383302283, -0.554140835, 0.017057900, -0.257889186, -0.235848272, -0.190222134, -0.311301282, -0.031991051, -0.047112430, -0.463647609, -0.178429054, -0.201848221, -0.075948861, -0.332136508, -0.116398476, -0.246924949, -0.213320253, -0.178429054, -0.103238229, 0.000000000, -0.089766292, -0.383302283, -0.166454709, 0.321750554, -0.213320253, -0.047112430, -0.154283264, -0.141897055, 0.017057900, -0.089766292, -0.224650010, 0.221583133, -0.075948861, -0.190222134, 0.179853500, -0.178429054, -0.342464683, 0.120392634, -0.166454709, 0.096237148, -0.352740374, -0.047112430, 0.321750554, -0.075948861, -0.129276257, -0.047112430, -0.332136508, 0.017057900, 0.321750554, 0.179853500, -0.268749461, 0.321750554, 0.321750554, 0.221583133, 0.321750554, -0.116398476, 0.000000000, 0.017057900, -0.129276257, -0.075948861, 0.147667544, 0.321750554, 0.321750554, 0.221583133, 0.053987227, 0.120392634, 0.034994002, -0.089766292, 0.147667544, 0.321750554, 0.120392634, 0.321750554, 0.074283491, 0.179853500, 0.321750554, 0.034994002, 0.120392634, 0.221583133, 0.147667544, 0.017057900, 0.221583133, 0.074283491, 0.179853500, -0.031991051, 0.074283491, 0.034994002, 0.179853500, 0.053987227, 0.179853500, 0.321750554, 0.321750554, 0.179853500, 0.321750554, 0.179853500, -0.031991051, 0.321750554, 0.074283491, 0.221583133, 0.179853500, 0.074283491, -0.031991051, 0.120392634, -0.047112430, 0.096237148, 0.096237148, 0.120392634, 0.053987227, 0.096237148, 0.321750554, 0.321750554, 0.321750554, 0.179853500, 0.321750554, 0.321750554, 0.321750554, 0.034994002, 0.321750554, 0.147667544, 0.221583133, 0.179853500, 0.321750554, 0.147667544, 0.034994002, 0.321750554, 0.179853500, 0.848817889, 1.930943814, 2.512800241, 2.085142686, 2.988037180, 2.347586614, 3.104631955, 2.881553835, 2.750553280, 2.782340901, 2.782340901, 2.951588508, 2.162805253, 1.724369955, 3.190278467, 2.484661929, 2.541227115, 2.658320765, 2.347586614, 3.064400604, 3.025593520, 1.956609247, 2.688586196, 2.628483898, 2.951588508, 2.294115672, 2.847779742, 2.512800241, 2.599042396, 2.688586196, 2.881553835, 3.146501547, 2.916127838, 2.162805253, 2.719316822, 3.972233202, 2.599042396, 3.025593520, 2.750553280, 2.782340901, 3.190278467, 2.916127838, 2.569966024, 3.715166324, 2.951588508, 2.658320765, 3.608072556, 2.688586196, 2.267609729, 3.455473846, 2.719316822, 3.393481883, 2.241238484, 3.025593520, 3.972233202, 2.951588508, 2.814730564, 3.025593520, 2.294115672, 3.190278467, 3.972233202, 3.608072556, 2.456790422, 3.972233202, 3.972233202, 3.715166324, 3.972233202, 2.847779742, 3.146501547, 3.190278467, 2.814730564, 2.951588508, 3.525471415, 3.972233202, 3.972233202, 3.715166324, 3.285052862, 3.455473846, 3.236309179, 2.916127838, 3.525471415, 3.972233202, 3.455473846, 3.972233202, 3.337140628, 3.608072556, 3.972233202, 3.236309179, 3.455473846, 3.715166324, 3.525471415, 3.190278467, 3.715166324, 3.337140628, 3.608072556, 3.064400604, 3.337140628, 3.236309179, 3.608072556, 3.285052862, 3.608072556, 3.972233202, 3.972233202, 3.608072556, 3.972233202, 3.608072556, 3.064400604, 3.972233202, 3.337140628, 3.715166324, 3.608072556, 3.337140628, 3.064400604, 3.455473846, 3.025593520, 3.393481883, 3.393481883, 3.455473846, 3.285052862, 3.393481883, 3.972233202, 3.972233202, 3.972233202, 3.608072556, 3.972233202, 3.972233202, 3.972233202, 3.236309179, 3.972233202, 3.525471415, 3.715166324, 3.608072556, 3.972233202, 3.525471415, 3.236309179, 3.972233202, 3.608072556, 0.537476472, -0.321505902, -0.721040772, -0.293383216, -1.042127031, -0.401676465, -0.907407377, -0.684329258, -0.447968187, -0.479755808, -0.479755808, -0.649003415, 0.235090020, 0.673525318, -0.705371817, 0.080287429, 0.023722242, -0.093371408, 0.217362743, -0.499451247, -0.386536191, 0.682448083, -0.049528866, 0.010573431, -0.312531178, 0.413934529, -0.139729541, 0.195249960, 0.109007805, 0.019464006, -0.108965113, -0.373912825, -0.143539116, 0.609783469, 0.053271901, -1.139019858, 0.234170948, -0.192380176, 0.082660064, 0.108030857, -0.299906709, -0.025756080, 0.320405734, -0.770727345, -0.007149529, 0.286118214, -0.663633577, 0.307146078, 0.728122544, -0.410951409, 0.325205616, -0.348959445, 0.803283954, 0.018928917, -0.927710764, 0.139453945, 0.276311890, 0.065448933, 0.796926781, -0.099236014, -0.881190748, -0.472578340, 0.678703794, -0.836738986, -0.794179371, -0.537112494, -0.794179371, 0.371096083, 0.072374278, 0.028597358, 0.404145261, 0.306508030, -0.267374877, -0.676396336, -0.676396336, -0.419329458, 0.010784004, -0.123269336, 0.095895331, 0.416076672, -0.158175585, -0.571035820, -0.054276465, -0.538245997, 0.096846576, -0.081712031, -0.416885140, 0.319038883, 0.099874215, -0.131647386, 0.058047523, 0.393240471, -0.104248411, 0.273777284, 0.002845357, 0.546517308, 0.300445531, 0.401276981, 0.055489090, 0.378508784, 0.105499511, -0.258661135, -0.258661135, 0.105499511, -0.234563583, 0.129597062, 0.673269014, -0.234563583, 0.400528990, 0.046033792, 0.176117078, 0.447049005, 0.742261885, 0.351188644, 0.803047876, 0.456665719, 0.456665719, 0.415727165, 0.586148149, 0.498338416, -0.060210196, -0.060210196, -0.060210196, 0.303950450, -0.060210196, -0.040407569, -0.040407569, 0.714934540, 0.016750845, 0.463512631, 0.273817723, 0.380911491, 0.035099984, 0.481861770, 0.771024006, 0.053118489, 0.417279135, -0.911389297, 0.393880180, 1.158058163, 0.730400608, 1.787445782, 1.146995216, 2.155354985, 1.932276865, 1.906636826, 1.938424447, 1.938424447, 2.107672054, 1.414198979, 0.975763681, 2.528683570, 1.903109739, 1.959674925, 2.076768576, 1.766034424, 2.482848415, 2.518149303, 1.449165029, 2.181141978, 2.121039681, 2.444144290, 1.855664326, 2.409328396, 2.074348895, 2.160591050, 2.250134850, 2.507641010, 2.772588722, 2.542215013, 1.788892428, 2.345403997, 3.658944999, 2.285754193, 2.712305317, 2.437265077, 2.526211112, 2.934148678, 2.659998049, 2.313836235, 3.513103756, 2.749525940, 2.456258197, 3.406009988, 2.537816922, 2.116840456, 3.353494737, 2.617337712, 3.291502773, 2.139259375, 2.923614411, 3.870254092, 2.896129414, 2.759271470, 2.970134427, 2.238656578, 3.134819373, 3.916774108, 3.597065225, 2.445783091, 3.961225870, 4.003785485, 3.746718607, 4.003785485, 2.920154020, 3.218875825, 3.262652745, 2.887104841, 3.063183499, 3.637066406, 4.121568521, 4.121568521, 3.864501643, 3.434388181, 3.641176809, 3.422012142, 3.101830801, 3.746265698, 4.226929036, 3.710169681, 4.259718859, 3.624626286, 3.987931533, 4.381079716, 3.645155693, 3.864320361, 4.152183715, 3.962488807, 3.627295859, 4.179582690, 3.801556994, 4.072488921, 3.528816970, 3.828225241, 3.727393792, 4.125132655, 3.802112961, 4.175143075, 4.539303721, 4.539303721, 4.175143075, 4.563401273, 4.199240627, 3.655568675, 4.563401273, 3.928308700, 4.329864893, 4.245760643, 3.974828715, 3.724561547, 4.115634789, 3.707733370, 4.097127937, 4.097127937, 4.180173310, 4.009752326, 4.138800634, 4.737754660, 4.737754660, 4.737754660, 4.373594014, 4.737754660, 4.757557287, 4.757557287, 4.041051350, 4.814715701, 4.367953915, 4.557648823, 4.450555055, 4.833064840, 4.386303054, 4.097140817, 4.851083345, 4.486922699
# Data 3
fit_example_3 = modALCC(data = data_3, RY = RY, STV = STV, target=90, confidence = 0.95)## Warning: 3 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 3 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
fit_example_3## n r target CSTV LL UL confidence p_value
## 1 107 0.3735166 90 21.76416 19.35018 24.47929 0.95 7.410056e-05
## CSTV90 n.90x2 CSTV100 n.100
## 1 21.76416 3 38.7896 3
## Curve
## 1 25.000000, 25.200000, 25.400000, 25.600000, 25.800000, 26.000000, 26.200000, 26.400000, 26.600000, 26.800000, 27.000000, 27.200000, 27.400000, 27.600000, 27.800000, 28.000000, 28.200000, 28.400000, 28.600000, 28.800000, 29.000000, 29.200000, 29.400000, 29.600000, 29.800000, 30.000000, 30.200000, 30.400000, 30.600000, 30.800000, 31.000000, 31.200000, 31.400000, 31.600000, 31.800000, 32.000000, 32.200000, 32.400000, 32.600000, 32.800000, 33.000000, 33.200000, 33.400000, 33.600000, 33.800000, 34.000000, 34.200000, 34.400000, 34.600000, 34.800000, 35.000000, 35.200000, 35.400000, 35.600000, 35.800000, 36.000000, 36.200000, 36.400000, 36.600000, 36.800000, 37.000000, 37.200000, 37.400000, 37.600000, 37.800000, 38.000000, 38.200000, 38.400000, 38.600000, 38.800000, 39.000000, 39.200000, 39.400000, 39.600000, 39.800000, 40.000000, 40.200000, 40.400000, 40.600000, 40.800000, 41.000000, 41.200000, 41.400000, 41.600000, 41.800000, 42.000000, 42.200000, 42.400000, 42.600000, 42.800000, 43.000000, 43.200000, 43.400000, 43.600000, 43.800000, 44.000000, 44.200000, 44.400000, 44.600000, 44.800000, 45.000000, 45.200000, 45.400000, 45.600000, 45.800000, 46.000000, 46.200000, 46.400000, 46.600000, 46.800000, 47.000000, 47.200000, 47.400000, 47.600000, 47.800000, 48.000000, 48.200000, 48.400000, 48.600000, 48.800000, 49.000000, 49.200000, 49.400000, 49.600000, 49.800000, 50.000000, 50.200000, 50.400000, 50.600000, 50.800000, 51.000000, 51.200000, 51.400000, 51.600000, 51.800000, 52.000000, 52.200000, 52.400000, 52.600000, 52.800000, 53.000000, 53.200000, 53.400000, 53.600000, 53.800000, 54.000000, 54.200000, 54.400000, 54.600000, 54.800000, 55.000000, 55.200000, 55.400000, 55.600000, 55.800000, 56.000000, 56.200000, 56.400000, 56.600000, 56.800000, 57.000000, 57.200000, 57.400000, 57.600000, 57.800000, 58.000000, 58.200000, 58.400000, 58.600000, 58.800000, 59.000000, 59.200000, 59.400000, 59.600000, 59.800000, 60.000000, 60.200000, 60.400000, 60.600000, 60.800000, 61.000000, 61.200000, 61.400000, 61.600000, 61.800000, 62.000000, 62.200000, 62.400000, 62.600000, 62.800000, 63.000000, 63.200000, 63.400000, 63.600000, 63.800000, 64.000000, 64.200000, 64.400000, 64.600000, 64.800000, 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 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97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 5.913921, 5.938470, 5.963055, 5.987678, 6.012339, 6.037039, 6.061779, 6.086559, 6.111380, 6.136242, 6.161146, 6.186093, 6.211083, 6.236117, 6.261195, 6.286319, 6.311488, 6.336704, 6.361966, 6.387276, 6.412635, 6.438041, 6.463498, 6.489003, 6.514560, 6.540167, 6.565827, 6.591538, 6.617302, 6.643120, 6.668991, 6.694917, 6.720899, 6.746936, 6.773029, 6.799179, 6.825387, 6.851653, 6.877977, 6.904361, 6.930804, 6.957308, 6.983873, 7.010500, 7.037188, 7.063940, 7.090755, 7.117633, 7.144577, 7.171585, 7.198659, 7.225800, 7.253007, 7.280282, 7.307625, 7.335037, 7.362518, 7.390069, 7.417691, 7.445384, 7.473148, 7.500985, 7.528895, 7.556879, 7.584937, 7.613070, 7.641278, 7.669563, 7.697925, 7.726364, 7.754881, 7.783476, 7.812151, 7.840907, 7.869743, 7.898660, 7.927659, 7.956741, 7.985907, 8.015156, 8.044490, 8.073910, 8.103416, 8.133008, 8.162688, 8.192457, 8.222314, 8.252260, 8.282298, 8.312426, 8.342646, 8.372958, 8.403364, 8.433864, 8.464458, 8.495148, 8.525934, 8.556817, 8.587798, 8.618878, 8.650057, 8.681336, 8.712716, 8.744197, 8.775781, 8.807469, 8.839260, 8.871157, 8.903160, 8.935269, 8.967485, 8.999810, 9.032244, 9.064789, 9.097444, 9.130211, 9.163091, 9.196084, 9.229192, 9.262416, 9.295756, 9.329213, 9.362788, 9.396483, 9.430298, 9.464234, 9.498292, 9.532473, 9.566779, 9.601209, 9.635766, 9.670449, 9.705261, 9.740203, 9.775274, 9.810477, 9.845812, 9.881281, 9.916885, 9.952624, 9.988500, 10.024514, 10.060667, 10.096961, 10.133396, 10.169974, 10.206695, 10.243562, 10.280575, 10.317736, 10.355045, 10.392504, 10.430115, 10.467879, 10.505796, 10.543869, 10.582098, 10.620485, 10.659032, 10.697739, 10.736609, 10.775642, 10.814840, 10.854205, 10.893737, 10.933439, 10.973312, 11.013357, 11.053576, 11.093971, 11.134543, 11.175294, 11.216225, 11.257338, 11.298635, 11.340117, 11.381786, 11.423644, 11.465692, 11.507933, 11.550368, 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29.334975, 29.688650, 30.062983, 30.461232, 30.887593, 31.347636, 31.849016, 32.402775, 33.025879, 33.746927, 34.621766, 35.794793, 38.789595
## SMA
## 1 1.6094379124, 1.7917594692, 1.7917594692, 1.9459101491, 1.9459101491, 2.0794415417, 2.0794415417, 2.1972245773, 2.1972245773, 2.1972245773, 2.1972245773, 2.1972245773, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.4849066498, 2.4849066498, 2.4849066498, 2.5649493575, 2.5649493575, 2.5649493575, 2.5649493575, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.7080502011, 2.7080502011, 2.7080502011, 2.7080502011, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.9444389792, 2.9444389792, 2.9444389792, 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-0.5660556242, 0.7075975324, 0.2274755222, -0.2604578788, -0.2382113469, -0.3540885188, -0.1422425741, -0.2090177759, -1.0190947185, -0.7064289759, 0.3915374795, 0.0990205601, -0.4350662327, 0.1104791082, -0.9501018470, -0.0517429079, -0.5728975833, 0.0127956132, 0.3989294162, -0.1967748275, 0.1943509178, -0.5728975833, 0.3807628249, 0.7242663294, 0.5856934940, 0.1360873641, 0.0078061078, -0.4199002327, -0.1624339689, 0.0300526397, 0.2931765745, -0.4199002327, -0.7677802902, 0.2135948450, -0.3233114545, 0.6608138324, -0.1605905161, -0.0534832289, -0.0286661184, 0.1932457779, 0.4620251758, 1.0861687817, -0.7137130689, 0.7148810537, 0.1412782748, -0.1986774546, -0.3007663106, 0.0518772868, 0.3589627709, 0.5421451620, -0.2085911391, 0.5698975248, -0.1620711234, 0.1661306662, -0.4800982177, -0.4800982177, 0.6756765546, 0.5420989120, 0.9713559748, 0.2352901303, 0.8297499560, 0.1149801042, 0.9025520012, -0.0006617181, 0.5145369623, 0.3093981024, -0.0710901123, 0.6350785302, 0.7502188940, -0.2569546664, 0.6953753233, 0.6085799682, 0.4646236548, -0.1616444866, -0.1616444866, 1.0681609794, 1.4886549434, 0.2336682500, 0.6040385628, 0.5315026939, 0.8847177874, 0.7041572318, 1.0851541134, 1.7846833634, 2.5237975352, 1.1023906826, 1.1023906826, 1.5821331094, 2.2941895622, 1.7145310084, 1.8555717966, 1.2745257803, 1.7813842652, 2.0477276674, 1.6690377384, 1.9400510138, 1.2890135492, 1.9194464111, 1.8590899338, 1.4208444137, 2.2124719091, 1.8013539597, 2.1430378472, 2.3404370186, 1.7828038049, 1.8576673804, 1.9257869165, 2.4556042619, 1.1819511053, 1.8221585308, 2.3100919318, 2.2878453999, 2.4037225718, 2.3400925714, 2.4068677733, 3.2169447158, 2.9042789733, 1.8063125178, 2.0988294373, 2.7709019730, 2.2253566321, 3.2859375873, 2.3875786482, 3.0378103659, 2.4521171694, 2.0659833664, 2.6616876101, 2.2705618648, 3.0378103659, 2.0841499577, 1.7406464532, 2.0004685322, 2.4500746622, 2.5783559184, 3.0060622590, 2.7485959951, 2.5561093865, 2.2929854517, 3.0060622590, 3.4682591441, 2.4868840089, 3.0237903084, 2.0396650215, 2.8610693700, 2.7539620828, 2.7291449723, 2.5072330760, 2.2384536781, 1.7224445147, 3.5223263654, 2.0937322428, 2.6673350216, 3.0072907511, 3.2119661958, 2.8593225984, 2.5522371144, 2.4666350515, 3.2173713526, 2.5319227200, 3.2638913683, 3.0245931037, 3.7559412165, 3.7559412165, 2.6001664442, 2.8153880759, 2.3861310130, 3.2006382839, 2.6061784582, 3.3209483099, 2.5333764130, 3.5120707882, 2.9968721078, 3.2747462560, 3.6552344707, 2.9490658283, 2.9041081041, 3.9790847678, 3.0923344238, 3.1791297788, 3.3230860923, 4.0743949477, 4.0743949477, 2.8445894816, 2.5417765177, 4.4697076843, 4.3303631458, 4.7675421282
# Run multiple examples at once with map()
fit_examples = data.all %>%
mutate(modALCC = map(data, ~ modALCC(RY = .$RY, STV = .$STV, target=90, confidence = 0.95))) %>%
unnest(., cols = c("modALCC"))## Warning: 7 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## Warning: 9 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 22 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## Warning: 3 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 3 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
head(fit_examples)## # A tibble: 3 x 16
## id data n r target CSTV LL UL confidence p_value CSTV90
## <chr> <list> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 <tibble> 15 0.968 90 4.48 3.95 5.08 0.95 3.30e- 9 4.48
## 2 2 <tibble> 137 0.716 90 23.3 21.6 25.1 0.95 7.31e-23 23.3
## 3 3 <tibble> 107 0.374 90 21.8 19.4 24.5 0.95 7.41e- 5 21.8
## # ... with 5 more variables: n.90x2 <int>, CSTV100 <dbl>, n.100 <int>,
## # Curve <list>, SMA <list>
# Alternative with group_map, this does not required nested data.
fit_all = bind_rows(data_1, data_2, data_3, .id = "id") %>%
group_by(id) %>%
group_map(~ modALCC(data = ., RY = RY, STV = STV, target = 90, confidence = 0.95))## Warning: 7 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## Warning: 9 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 22 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## Warning: 3 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 3 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
head(fit_all)## [[1]]
## n r target CSTV LL UL confidence p_value
## 1 15 0.9682908 90 4.478476 3.947041 5.081463 0.95 3.296044e-09
## CSTV90 n.90x2 CSTV100 n.100
## 1 4.478476 7 19.15054 0
## Curve
## 1 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 1.097927, 1.108379, 1.118944, 1.129625, 1.140423, 1.151339, 1.162376, 1.173535, 1.184817, 1.196225, 1.207760, 1.219425, 1.231221, 1.243150, 1.255214, 1.267415, 1.279755, 1.292236, 1.304860, 1.317630, 1.330548, 1.343616, 1.356836, 1.370210, 1.383742, 1.397433, 1.411286, 1.425303, 1.439488, 1.453842, 1.468369, 1.483071, 1.497951, 1.513012, 1.528257, 1.543689, 1.559311, 1.575127, 1.591138, 1.607350, 1.623765, 1.640386, 1.657217, 1.674262, 1.691525, 1.709008, 1.726717, 1.744655, 1.762826, 1.781234, 1.799883, 1.818779, 1.837924, 1.857325, 1.876985, 1.896910, 1.917103, 1.937572, 1.958319, 1.979352, 2.000675, 2.022293, 2.044214, 2.066441, 2.088983, 2.111844, 2.135031, 2.158551, 2.182410, 2.206616, 2.231175, 2.256095, 2.281384, 2.307048, 2.333097, 2.359537, 2.386379, 2.413629, 2.441298, 2.469395, 2.497929, 2.526910, 2.556347, 2.586252, 2.616636, 2.647508, 2.678882, 2.710768, 2.743179, 2.776127, 2.809626, 2.843690, 2.878331, 2.913565, 2.949407, 2.985872, 3.022976, 3.060736, 3.099169, 3.138294, 3.178128, 3.218691, 3.260004, 3.302086, 3.344960, 3.388649, 3.433176, 3.478564, 3.524841, 3.572032, 3.620165, 3.669269, 3.719374, 3.770512, 3.822716, 3.876020, 3.930460, 3.986075, 4.042904, 4.100988, 4.160372, 4.221100, 4.283223, 4.346790, 4.411856, 4.478476, 4.546710, 4.616622, 4.688278, 4.761749, 4.837110, 4.914440, 4.993823, 5.075351, 5.159117, 5.245225, 5.333784, 5.424910, 5.518728, 5.615374, 5.714992, 5.817737, 5.923779, 6.033299, 6.146495, 6.263582, 6.384794, 6.510388, 6.640644, 6.775870, 6.916408, 7.062634, 7.214969, 7.373879, 7.539891, 7.713596, 7.895664, 8.086860, 8.288063, 8.500287, 8.724716, 8.962742, 9.216022, 9.486552, 9.776766, 10.089688, 10.429142, 10.800084, 11.209119, 11.665380, 12.182103, 12.779738, 13.492946, 14.389790, 15.647308, 19.150544
## SMA
## 1 0.00000000, 0.69314718, 1.09861229, 1.38629436, 1.60943791, 1.79175947, 1.94591015, 2.07944154, 2.19722458, 2.30258509, 2.39789527, 2.48490665, 2.56494936, 2.63905733, 2.70805020, -0.31130128, -0.14189705, -0.07594886, -0.03199105, 0.00000000, 0.07428349, 0.05398723, 0.12039263, 0.14766754, 0.09623715, 0.17985350, 0.32175055, 0.22158313, 0.22158313, 0.32175055, 0.09342397, 0.85846552, 1.15629226, 1.35480886, 1.49928272, 1.83475226, 1.74309289, 2.04298443, 2.16615987, 1.93389654, 2.31151393, 2.95233114, 2.49996793, 2.49996793, 2.95233114, -0.09342397, -0.16531834, -0.05767997, 0.03148550, 0.11015519, -0.04299279, 0.20281726, 0.03645711, 0.03106471, 0.36868855, 0.08638134, -0.46742449, 0.06498143, 0.13908940, -0.24428093, -1.40585875, 0.05232998, 0.75562183, 1.24182049, 1.60943791, 2.12722900, 2.18972031, 2.62314325, 2.86410172, 2.73719891, 3.21012648, 3.93795506, 3.56563456, 3.63974254, 4.16109861
##
## [[2]]
## n r target CSTV LL UL confidence p_value
## 1 137 0.7164928 90 23.25457 21.57156 25.06888 0.95 7.314913e-23
## CSTV90 n.90x2 CSTV100 n.100
## 1 23.25457 22 53.10299 9
## Curve
## 1 12.000000, 12.200000, 12.400000, 12.600000, 12.800000, 13.000000, 13.200000, 13.400000, 13.600000, 13.800000, 14.000000, 14.200000, 14.400000, 14.600000, 14.800000, 15.000000, 15.200000, 15.400000, 15.600000, 15.800000, 16.000000, 16.200000, 16.400000, 16.600000, 16.800000, 17.000000, 17.200000, 17.400000, 17.600000, 17.800000, 18.000000, 18.200000, 18.400000, 18.600000, 18.800000, 19.000000, 19.200000, 19.400000, 19.600000, 19.800000, 20.000000, 20.200000, 20.400000, 20.600000, 20.800000, 21.000000, 21.200000, 21.400000, 21.600000, 21.800000, 22.000000, 22.200000, 22.400000, 22.600000, 22.800000, 23.000000, 23.200000, 23.400000, 23.600000, 23.800000, 24.000000, 24.200000, 24.400000, 24.600000, 24.800000, 25.000000, 25.200000, 25.400000, 25.600000, 25.800000, 26.000000, 26.200000, 26.400000, 26.600000, 26.800000, 27.000000, 27.200000, 27.400000, 27.600000, 27.800000, 28.000000, 28.200000, 28.400000, 28.600000, 28.800000, 29.000000, 29.200000, 29.400000, 29.600000, 29.800000, 30.000000, 30.200000, 30.400000, 30.600000, 30.800000, 31.000000, 31.200000, 31.400000, 31.600000, 31.800000, 32.000000, 32.200000, 32.400000, 32.600000, 32.800000, 33.000000, 33.200000, 33.400000, 33.600000, 33.800000, 34.000000, 34.200000, 34.400000, 34.600000, 34.800000, 35.000000, 35.200000, 35.400000, 35.600000, 35.800000, 36.000000, 36.200000, 36.400000, 36.600000, 36.800000, 37.000000, 37.200000, 37.400000, 37.600000, 37.800000, 38.000000, 38.200000, 38.400000, 38.600000, 38.800000, 39.000000, 39.200000, 39.400000, 39.600000, 39.800000, 40.000000, 40.200000, 40.400000, 40.600000, 40.800000, 41.000000, 41.200000, 41.400000, 41.600000, 41.800000, 42.000000, 42.200000, 42.400000, 42.600000, 42.800000, 43.000000, 43.200000, 43.400000, 43.600000, 43.800000, 44.000000, 44.200000, 44.400000, 44.600000, 44.800000, 45.000000, 45.200000, 45.400000, 45.600000, 45.800000, 46.000000, 46.200000, 46.400000, 46.600000, 46.800000, 47.000000, 47.200000, 47.400000, 47.600000, 47.800000, 48.000000, 48.200000, 48.400000, 48.600000, 48.800000, 49.000000, 49.200000, 49.400000, 49.600000, 49.800000, 50.000000, 50.200000, 50.400000, 50.600000, 50.800000, 51.000000, 51.200000, 51.400000, 51.600000, 51.800000, 52.000000, 52.200000, 52.400000, 52.600000, 52.800000, 53.000000, 53.200000, 53.400000, 53.600000, 53.800000, 54.000000, 54.200000, 54.400000, 54.600000, 54.800000, 55.000000, 55.200000, 55.400000, 55.600000, 55.800000, 56.000000, 56.200000, 56.400000, 56.600000, 56.800000, 57.000000, 57.200000, 57.400000, 57.600000, 57.800000, 58.000000, 58.200000, 58.400000, 58.600000, 58.800000, 59.000000, 59.200000, 59.400000, 59.600000, 59.800000, 60.000000, 60.200000, 60.400000, 60.600000, 60.800000, 61.000000, 61.200000, 61.400000, 61.600000, 61.800000, 62.000000, 62.200000, 62.400000, 62.600000, 62.800000, 63.000000, 63.200000, 63.400000, 63.600000, 63.800000, 64.000000, 64.200000, 64.400000, 64.600000, 64.800000, 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 2.336883, 2.355345, 2.373822, 2.392314, 2.410824, 2.429353, 2.447902, 2.466472, 2.485066, 2.503683, 2.522326, 2.540994, 2.559691, 2.578416, 2.597171, 2.615957, 2.634775, 2.653625, 2.672510, 2.691430, 2.710385, 2.729377, 2.748407, 2.767476, 2.786584, 2.805733, 2.824922, 2.844155, 2.863430, 2.882748, 2.902112, 2.921521, 2.940976, 2.960478, 2.980028, 2.999627, 3.019275, 3.038973, 3.058722, 3.078522, 3.098374, 3.118280, 3.138239, 3.158253, 3.178322, 3.198446, 3.218628, 3.238866, 3.259162, 3.279517, 3.299931, 3.320405, 3.340940, 3.361536, 3.382194, 3.402915, 3.423698, 3.444546, 3.465459, 3.486436, 3.507480, 3.528590, 3.549767, 3.571012, 3.592326, 3.613709, 3.635161, 3.656685, 3.678279, 3.699945, 3.721683, 3.743495, 3.765380, 3.787340, 3.809375, 3.831485, 3.853672, 3.875936, 3.898277, 3.920697, 3.943195, 3.965774, 3.988432, 4.011172, 4.033993, 4.056896, 4.079883, 4.102953, 4.126107, 4.149347, 4.172672, 4.196083, 4.219582, 4.243168, 4.266843, 4.290606, 4.314460, 4.338404, 4.362439, 4.386567, 4.410787, 4.435100, 4.459507, 4.484009, 4.508607, 4.533301, 4.558092, 4.582980, 4.607967, 4.633054, 4.658240, 4.683527, 4.708916, 4.734406, 4.760000, 4.785698, 4.811500, 4.837408, 4.863422, 4.889542, 4.915771, 4.942108, 4.968555, 4.995111, 5.021779, 5.048559, 5.075451, 5.102457, 5.129578, 5.156813, 5.184165, 5.211634, 5.239220, 5.266926, 5.294751, 5.322696, 5.350763, 5.378953, 5.407266, 5.435703, 5.464265, 5.492953, 5.521768, 5.550712, 5.579784, 5.608986, 5.638319, 5.667784, 5.697382, 5.727114, 5.756981, 5.786984, 5.817124, 5.847402, 5.877819, 5.908377, 5.939075, 5.969916, 6.000901, 6.032030, 6.063304, 6.094726, 6.126295, 6.158014, 6.189883, 6.221903, 6.254076, 6.286402, 6.318884, 6.351522, 6.384317, 6.417271, 6.450385, 6.483660, 6.517098, 6.550699, 6.584466, 6.618399, 6.652499, 6.686769, 6.721209, 6.755821, 6.790607, 6.825566, 6.860702, 6.896016, 6.931508, 6.967181, 7.003035, 7.039073, 7.075296, 7.111705, 7.148302, 7.185089, 7.222066, 7.259237, 7.296601, 7.334162, 7.371920, 7.409878, 7.448036, 7.486397, 7.524963, 7.563734, 7.602714, 7.641903, 7.681304, 7.720918, 7.760747, 7.800794, 7.841059, 7.881546, 7.922255, 7.963189, 8.004350, 8.045739, 8.087360, 8.129213, 8.171302, 8.213628, 8.256193, 8.298999, 8.342049, 8.385345, 8.428890, 8.472684, 8.516732, 8.561034, 8.605594, 8.650414, 8.695497, 8.740844, 8.786458, 8.832342, 8.878499, 8.924930, 8.971640, 9.018629, 9.065902, 9.113461, 9.161308, 9.209446, 9.257879, 9.306609, 9.355639, 9.404972, 9.454611, 9.504560, 9.554821, 9.605397, 9.656292, 9.707509, 9.759051, 9.810922, 9.863125, 9.915663, 9.968541, 10.021761, 10.075327, 10.129242, 10.183511, 10.238138, 10.293126, 10.348478, 10.404200, 10.460295, 10.516766, 10.573619, 10.630857, 10.688485, 10.746507, 10.804928, 10.863751, 10.922982, 10.982625, 11.042685, 11.103166, 11.164074, 11.225413, 11.287189, 11.349407, 11.412071, 11.475188, 11.538762, 11.602799, 11.667304, 11.732284, 11.797744, 11.863690, 11.930128, 11.997064, 12.064504, 12.132455, 12.200922, 12.269914, 12.339435, 12.409494, 12.480096, 12.551250, 12.622962, 12.695240, 12.768091, 12.841522, 12.915543, 12.990159, 13.065381, 13.141215, 13.217670, 13.294756, 13.372480, 13.450851, 13.529880, 13.609574, 13.689945, 13.771001, 13.852752, 13.935209, 14.018381, 14.102280, 14.186917, 14.272302, 14.358448, 14.445364, 14.533064, 14.621560, 14.710863, 14.800987, 14.891945, 14.983749, 15.076415, 15.169955, 15.264384, 15.359717, 15.455968, 15.553154, 15.651289, 15.750391, 15.850475, 15.951559, 16.053661, 16.156798, 16.260989, 16.366253, 16.472609, 16.580077, 16.688679, 16.798434, 16.909365, 17.021495, 17.134845, 17.249441, 17.365306, 17.482466, 17.600946, 17.720773, 17.841975, 17.964580, 18.088618, 18.214118, 18.341112, 18.469631, 18.599711, 18.731384, 18.864686, 18.999655, 19.136328, 19.274745, 19.414946, 19.556974, 19.700873, 19.846689, 19.994468, 20.144260, 20.296115, 20.450087, 20.606231, 20.764604, 20.925266, 21.088278, 21.253707, 21.421618, 21.592084, 21.765177, 21.940974, 22.119557, 22.301010, 22.485420, 22.672882, 22.863491, 23.057350, 23.254567, 23.455255, 23.659532, 23.867524, 24.079364, 24.295192, 24.515156, 24.739412, 24.968128, 25.201479, 25.439655, 25.682855, 25.931293, 26.185196, 26.444810, 26.710396, 26.982235, 27.260631, 27.545908, 27.838422, 28.138553, 28.446718, 28.763369, 29.089000, 29.424154, 29.769426, 30.125473, 30.493024, 30.872890, 31.265974, 31.673293, 32.095997, 32.535388, 32.992958, 33.470424, 33.969784, 34.493376, 35.043972, 35.624899, 36.240199, 36.894871, 37.595217, 38.349366, 39.168111, 40.066313, 41.065417, 42.198418, 43.520998, 45.142004, 47.343203, 53.102988
## SMA
## 1 1.386294361, 1.609437912, 1.791759469, 1.791759469, 1.945910149, 1.945910149, 2.197224577, 2.197224577, 2.302585093, 2.302585093, 2.302585093, 2.302585093, 2.397895273, 2.397895273, 2.484906650, 2.564949357, 2.564949357, 2.564949357, 2.564949357, 2.564949357, 2.639057330, 2.639057330, 2.639057330, 2.639057330, 2.639057330, 2.708050201, 2.708050201, 2.708050201, 2.708050201, 2.708050201, 2.772588722, 2.772588722, 2.772588722, 2.772588722, 2.772588722, 2.833213344, 2.833213344, 2.833213344, 2.833213344, 2.890371758, 2.890371758, 2.890371758, 2.890371758, 2.944438979, 2.944438979, 2.944438979, 2.944438979, 2.995732274, 2.995732274, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.135494216, 3.135494216, 3.135494216, 3.178053830, 3.178053830, 3.178053830, 3.218875825, 3.218875825, 3.218875825, 3.218875825, 3.258096538, 3.258096538, 3.295836866, 3.295836866, 3.295836866, 3.295836866, 3.332204510, 3.332204510, 3.332204510, 3.367295830, 3.401197382, 3.401197382, 3.433987204, 3.433987204, 3.526360525, 3.555348061, 3.555348061, 3.555348061, 3.583518938, 3.583518938, 3.583518938, 3.610917913, 3.610917913, 3.610917913, 3.610917913, 3.637586160, 3.637586160, 3.663561646, 3.663561646, 3.713572067, 3.713572067, 3.713572067, 3.713572067, 3.737669618, 3.737669618, 3.737669618, 3.737669618, 3.737669618, 3.761200116, 3.784189634, 3.784189634, 3.806662490, 3.806662490, 3.828641396, 3.850147602, 3.850147602, 3.871201011, 3.871201011, 3.891820298, 3.912023005, 3.912023005, 3.912023005, 3.912023005, 3.912023005, 3.931825633, 3.931825633, 3.951243719, 3.988984047, 3.988984047, 3.988984047, 3.988984047, 4.007333185, 4.007333185, 4.007333185, 4.025351691, 4.025351691, -0.895304167, -0.473648276, -0.246924949, -0.413563898, -0.061746450, -0.311301282, -0.016314700, -0.103238229, -0.154283264, -0.141897055, -0.141897055, -0.075948861, -0.383302283, -0.554140835, 0.017057900, -0.257889186, -0.235848272, -0.190222134, -0.311301282, -0.031991051, -0.047112430, -0.463647609, -0.178429054, -0.201848221, -0.075948861, -0.332136508, -0.116398476, -0.246924949, -0.213320253, -0.178429054, -0.103238229, 0.000000000, -0.089766292, -0.383302283, -0.166454709, 0.321750554, -0.213320253, -0.047112430, -0.154283264, -0.141897055, 0.017057900, -0.089766292, -0.224650010, 0.221583133, -0.075948861, -0.190222134, 0.179853500, -0.178429054, -0.342464683, 0.120392634, -0.166454709, 0.096237148, -0.352740374, -0.047112430, 0.321750554, -0.075948861, -0.129276257, -0.047112430, -0.332136508, 0.017057900, 0.321750554, 0.179853500, -0.268749461, 0.321750554, 0.321750554, 0.221583133, 0.321750554, -0.116398476, 0.000000000, 0.017057900, -0.129276257, -0.075948861, 0.147667544, 0.321750554, 0.321750554, 0.221583133, 0.053987227, 0.120392634, 0.034994002, -0.089766292, 0.147667544, 0.321750554, 0.120392634, 0.321750554, 0.074283491, 0.179853500, 0.321750554, 0.034994002, 0.120392634, 0.221583133, 0.147667544, 0.017057900, 0.221583133, 0.074283491, 0.179853500, -0.031991051, 0.074283491, 0.034994002, 0.179853500, 0.053987227, 0.179853500, 0.321750554, 0.321750554, 0.179853500, 0.321750554, 0.179853500, -0.031991051, 0.321750554, 0.074283491, 0.221583133, 0.179853500, 0.074283491, -0.031991051, 0.120392634, -0.047112430, 0.096237148, 0.096237148, 0.120392634, 0.053987227, 0.096237148, 0.321750554, 0.321750554, 0.321750554, 0.179853500, 0.321750554, 0.321750554, 0.321750554, 0.034994002, 0.321750554, 0.147667544, 0.221583133, 0.179853500, 0.321750554, 0.147667544, 0.034994002, 0.321750554, 0.179853500, 0.848817889, 1.930943814, 2.512800241, 2.085142686, 2.988037180, 2.347586614, 3.104631955, 2.881553835, 2.750553280, 2.782340901, 2.782340901, 2.951588508, 2.162805253, 1.724369955, 3.190278467, 2.484661929, 2.541227115, 2.658320765, 2.347586614, 3.064400604, 3.025593520, 1.956609247, 2.688586196, 2.628483898, 2.951588508, 2.294115672, 2.847779742, 2.512800241, 2.599042396, 2.688586196, 2.881553835, 3.146501547, 2.916127838, 2.162805253, 2.719316822, 3.972233202, 2.599042396, 3.025593520, 2.750553280, 2.782340901, 3.190278467, 2.916127838, 2.569966024, 3.715166324, 2.951588508, 2.658320765, 3.608072556, 2.688586196, 2.267609729, 3.455473846, 2.719316822, 3.393481883, 2.241238484, 3.025593520, 3.972233202, 2.951588508, 2.814730564, 3.025593520, 2.294115672, 3.190278467, 3.972233202, 3.608072556, 2.456790422, 3.972233202, 3.972233202, 3.715166324, 3.972233202, 2.847779742, 3.146501547, 3.190278467, 2.814730564, 2.951588508, 3.525471415, 3.972233202, 3.972233202, 3.715166324, 3.285052862, 3.455473846, 3.236309179, 2.916127838, 3.525471415, 3.972233202, 3.455473846, 3.972233202, 3.337140628, 3.608072556, 3.972233202, 3.236309179, 3.455473846, 3.715166324, 3.525471415, 3.190278467, 3.715166324, 3.337140628, 3.608072556, 3.064400604, 3.337140628, 3.236309179, 3.608072556, 3.285052862, 3.608072556, 3.972233202, 3.972233202, 3.608072556, 3.972233202, 3.608072556, 3.064400604, 3.972233202, 3.337140628, 3.715166324, 3.608072556, 3.337140628, 3.064400604, 3.455473846, 3.025593520, 3.393481883, 3.393481883, 3.455473846, 3.285052862, 3.393481883, 3.972233202, 3.972233202, 3.972233202, 3.608072556, 3.972233202, 3.972233202, 3.972233202, 3.236309179, 3.972233202, 3.525471415, 3.715166324, 3.608072556, 3.972233202, 3.525471415, 3.236309179, 3.972233202, 3.608072556, 0.537476472, -0.321505902, -0.721040772, -0.293383216, -1.042127031, -0.401676465, -0.907407377, -0.684329258, -0.447968187, -0.479755808, -0.479755808, -0.649003415, 0.235090020, 0.673525318, -0.705371817, 0.080287429, 0.023722242, -0.093371408, 0.217362743, -0.499451247, -0.386536191, 0.682448083, -0.049528866, 0.010573431, -0.312531178, 0.413934529, -0.139729541, 0.195249960, 0.109007805, 0.019464006, -0.108965113, -0.373912825, -0.143539116, 0.609783469, 0.053271901, -1.139019858, 0.234170948, -0.192380176, 0.082660064, 0.108030857, -0.299906709, -0.025756080, 0.320405734, -0.770727345, -0.007149529, 0.286118214, -0.663633577, 0.307146078, 0.728122544, -0.410951409, 0.325205616, -0.348959445, 0.803283954, 0.018928917, -0.927710764, 0.139453945, 0.276311890, 0.065448933, 0.796926781, -0.099236014, -0.881190748, -0.472578340, 0.678703794, -0.836738986, -0.794179371, -0.537112494, -0.794179371, 0.371096083, 0.072374278, 0.028597358, 0.404145261, 0.306508030, -0.267374877, -0.676396336, -0.676396336, -0.419329458, 0.010784004, -0.123269336, 0.095895331, 0.416076672, -0.158175585, -0.571035820, -0.054276465, -0.538245997, 0.096846576, -0.081712031, -0.416885140, 0.319038883, 0.099874215, -0.131647386, 0.058047523, 0.393240471, -0.104248411, 0.273777284, 0.002845357, 0.546517308, 0.300445531, 0.401276981, 0.055489090, 0.378508784, 0.105499511, -0.258661135, -0.258661135, 0.105499511, -0.234563583, 0.129597062, 0.673269014, -0.234563583, 0.400528990, 0.046033792, 0.176117078, 0.447049005, 0.742261885, 0.351188644, 0.803047876, 0.456665719, 0.456665719, 0.415727165, 0.586148149, 0.498338416, -0.060210196, -0.060210196, -0.060210196, 0.303950450, -0.060210196, -0.040407569, -0.040407569, 0.714934540, 0.016750845, 0.463512631, 0.273817723, 0.380911491, 0.035099984, 0.481861770, 0.771024006, 0.053118489, 0.417279135, -0.911389297, 0.393880180, 1.158058163, 0.730400608, 1.787445782, 1.146995216, 2.155354985, 1.932276865, 1.906636826, 1.938424447, 1.938424447, 2.107672054, 1.414198979, 0.975763681, 2.528683570, 1.903109739, 1.959674925, 2.076768576, 1.766034424, 2.482848415, 2.518149303, 1.449165029, 2.181141978, 2.121039681, 2.444144290, 1.855664326, 2.409328396, 2.074348895, 2.160591050, 2.250134850, 2.507641010, 2.772588722, 2.542215013, 1.788892428, 2.345403997, 3.658944999, 2.285754193, 2.712305317, 2.437265077, 2.526211112, 2.934148678, 2.659998049, 2.313836235, 3.513103756, 2.749525940, 2.456258197, 3.406009988, 2.537816922, 2.116840456, 3.353494737, 2.617337712, 3.291502773, 2.139259375, 2.923614411, 3.870254092, 2.896129414, 2.759271470, 2.970134427, 2.238656578, 3.134819373, 3.916774108, 3.597065225, 2.445783091, 3.961225870, 4.003785485, 3.746718607, 4.003785485, 2.920154020, 3.218875825, 3.262652745, 2.887104841, 3.063183499, 3.637066406, 4.121568521, 4.121568521, 3.864501643, 3.434388181, 3.641176809, 3.422012142, 3.101830801, 3.746265698, 4.226929036, 3.710169681, 4.259718859, 3.624626286, 3.987931533, 4.381079716, 3.645155693, 3.864320361, 4.152183715, 3.962488807, 3.627295859, 4.179582690, 3.801556994, 4.072488921, 3.528816970, 3.828225241, 3.727393792, 4.125132655, 3.802112961, 4.175143075, 4.539303721, 4.539303721, 4.175143075, 4.563401273, 4.199240627, 3.655568675, 4.563401273, 3.928308700, 4.329864893, 4.245760643, 3.974828715, 3.724561547, 4.115634789, 3.707733370, 4.097127937, 4.097127937, 4.180173310, 4.009752326, 4.138800634, 4.737754660, 4.737754660, 4.737754660, 4.373594014, 4.737754660, 4.757557287, 4.757557287, 4.041051350, 4.814715701, 4.367953915, 4.557648823, 4.450555055, 4.833064840, 4.386303054, 4.097140817, 4.851083345, 4.486922699
##
## [[3]]
## n r target CSTV LL UL confidence p_value
## 1 107 0.3735166 90 21.76416 19.35018 24.47929 0.95 7.410056e-05
## CSTV90 n.90x2 CSTV100 n.100
## 1 21.76416 3 38.7896 3
## Curve
## 1 25.000000, 25.200000, 25.400000, 25.600000, 25.800000, 26.000000, 26.200000, 26.400000, 26.600000, 26.800000, 27.000000, 27.200000, 27.400000, 27.600000, 27.800000, 28.000000, 28.200000, 28.400000, 28.600000, 28.800000, 29.000000, 29.200000, 29.400000, 29.600000, 29.800000, 30.000000, 30.200000, 30.400000, 30.600000, 30.800000, 31.000000, 31.200000, 31.400000, 31.600000, 31.800000, 32.000000, 32.200000, 32.400000, 32.600000, 32.800000, 33.000000, 33.200000, 33.400000, 33.600000, 33.800000, 34.000000, 34.200000, 34.400000, 34.600000, 34.800000, 35.000000, 35.200000, 35.400000, 35.600000, 35.800000, 36.000000, 36.200000, 36.400000, 36.600000, 36.800000, 37.000000, 37.200000, 37.400000, 37.600000, 37.800000, 38.000000, 38.200000, 38.400000, 38.600000, 38.800000, 39.000000, 39.200000, 39.400000, 39.600000, 39.800000, 40.000000, 40.200000, 40.400000, 40.600000, 40.800000, 41.000000, 41.200000, 41.400000, 41.600000, 41.800000, 42.000000, 42.200000, 42.400000, 42.600000, 42.800000, 43.000000, 43.200000, 43.400000, 43.600000, 43.800000, 44.000000, 44.200000, 44.400000, 44.600000, 44.800000, 45.000000, 45.200000, 45.400000, 45.600000, 45.800000, 46.000000, 46.200000, 46.400000, 46.600000, 46.800000, 47.000000, 47.200000, 47.400000, 47.600000, 47.800000, 48.000000, 48.200000, 48.400000, 48.600000, 48.800000, 49.000000, 49.200000, 49.400000, 49.600000, 49.800000, 50.000000, 50.200000, 50.400000, 50.600000, 50.800000, 51.000000, 51.200000, 51.400000, 51.600000, 51.800000, 52.000000, 52.200000, 52.400000, 52.600000, 52.800000, 53.000000, 53.200000, 53.400000, 53.600000, 53.800000, 54.000000, 54.200000, 54.400000, 54.600000, 54.800000, 55.000000, 55.200000, 55.400000, 55.600000, 55.800000, 56.000000, 56.200000, 56.400000, 56.600000, 56.800000, 57.000000, 57.200000, 57.400000, 57.600000, 57.800000, 58.000000, 58.200000, 58.400000, 58.600000, 58.800000, 59.000000, 59.200000, 59.400000, 59.600000, 59.800000, 60.000000, 60.200000, 60.400000, 60.600000, 60.800000, 61.000000, 61.200000, 61.400000, 61.600000, 61.800000, 62.000000, 62.200000, 62.400000, 62.600000, 62.800000, 63.000000, 63.200000, 63.400000, 63.600000, 63.800000, 64.000000, 64.200000, 64.400000, 64.600000, 64.800000, 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 5.913921, 5.938470, 5.963055, 5.987678, 6.012339, 6.037039, 6.061779, 6.086559, 6.111380, 6.136242, 6.161146, 6.186093, 6.211083, 6.236117, 6.261195, 6.286319, 6.311488, 6.336704, 6.361966, 6.387276, 6.412635, 6.438041, 6.463498, 6.489003, 6.514560, 6.540167, 6.565827, 6.591538, 6.617302, 6.643120, 6.668991, 6.694917, 6.720899, 6.746936, 6.773029, 6.799179, 6.825387, 6.851653, 6.877977, 6.904361, 6.930804, 6.957308, 6.983873, 7.010500, 7.037188, 7.063940, 7.090755, 7.117633, 7.144577, 7.171585, 7.198659, 7.225800, 7.253007, 7.280282, 7.307625, 7.335037, 7.362518, 7.390069, 7.417691, 7.445384, 7.473148, 7.500985, 7.528895, 7.556879, 7.584937, 7.613070, 7.641278, 7.669563, 7.697925, 7.726364, 7.754881, 7.783476, 7.812151, 7.840907, 7.869743, 7.898660, 7.927659, 7.956741, 7.985907, 8.015156, 8.044490, 8.073910, 8.103416, 8.133008, 8.162688, 8.192457, 8.222314, 8.252260, 8.282298, 8.312426, 8.342646, 8.372958, 8.403364, 8.433864, 8.464458, 8.495148, 8.525934, 8.556817, 8.587798, 8.618878, 8.650057, 8.681336, 8.712716, 8.744197, 8.775781, 8.807469, 8.839260, 8.871157, 8.903160, 8.935269, 8.967485, 8.999810, 9.032244, 9.064789, 9.097444, 9.130211, 9.163091, 9.196084, 9.229192, 9.262416, 9.295756, 9.329213, 9.362788, 9.396483, 9.430298, 9.464234, 9.498292, 9.532473, 9.566779, 9.601209, 9.635766, 9.670449, 9.705261, 9.740203, 9.775274, 9.810477, 9.845812, 9.881281, 9.916885, 9.952624, 9.988500, 10.024514, 10.060667, 10.096961, 10.133396, 10.169974, 10.206695, 10.243562, 10.280575, 10.317736, 10.355045, 10.392504, 10.430115, 10.467879, 10.505796, 10.543869, 10.582098, 10.620485, 10.659032, 10.697739, 10.736609, 10.775642, 10.814840, 10.854205, 10.893737, 10.933439, 10.973312, 11.013357, 11.053576, 11.093971, 11.134543, 11.175294, 11.216225, 11.257338, 11.298635, 11.340117, 11.381786, 11.423644, 11.465692, 11.507933, 11.550368, 11.592999, 11.635828, 11.678856, 11.722086, 11.765520, 11.809159, 11.853005, 11.897061, 11.941328, 11.985809, 12.030505, 12.075419, 12.120553, 12.165909, 12.211490, 12.257296, 12.303332, 12.349599, 12.396099, 12.442835, 12.489809, 12.537024, 12.584482, 12.632185, 12.680137, 12.728340, 12.776796, 12.825509, 12.874480, 12.923713, 12.973210, 13.022975, 13.073010, 13.123318, 13.173903, 13.224766, 13.275912, 13.327344, 13.379064, 13.431076, 13.483383, 13.535988, 13.588896, 13.642110, 13.695632, 13.749467, 13.803618, 13.858089, 13.912884, 13.968007, 14.023461, 14.079251, 14.135381, 14.191855, 14.248676, 14.305850, 14.363381, 14.421274, 14.479531, 14.538160, 14.597164, 14.656547, 14.716316, 14.776475, 14.837028, 14.897983, 14.959342, 15.021113, 15.083301, 15.145911, 15.208949, 15.272421, 15.336333, 15.400691, 15.465502, 15.530772, 15.596507, 15.662715, 15.729402, 15.796574, 15.864241, 15.932407, 16.001082, 16.070273, 16.139988, 16.210234, 16.281021, 16.352355, 16.424248, 16.496706, 16.569739, 16.643357, 16.717568, 16.792384, 16.867813, 16.943866, 17.020554, 17.097888, 17.175878, 17.254537, 17.333875, 17.413906, 17.494641, 17.576093, 17.658275, 17.741202, 17.824886, 17.909343, 17.994586, 18.080632, 18.167495, 18.255192, 18.343740, 18.433156, 18.523457, 18.614662, 18.706790, 18.799859, 18.893892, 18.988907, 19.084928, 19.181976, 19.280074, 19.379246, 19.479518, 19.580915, 19.683463, 19.787191, 19.892127, 19.998301, 20.105744, 20.214490, 20.324570, 20.436021, 20.548879, 20.663183, 20.778971, 20.896287, 21.015172, 21.135673, 21.257837, 21.381715, 21.507357, 21.634821, 21.764162, 21.895441, 22.028724, 22.164075, 22.301567, 22.441275, 22.583277, 22.727657, 22.874504, 23.023912, 23.175981, 23.330817, 23.488535, 23.649255, 23.813106, 23.980228, 24.150769, 24.324889, 24.502761, 24.684571, 24.870521, 25.060830, 25.255736, 25.455500, 25.660405, 25.870765, 26.086925, 26.309266, 26.538212, 26.774237, 27.017872, 27.269717, 27.530450, 27.800851, 28.081811, 28.374371, 28.679745, 28.999371, 29.334975, 29.688650, 30.062983, 30.461232, 30.887593, 31.347636, 31.849016, 32.402775, 33.025879, 33.746927, 34.621766, 35.794793, 38.789595
## SMA
## 1 1.6094379124, 1.7917594692, 1.7917594692, 1.9459101491, 1.9459101491, 2.0794415417, 2.0794415417, 2.1972245773, 2.1972245773, 2.1972245773, 2.1972245773, 2.1972245773, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.4849066498, 2.4849066498, 2.4849066498, 2.5649493575, 2.5649493575, 2.5649493575, 2.5649493575, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.7080502011, 2.7080502011, 2.7080502011, 2.7080502011, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.9444389792, 2.9444389792, 2.9444389792, 2.9444389792, 2.9444389792, 2.9957322736, 2.9957322736, 2.9957322736, 3.0445224377, 3.0445224377, 3.0910424534, 3.0910424534, 3.1354942159, 3.1780538303, 3.1780538303, 3.1780538303, 3.2188758249, 3.2188758249, 3.2580965380, 3.2580965380, 3.2580965380, 3.2580965380, 3.2958368660, 3.2958368660, 3.3322045102, 3.3322045102, 3.3322045102, 3.3672958300, 3.4011973817, 3.4339872045, 3.4339872045, 3.4339872045, 3.4965075615, 3.4965075615, 3.4965075615, 3.5553480615, 3.8918202981, 4.0073331852, 4.1896547420, -0.4035026678, -0.6055446636, -0.3934169016, -0.0897662917, 0.3217505544, -0.5439929355, -0.5439929355, -0.3424646835, 0.0539872272, -0.2687494608, -0.1902221337, -0.5137313196, -0.2901891602, -0.1418970546, -0.3527403738, -0.2018482212, -0.5643265694, -0.2133202528, -0.2469249490, -0.5439929355, -0.1032382286, -0.3321365075, -0.1418970546, -0.0319910515, -0.3424646835, -0.3007828654, -0.3113012820, -0.0163147004, -0.7254469968, -0.4135638984, -0.1418970546, -0.1542832637, -0.0897662917, -0.1664547090, -0.1292762574, 0.3217505544, 0.1476675438, -0.4636476090, -0.3007828654, 0.0349940022, -0.2687494608, 0.3217505544, -0.1784290543, 0.1476675438, -0.1784290543, -0.3934169016, -0.0617464495, -0.2795136623, 0.1476675438, -0.3833022825, -0.5745548442, -0.4636476090, -0.2133202528, -0.1418970546, 0.0962371485, -0.0471124298, -0.1542832637, -0.3007828654, 0.0962371485, 0.3217505544, -0.2246500097, 0.0742834912, -0.4736482758, -0.0163147004, -0.0759488607, -0.0897662917, -0.2133202528, -0.3629686486, -0.6803702690, 0.3217505544, -0.4736482758, -0.1542832637, 0.0349940022, 0.1203926336, -0.0759488607, -0.2469249490, -0.3217505544, 0.0962371485, -0.3113012820, 0.0962371485, -0.0617464495, 0.3217505544, 0.3217505544, -0.3217505544, -0.2246500097, -0.4636476090, -0.0319910515, -0.3629686486, 0.0349940022, -0.4035026678, 0.1203926336, -0.1664547090, -0.0319910515, 0.1798534998, -0.2133202528, -0.2578891860, 0.3217505544, -0.1902221337, -0.1418970546, -0.0617464495, 0.3217505544, 0.3217505544, -0.3629686486, -0.5643265694, 0.3217505544, 0.1798534998, 0.3217505544, 2.3555445368, 1.9926624244, 2.3736593061, 2.9190378763, 3.6581520481, 2.1032138028, 2.1032138028, 2.4651731940, 3.1772296468, 2.5975710929, 2.7386118812, 2.1575658649, 2.5590638341, 2.8254072363, 2.4467173073, 2.7177305827, 2.0666931181, 2.6971259800, 2.6367695027, 2.1032138028, 2.8948412982, 2.4837233488, 2.8254072363, 3.0228064077, 2.4651731940, 2.5400367695, 2.5211449286, 3.0509622740, 1.7773091174, 2.3374738352, 2.8254072363, 2.8031607043, 2.9190378763, 2.7812999037, 2.8480751055, 3.6581520481, 3.3454863056, 2.2475198501, 2.5400367695, 3.1431164338, 2.5975710929, 3.6581520481, 2.7597931090, 3.3454863056, 2.7597931090, 2.3736593061, 2.9693635497, 2.5782378045, 3.3454863056, 2.3918258973, 2.0483223929, 2.2475198501, 2.6971259800, 2.8254072363, 3.2531135768, 2.9956473130, 2.8031607043, 2.5400367695, 3.2531135768, 3.6581520481, 2.6767769129, 3.2136832124, 2.2295579255, 3.0509622740, 2.9438549868, 2.9190378763, 2.6971259800, 2.4283465821, 1.8582701974, 3.6581520481, 2.2295579255, 2.8031607043, 3.1431164338, 3.2964985841, 2.9438549868, 2.6367695027, 2.5023772757, 3.2531135768, 2.5211449286, 3.2531135768, 2.9693635497, 3.6581520481, 3.6581520481, 2.5023772757, 2.6767769129, 2.2475198501, 3.0228064077, 2.4283465821, 3.1431164338, 2.3555445368, 3.2964985841, 2.7812999037, 3.0228064077, 3.4032946224, 2.6971259800, 2.6170769360, 3.6581520481, 2.7386118812, 2.8254072363, 2.9693635497, 3.6581520481, 3.6581520481, 2.4283465821, 2.0666931181, 3.6581520481, 3.4032946224, 3.6581520481, -0.7461066244, -0.2009029552, -0.5818998369, -0.9731277272, -1.7122418990, -0.0237722611, -0.0237722611, -0.2679486167, -0.9800050694, -0.4003465156, -0.5413873038, 0.0396587124, -0.2564787411, -0.5228221433, -0.1441322143, -0.4151454897, 0.2358919749, -0.3945408870, -0.3341844097, 0.2946814700, -0.4969460254, -0.0858280760, -0.4275119635, -0.6249111349, -0.0672779212, -0.1421414967, -0.0362382788, -0.5660556242, 0.7075975324, 0.2274755222, -0.2604578788, -0.2382113469, -0.3540885188, -0.1422425741, -0.2090177759, -1.0190947185, -0.7064289759, 0.3915374795, 0.0990205601, -0.4350662327, 0.1104791082, -0.9501018470, -0.0517429079, -0.5728975833, 0.0127956132, 0.3989294162, -0.1967748275, 0.1943509178, -0.5728975833, 0.3807628249, 0.7242663294, 0.5856934940, 0.1360873641, 0.0078061078, -0.4199002327, -0.1624339689, 0.0300526397, 0.2931765745, -0.4199002327, -0.7677802902, 0.2135948450, -0.3233114545, 0.6608138324, -0.1605905161, -0.0534832289, -0.0286661184, 0.1932457779, 0.4620251758, 1.0861687817, -0.7137130689, 0.7148810537, 0.1412782748, -0.1986774546, -0.3007663106, 0.0518772868, 0.3589627709, 0.5421451620, -0.2085911391, 0.5698975248, -0.1620711234, 0.1661306662, -0.4800982177, -0.4800982177, 0.6756765546, 0.5420989120, 0.9713559748, 0.2352901303, 0.8297499560, 0.1149801042, 0.9025520012, -0.0006617181, 0.5145369623, 0.3093981024, -0.0710901123, 0.6350785302, 0.7502188940, -0.2569546664, 0.6953753233, 0.6085799682, 0.4646236548, -0.1616444866, -0.1616444866, 1.0681609794, 1.4886549434, 0.2336682500, 0.6040385628, 0.5315026939, 0.8847177874, 0.7041572318, 1.0851541134, 1.7846833634, 2.5237975352, 1.1023906826, 1.1023906826, 1.5821331094, 2.2941895622, 1.7145310084, 1.8555717966, 1.2745257803, 1.7813842652, 2.0477276674, 1.6690377384, 1.9400510138, 1.2890135492, 1.9194464111, 1.8590899338, 1.4208444137, 2.2124719091, 1.8013539597, 2.1430378472, 2.3404370186, 1.7828038049, 1.8576673804, 1.9257869165, 2.4556042619, 1.1819511053, 1.8221585308, 2.3100919318, 2.2878453999, 2.4037225718, 2.3400925714, 2.4068677733, 3.2169447158, 2.9042789733, 1.8063125178, 2.0988294373, 2.7709019730, 2.2253566321, 3.2859375873, 2.3875786482, 3.0378103659, 2.4521171694, 2.0659833664, 2.6616876101, 2.2705618648, 3.0378103659, 2.0841499577, 1.7406464532, 2.0004685322, 2.4500746622, 2.5783559184, 3.0060622590, 2.7485959951, 2.5561093865, 2.2929854517, 3.0060622590, 3.4682591441, 2.4868840089, 3.0237903084, 2.0396650215, 2.8610693700, 2.7539620828, 2.7291449723, 2.5072330760, 2.2384536781, 1.7224445147, 3.5223263654, 2.0937322428, 2.6673350216, 3.0072907511, 3.2119661958, 2.8593225984, 2.5522371144, 2.4666350515, 3.2173713526, 2.5319227200, 3.2638913683, 3.0245931037, 3.7559412165, 3.7559412165, 2.6001664442, 2.8153880759, 2.3861310130, 3.2006382839, 2.6061784582, 3.3209483099, 2.5333764130, 3.5120707882, 2.9968721078, 3.2747462560, 3.6552344707, 2.9490658283, 2.9041081041, 3.9790847678, 3.0923344238, 3.1791297788, 3.3230860923, 4.0743949477, 4.0743949477, 2.8445894816, 2.5417765177, 4.4697076843, 4.3303631458, 4.7675421282
Examples using ggplot
# Extracting curve data as a data.frame to plot
curve_example1 = fit_example_1 %>% unnest(., cols = Curve)
# Plot
data_1 %>%
# Want to remove leverage points?
#dplyr::filter(STV < fit_example_1$CSTV100) %>%
#dplyr::filter(STV < 2*fit_example_1$CSTV90) %>%
ggplot()+
# Points
geom_point(aes(x = STV, y = RY), fill = "orange", shape = 21, size = 4, alpha = 0.75)+
# Highlight potential leverage points >2xCSTV90
geom_point(data = data_1 %>% dplyr::filter(STV > 2*fit_example_1$CSTV90),
aes(x = STV, y = RY, shape = ">2xCSTV90"), col = "dark red", size = 4, alpha = 1)+
# Highlight potential leverage points >2xCSTV90
#geom_point(data = data_1 %>% dplyr::filter(STV > fit_example_1$CSTV100),
# aes(x = STV, y = RY, shape = ">CSTV100"), col = "dark red", size = 4, alpha = 1)+
scale_shape_manual(name = "", values = c(7,10))+
# Fitted ALCC
geom_line(data = curve_example1, aes(x= STV.fitted, y = RY.fitted), size = 2)+
# Critical value
geom_vline(xintercept = fit_example_1$CSTV, col = "red", size = 1.25, linetype = "dashed")+
# Confidence limits
# Lines
geom_vline(xintercept = fit_example_1$LL, col = "red", size = 0.75, linetype = "dotted")+
geom_vline(xintercept = fit_example_1$UL, col = "red", size = 0.75, linetype = "dotted")+
# Shade
ggpp::annotate(geom = "rect", xmin = fit_example_1$LL, xmax = fit_example_1$UL,
ymin = min(data_1$RY), ymax = 100, alpha = .3, fill = "red")+
# Axis titles
labs(x = "Soil Test Value (units)", y = "Relative Yield (%)")+
theme_bw()+
theme(legend.position = "top")+
# Annotate critical values data
ggpp::annotate(geom = "table", y = min(data_1$RY), x = fit_example_1$UL + 0.5, hjust= 0, vjust = 0,
label = fit_example_1 %>% dplyr::select(CSTV, LL, UL, r) %>%
mutate_at(.vars = c("r"), ~round(.,2)) %>%
mutate_at(.vars = c("CSTV","LL","UL"), ~round(.,1))
)
# SMA regression
SMA_example1 = fit_example_1 %>% unnest(., cols = SMA)
SMA_example1 %>%
ggplot(aes(x = arc_RY, y = ln_STV))+
ggtitle("SMA Regression. Dataset 1")+
geom_point(shape=21, fill = "orange", size = 4, alpha = 0.75)+
#SMA Line
geom_path(aes(x=arc_RY, y = SMA_line, linetype = "SMA_fit"), size = 2, col = "grey25")+
scale_linetype_manual(name="", values = c("solid"))+
#Critical value
geom_vline(xintercept = 0, col = "grey10", size = 1.25, linetype = "dashed")+
theme_bw()+
# Axis titles
labs(y = "ln_STV", y = "asin(sqrt(RY))-centered")
# Residuals plot
SMA_example1 %>%
ggplot(aes(x = fitted_axis, y = residuals))+
ggtitle("Residuals SMA. Dataset 2")+
geom_point(shape=21, fill = "orange", size = 4, alpha = 0.75)+
geom_hline(yintercept = 0, col = "grey10", size = 1.25, linetype = "dashed")+
theme_bw()+
# Axis titles
labs(x = "Fitted Axis -SMA- (see Warton et al. 2006)", y = "Residuals (STV units)")
# Extracting curve data as a data.frame to plot
curve_example2 = fit_example_2 %>% unnest(., cols = Curve)
# Plot
data_2 %>% ggplot()+
# Want to remove leverage points?
#dplyr::filter(STV < fit_example_2$CSTV100) %>%
#dplyr::filter(STV < 2*fit_example_2$CSTV90) %>%
# Points
geom_point(aes(x = STV, y = RY), fill = "#88dbc8", shape = 21, size = 4, alpha = 0.75)+
# Highlight potential leverage points >2xCSTV90
geom_point(data = data_2 %>% dplyr::filter(STV > 2*fit_example_2$CSTV90),
aes(x = STV, y = RY, shape = ">2xCSTV90"), col = "dark red", size = 4, alpha = 1)+
# Highlight potential leverage points >CSTV100
geom_point(data = data_2 %>% dplyr::filter(STV > fit_example_2$CSTV100),
aes(x = STV, y = RY, shape = ">CSTV100"), col = "dark red", size = 4, alpha = 1)+
scale_shape_manual(name = "", values = c(7,10))+
# Fitted ALCC
geom_line(data = curve_example2, aes(x= STV.fitted, y = RY.fitted), size = 2)+
# Critical value
geom_vline(xintercept = fit_example_2$CSTV, col = "red", size = 1.25, linetype = "dashed")+
# Confidence limits
geom_vline(xintercept = fit_example_2$LL, col = "red", size = 0.75, linetype = "dotted")+
geom_vline(xintercept = fit_example_2$UL, col = "red", size = 0.75, linetype = "dotted")+
ggpp::annotate(geom = "rect", xmin = fit_example_2$LL, xmax = fit_example_2$UL,
ymin = min(data_2$RY), ymax = 100, alpha = .3, fill = "red")+
# Axis titles
labs(x = "Soil Test Value (units)", y = "Relative Yield (%)")+
theme_bw()+
theme(legend.position = "top")+
# Annotate critical values data
ggpp::annotate(geom = "table", y = min(data_2$RY), x = fit_example_2$UL + 0.5, hjust= 0, vjust = 0,
label = fit_example_2 %>% dplyr::select(CSTV, LL, UL, r) %>%
mutate_at(.vars = c("r"), ~round(.,2)) %>%
mutate_at(.vars = c("CSTV","LL","UL"), ~round(.,1))
)
# SMA regression
SMA_example2 = fit_example_2 %>% unnest(., cols = SMA)
SMA_example2 %>%
ggplot(aes(x = arc_RY, y = ln_STV))+
ggtitle("SMA Regression. Dataset 2")+
geom_point(shape=21, fill = "#88dbc8", size = 4, alpha = 0.5)+
#SMA Line
geom_path(aes(x=arc_RY, y = SMA_line, linetype = "SMA_fit"), size = 2, col = "grey25")+
scale_linetype_manual(name="", values = c("solid"))+
#Critical value
geom_vline(xintercept = 0, col = "grey10", size = 1.25, linetype = "dashed")+
theme_bw()+
# Axis titles
labs(y = "ln_STV", y = "asin(sqrt(RY))-centered")
# Residuals plot
resid_example2 = fit_example_2 %>% unnest(., cols = SMA)
resid_example2 %>%
ggplot(aes(x = fitted_axis, y = residuals))+
ggtitle("Residuals SMA. Dataset 2")+
geom_point(shape = 21, fill = "#88dbc8", size = 4, alpha = 0.5)+
geom_hline(yintercept = 0, col = "grey10", size = 1.25, linetype = "dashed")+
theme_bw()+
# Axis titles
labs(x = "Fitted Axis -SMA- (see Warton et al. 2006)", y = "Residuals (STV units)")
Great initiative from Dr. Austin Pearce working for automatize critical
nutrient values estimations for the FRST (Fertilizer Recommendation
System Tool) Project.
Original source: https://github.com/austinwpearce/SoilTestCocaCola.git
Copyright (c) 2022 Austin Pearce
Adapted by Adrian Correndo on 03/22/2022
List of modifications:
- Modified variables (e.g. x, xt_centered, y, yt) and arguments names
(inside functions; e.g. sufficiency for target) for more familiar
terminology I personally use.
(i). For example, replaced “lower_cl” with “lower_cstv” to maintain
consistency.
-
Removed sma argument from formulae. Not needed as the modified ALCC is entirely based on SMA. OLS steps described by Correndo et al. (2017) are just some tricks to obtain parameters using a spreadsheet where we cannot run a sma() model (Warton et al., 2006).
-
Modified slope formula for more explicit one that removes the need of estimating an OLS slope and then rotate. New formula is simply the ratio between standard deviations of variables, as follows:
(i). slope = sd(ln_STV) / sd(arc_ry)
-
Shortened some steps regarding centering variables.
-
Fixed model pvalue (replaced student-t pvalue for Pearson-r pvalue)
-
Modified df as n-2 for the t-test. (see Table 4, Warton et al., 2006)
-
Modified test_stat formula, obtained directly from qt() instead of pt()
-
Added probability formula (prob), which includes confidence to later estimate the t_stat.
-
Shortened se formula, obtained directly from qt() instead of pt()
-
Modified ssx formula for more explicit one
-
Fixed model pvalue (replaced student-t pvalue for Pearson-r pvalue)
-
Fixed issue with dplyr::if_else() when capping RY to 100%
-
Modified data points removal criteria (remove2x replaced by remove.leverage, which gives users more autonomy)
(i). Users can choose now between options remove.leverage = c(“none”,
“cstv90_2x”, “cstv100”)
(ii). Added sample size (n) used for CSTV
calculations as outcome to show when removing points.
(ii).
Modified printed text in the alcc_plot() in accordance with the new
remove.leverage criteria.
-
Added some extra warning regarding the specification of relative yield “target” and “confidence”. Although defaults are provided, I consider important to create awareness on users about this, which are key features the ALCC model brings.
-
By the end of stage_3 of alcc(), I replaced “mutate(remove2x =”TRUE”)” with “mutate(remove.leverage = remove.leverage)”, otherwise the summary table always printed “TRUE” even though STV > cstv90_2x were NOT removed (remove2x = FALSE). It currently prints the user specification (“none”, “cstv90_2x”, “cstv100”).
# ALCC
# =============================================================================
alcc_core.rev <- function(data,
# # AC: I would rather use the acronym of soil test value (stv),
# as the same is done for "ry".
#stv,
stv,
ry,
# AC: WARNING: There is no really an option for "SMA" or not, it is ALWAYS SMA.
# sma,
# AC: I think the word sufficiency is not appropriate for the case...
# most likely this is just a "target" RY value
# sufficiency sounds like 100%, a target would be just an "acceptable" RY
target,
# AC: I added confidence as a needed arg. to define
confidence) {
if (nrow(data) < 8) {
stop("Too few data points. Try at least 8.")
}
if (missing(stv)) {
stop("Specify the column containing soil test values (e.g., stv = STK)")
}
if (missing(ry)) {
stop("Specify the column containing relative yield (%) values (e.g., ry = RY)")
}
# AC: # Add statement for missing target, optional since a DEFAULT is provided (90)
if (missing(target)) {
stop("Specify the target value of relative yield (%) (e.g., target = 90)")
}
# AC: # Add statement for missing confidence, optional since a DEFAULT is provided (95)
if (missing(confidence)) {
stop("Specify the desired confidence level (%) for cstv estimation (e.g., confidence = 95)")
}
# enquo let's the user enter their own column names for x and y variables
# AC: I think this is particularly confusing because in the SMA regression
# Soil test is not in the x-axis but on the y-axis,
# I would rather use "STV" instead of "x", and then you flip them for transformed (xt, yt)
#x <- enquo(soil_test)
STV <- enquo(stv)
# AC: for SMA regression RY is not in the y-axis but on the x-axis,
# I would rather use "STV" instead of "x"
RY <- enquo(ry)
#y <- enquo(ry)
steps_1_4 <- data %>%
mutate(
stv = !!STV,
# RY values greater than 100 are capped at 100
ry_cap = if_else(!!RY > 100, 100, as.double(!!RY)),
# Tranform back to numeric, just in case
ry_cap = as.numeric(ry_cap),
# AC: Model is not necessary, it is always SMA
#model = case_when(sma == TRUE ~ "ALCC-SMA",
# sma == FALSE ~ "ALCC"),
# get sample size
n = nrow(data),
# AC: added degrees of freedom of the model with two pars
# (See Warton et al. 2006, Table 4)
# n-1 was used
df = n-2,
# Step 1 Transform (t for "transformed" added to x and y)
# AC: ### THIS IS NOT ADDED TO X AND Y, note you have flipped them...
# Thus, I would avoid using x & y
# for ALCC, soil test goes to Y-axis and RY goes to X-axis
# the names of variables are difficult to follow, at least for me,
# AC: I would suggest use ln_STV and arc_RY
ln_stv = log(stv),
# Step 2 Center
# AC: I would center right here as well
arc_ry = asin(sqrt(ry_cap / 100)) - asin(sqrt(target/100)),
target = target, # I think its not necessary
# AC: UNNECESSARY
# adjust_by = asin(sqrt(sufficiency / 100)),
### NOT NEEDED, adjust_by = asin(sqrt(target / 100)),
### xt_centered = xt - adjust_by,
# Step 3 Correlation (Pearson)
r = cor(ln_stv, arc_ry, method = "pearson"),
# AC: The student-t formula here DID NOT include the confidence level so it
# was always estimated for 95% confidence level
#t_stat = (r * sqrt(df)) / sqrt(1 - r ^ 2),
# AC: Warning: the df here are n-2, also this is informed later as the p-value
#of the model
# but this is not the pvalue of the model, it's just the pvalue of the t-test
# (if B0 =/ from zero)
# the pvalue of the model is the pvalue of the Pearson correlation test
#pvalue = pt(t_stat, df = n - 1, lower.tail = FALSE),
# AC: I would replace with the following
prob = 1-((1-confidence/100)/2), # Probability for t-dist
# AC: The Student-t value from quantile fn (qt) saves a step for the LL
#and UL estimations
t_stat = qt(p=prob, df = df),
# AC: This is the pvalue of the model
# p-value of Pearson correlation (r)
pvalue = stats::cor.test(ln_stv, arc_ry, method = "pearson")$p.value,
# Step 4 Means
# AC: We DON'T ACTUALLY NEED THE MEANS HERE, can be included into the intercept formula
#mean_xt = mean(xt_centered),
#mean_yt = mean(yt),
)
# Step 5 Fit linear model to transformed, centered data
# AC: # THIS STEP IS UNNECESSARY AS THE SMA-slope = sd(ln_stv)/ sd(arc_ry)
# ols_center <- lm(yt ~ xt_centered, data = steps_1_4)
steps_5_9 <- steps_1_4 %>%
mutate(
#intercept = coef(ols_center)[[1]],
#slope = coef(ols_center)[[2]],
# Step 6 Rotate the regression (SMA)
# slope must come first
# AC: I replaced the slope for the direct formula for SMA regression
slope = sd(ln_stv) / sd (arc_ry),
#slope = case_when(sma == TRUE ~ slope / pearson,
# sma == FALSE ~ slope),
# AC: I replaced the slope for the direct formula for SMA regression
intercept = mean(ln_stv) - (mean(arc_ry)*slope),
#intercept = case_when(sma == TRUE ~ mean_yt - slope * mean_xt,
# sma == FALSE ~ intercept),
# Step 7 Estimate Critical Soil Test Concentration
cstv = exp(intercept),
# Step 8 Estimate the confidence interval
pred_ln_stv = intercept + slope * arc_ry, # Fitted ln_STV for observed RY
mse = sum((pred_ln_stv - ln_stv) ^ 2) / df,
# AC: I would use a more explicit formula here and not this indirect way
#ssx = var(xt_centered) * (n - 1),
ssx = sum((mean(arc_ry)-arc_ry)^2),
confidence = confidence,
se = sqrt(mse * ((1/n) + ((mean(arc_ry) ^ 2) / ssx))),
#lower_cstv = exp(intercept - se * qt(1 - (1 - confidence / 100) / 2,
# df = n - 2)),
#upper_cstv = exp(intercept + se * qt(1 - (1 - confidence / 100) / 2,
# df = n - 2)),
# AC: I replaced boundaries formula for simpler ones
lower_cstv = exp(intercept - (t_stat * se)), # Lower limit of CSTV
upper_cstv = exp(intercept + (t_stat * se)), # Upper limit of CSTV
# Step 9 Back-transform
fitted_stv = exp(pred_ln_stv),
fitted_ry = 100 * (sin(
asin(sqrt(target/100)) + ((pred_ln_stv - intercept) / slope))) ^ 2
) %>%
# 'dataset' might be problematic, not defined in scope
select(target, cstv,
lower_cstv, upper_cstv, confidence,
fitted_stv, fitted_ry, pvalue, r, everything())
}
alcc.rev <- function(data,
stv,
ry,
#sma = TRUE,
target = 90,
confidence = 95,
remove.leverage = "none",
#remove2x = FALSE,
summary = FALSE){
if (missing(stv)) {
stop("Specify the soil test variable (e.g., stv = STK)")
}
if (missing(ry)) {
stop("Enter name of relative yield (%) variable (e.g., ry = RY)")
}
# AC: # Add statement for missing target
if (missing(target)) {
stop("Specify the target value of relative yield (%) (e.g., target = 90)")
}
# AC: # Add statement for missing confidence
if (missing(confidence)) {
stop("Specify the desired confidence level (%) for cstv estimation (e.g., confidence = 95)")
}
# enquo let's the user enter their own column names for x and y variables
# AC: # I think this is particularly confusing because in the SMA regression
# Soil test is not in the x-axis but on the y-axis, I will rather use "STV"
# instead of "x"
#x <- enquo(stv)
STV <- enquo(stv)
# AC: for SMA regression RY is not in the y-axis but on the x-axis, I will
#rather use "STV" instead of "x"
RY <- enquo(ry)
#y <- enquo(ry)
test <- data %>%
select(!!STV, !!RY)
if (max(test[,2]) > 100) {
warning("One or more original RY values exceeded 100%.\nAll RY values greater than 100% have been capped to 100% for arcsine transformation.", call. = FALSE)
}
if (min(test[,1]) < 0) {
stop("One or more soil test values are less than 0. Remove all data with STV values less than 0 prior to fitting.", call. = FALSE)
}
# stage 1, 2, and 3 described by Dyson and Conyers 2013
stage_1 <- data %>%
alcc_core.rev(
stv = !!STV,
ry = !!RY,
# AC: sma arg. not needed.
#sma = sma,
target = 100,
confidence = confidence
)
# AC: Added a small note
# identify CSTV for 100%
cstv_100 <<- unique(stage_1$cstv)
# AC: Added a small note
# identify CSTV for 90%
stage_2 <- data %>%
# AC: Warning! This filter line ALWAYS filter out stv > cstv100.
# The user should be the one deciding. I don't agree with Dyson here,
# as many others may share. The cstv90 estimate should be obtained
# without removing anything.
# All removes must be OPTIONAL and decision exclusive to researchers.
# So the filter step should be at stage 3 only
#filter(!!STV <= cstv_100) %>%
alcc_core.rev(
stv = !!STV,
ry = !!RY,
# AC: sma arg. not needed.
#sma = sma,
target = 90,
confidence = confidence
)
# Extract cstv_90
cstv90_2x <<- unique(stage_2$cstv) * 2
# AC: What if I don't want to remove soil test values > CSTV_100 ????
stage_3 <- data %>%
# AC: I would suggest use 3 options as a string:
#(i) "cstv90_2x", (ii) "cstv100", (iii) "none"
#filter(case_when(remove2x == TRUE ~ !!STV <= cstv90_2x,
# remove2x == FALSE ~ !!STV <= cstv_100)) %>%
filter(case_when(remove.leverage == "none" ~ !!STV != 0,
remove.leverage == "cstv90_2x" ~ !!STV <= cstv90_2x,
remove.leverage == "cstv100" ~ !!STV <= cstv_100 ) ) %>%
alcc_core.rev(stv = !!STV,
ry = !!RY,
#sma = sma,
target = target,
confidence = confidence) %>%
# AC: With this line, in the summary tabla always printed remove2x = "TRUE",
#It should print the chosen option instead
mutate(remove.leverage = remove.leverage,
# AC: I added a line to count the number of observation used for the CSTV estimations
n = nrow(.))
#mutate(remove2x = "TRUE")
if(summary == TRUE) {
return(
stage_3 %>%
select(
#model,
n, # new outcome
target,
cstv,
lower_cstv,
upper_cstv,
confidence,
pvalue,
r,
# Replaced remove2x
remove.leverage) %>%
distinct(across(everything()))
)
} else {
return(stage_3)
}
}# Function alcc_plot() creates a scatter plot of soil test correlation data
# arguments are passed to alcc()
alcc_plot.rev <- function(data,
stv,
ry,
#sma = TRUE,
target,
#sufficiency = 90,
confidence,
remove.leverage = "none") {
if (missing(stv)) {
stop("Specify the soil test variable (e.g., stv = STK)")
}
if (missing(ry)) {
stop("Enter name of relative yield (%) variable (e.g., ry = RY)")
}
# AC: # Add statement for missing target
if (missing(target)) {
stop("Specify the target value of relative yield (%) (e.g., target = 90)")
}
# AC: # Add statement for missing confidence
if (missing(confidence)) {
stop("Specify the desired confidence level (%) for cstv estimation (e.g., confidence = 95)")
}
# enquo let's the user enter their own column names for x and y variables
# AC: Replaced names
STV <- enquo(stv)
RY <- enquo(ry)
#x <- enquo(stv)
#y <- enquo(ry)
input <- data %>%
transmute(stv = !!STV,
# RY values greater than 100 are capped at 100
# AC: the false statement should always be of type double, just in case,
# use as.double()
# I have just tried with a dataset where I found this problem (data_2)
ry_cap = if_else(!!RY > 100, 100, as.double(!!RY)))
# pass to alcc function
output <- alcc.rev(data,
stv = !!STV,
ry = !!RY,
# AC: sma not needed
# sma = sma,
target = target,
confidence = confidence,
# AC: I changed remove2x for remove.leverage
remove.leverage = remove.leverage)
# for plot annotations
maxx <- max(input$stv)
cstv <- (unique(output$cstv))
cstv <- if_else(cstv < 10, round(cstv, 1), round(cstv, 0))
lower_cstv <- (unique(output$lower_cstv))
lower_cstv <- if_else(lower_cstv < 10, round(lower_cstv, 1), round(lower_cstv, 0))
upper_cstv <- (unique(output$upper_cstv))
upper_cstv <- if_else(upper_cstv < 10, round(upper_cstv, 1), round(upper_cstv, 0))
#sufficiency <- unique(output$sufficiency)
r <- round(unique(output$r), 2)
# AC: WARNING! WHAT IF I DON'T WANT TO REMOVE ANYTHING? Currently, the default
# is to remove STV > CSTV100
# Default option should be using all available data, then the remove2x = TRUE/FALSE
# plot includes all data, even if remove2x == TRUE, but curve will follow remove2x
output %>%
ggplot() +
geom_point(data = input,
aes(stv, ry_cap),
size = 2, alpha = 0.7,
color = case_when(
# AC: I changed the remove2x arg. for remove.leverage
# None
remove.leverage == "none" & input$stv <= cstv_100 ~ "black",
remove.leverage == "none" & input$stv > cstv_100 ~ "purple",
# >100
remove.leverage == "cstv100" & input$stv <= cstv_100 ~ "black",
remove.leverage == "cstv100" & input$stv > cstv_100 ~ 'red',
# >90_2x
remove.leverage == "cstv90_2x" & input$stv <= cstv90_2x ~ "black",
remove.leverage == "cstv90_2x" & input$stv > cstv90_2x ~ "red"
#remove.leverage == TRUE & input$stv > cstv90_2x ~ "red"
#remove2x == FALSE & input$stv > cstv_100 ~ red,
#remove.leverage == FALSE & input$stv > cstv90_2x ~ gold,
#remove.leverage == TRUE & input$stv > cstv90_2x ~ red,
#TRUE ~ black
)) +
geom_vline(xintercept = lower_cstv,
alpha = 0.5,
linetype = 3) +
geom_vline(xintercept = upper_cstv,
alpha = 0.5,
linetype = 3) +
geom_line(aes(x = fitted_stv,
y = fitted_ry),
color = "red", size = 1.5) +
# the cstv at X% sufficiency
geom_vline(xintercept = cstv, color = "blue", alpha = 1) +
geom_hline(yintercept = target, alpha = 0.2) +
annotate(
"text",
label = paste0(
"CSTV = ", cstv, " ppm at ", target, "% RY",
"\n", confidence,"% CI [", lower_cstv, " - ", upper_cstv, "]",
"\n r = ", r),
x = maxx,
y = 0,
hjust = 1,
vjust = 0,
alpha = 0.8
) +
scale_x_continuous(breaks =
seq(0, 10000, by = if_else(
maxx >= 200, 40,
if_else(maxx >= 100, 20,
if_else(maxx >= 50, 10, 5))
))) +
scale_y_continuous(breaks = seq(0, 105, 10)) +
labs(subtitle = "Modified Arcsine-Log Calibration Curve",
# AC: Here there could be a problem for people using STV in other than mg/kg ...
x = expression(Soil ~ Test ~ Value ~ (mg ~ kg ^ -1)),
y = "Relative yield (%)",
caption = paste0(
# AC: I Replaced this in line with the new arg. remove.leverage
#if_else(remove.leverage == TRUE,
#"Red points > CSTV90 * 2 excluded from model",
#"Red points > CSTV100 excluded from model. Yellow points > CSTV90 * 2 not excluded."),
case_when(remove.leverage == "none" ~ "No points excluded from model. Purple points (>CSTV100).",
remove.leverage == "cstv100" ~ "Red points (STV > CSTV100) were excluded from model.",
remove.leverage == "cstv90_2x" ~ "Red points (STV > 2*CSTV90) were excluded from model."),
"\nVertical dotted lines show lower and upper confidence limits."
)
)
}For the cotton dataset, Austin’s Code using alcc() produces:
-
different cstv, lower & upper limits when compared to Adrian’s modALCC() and the reference (SMA regression). This issue is nothing wrong with formulae but a result of using a dataset that presents points with STV > cstv100, since the alcc() removes those points by default, while Adrian’s modALCC() does not, as I prefer to leave this decision up to the user.
-
wrong p=values, since it uses the student-t one instead of the pvalue to test correlation significance (used by SMA regression).
# Load Austin's ALCC functions
# alcc.core() and alcc()
source_url("https://raw.githubusercontent.com/austinwpearce/SoilTestCocaCola/main/alcc.R")
# alcc_plot()
#source_url("https://raw.githubusercontent.com/austinwpearce/SoilTestCocaCola/main/alcc_plot.R")
# EXAMPLE 1. Cotton. Relative yield vs soil test potassium
cotton <- tibble(stk = agridat::cate.potassium$potassium,
ry = agridat::cate.potassium$yield,
dataset = "cotton")
### CODES COMPARISON
# Adrian's
modALCC(data = cotton, RY = ry, STV = stk, target=90, confidence = 0.95)## Warning: One or more original RY values exceeded 100%. All RY values greater
## than 100% have been capped to 100%.
## Warning: 2 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 2 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## n r target CSTV LL UL confidence p_value
## 1 24 0.7277644 90 76.89175 62.34761 94.82868 0.95 5.567174e-05
## CSTV90 n.90x2 CSTV100 n.100
## 1 76.89175 2 170.7629 2
## Curve
## 1 40.80000, 41.00000, 41.20000, 41.40000, 41.60000, 41.80000, 42.00000, 42.20000, 42.40000, 42.60000, 42.80000, 43.00000, 43.20000, 43.40000, 43.60000, 43.80000, 44.00000, 44.20000, 44.40000, 44.60000, 44.80000, 45.00000, 45.20000, 45.40000, 45.60000, 45.80000, 46.00000, 46.20000, 46.40000, 46.60000, 46.80000, 47.00000, 47.20000, 47.40000, 47.60000, 47.80000, 48.00000, 48.20000, 48.40000, 48.60000, 48.80000, 49.00000, 49.20000, 49.40000, 49.60000, 49.80000, 50.00000, 50.20000, 50.40000, 50.60000, 50.80000, 51.00000, 51.20000, 51.40000, 51.60000, 51.80000, 52.00000, 52.20000, 52.40000, 52.60000, 52.80000, 53.00000, 53.20000, 53.40000, 53.60000, 53.80000, 54.00000, 54.20000, 54.40000, 54.60000, 54.80000, 55.00000, 55.20000, 55.40000, 55.60000, 55.80000, 56.00000, 56.20000, 56.40000, 56.60000, 56.80000, 57.00000, 57.20000, 57.40000, 57.60000, 57.80000, 58.00000, 58.20000, 58.40000, 58.60000, 58.80000, 59.00000, 59.20000, 59.40000, 59.60000, 59.80000, 60.00000, 60.20000, 60.40000, 60.60000, 60.80000, 61.00000, 61.20000, 61.40000, 61.60000, 61.80000, 62.00000, 62.20000, 62.40000, 62.60000, 62.80000, 63.00000, 63.20000, 63.40000, 63.60000, 63.80000, 64.00000, 64.20000, 64.40000, 64.60000, 64.80000, 65.00000, 65.20000, 65.40000, 65.60000, 65.80000, 66.00000, 66.20000, 66.40000, 66.60000, 66.80000, 67.00000, 67.20000, 67.40000, 67.60000, 67.80000, 68.00000, 68.20000, 68.40000, 68.60000, 68.80000, 69.00000, 69.20000, 69.40000, 69.60000, 69.80000, 70.00000, 70.20000, 70.40000, 70.60000, 70.80000, 71.00000, 71.20000, 71.40000, 71.60000, 71.80000, 72.00000, 72.20000, 72.40000, 72.60000, 72.80000, 73.00000, 73.20000, 73.40000, 73.60000, 73.80000, 74.00000, 74.20000, 74.40000, 74.60000, 74.80000, 75.00000, 75.20000, 75.40000, 75.60000, 75.80000, 76.00000, 76.20000, 76.40000, 76.60000, 76.80000, 77.00000, 77.20000, 77.40000, 77.60000, 77.80000, 78.00000, 78.20000, 78.40000, 78.60000, 78.80000, 79.00000, 79.20000, 79.40000, 79.60000, 79.80000, 80.00000, 80.20000, 80.40000, 80.60000, 80.80000, 81.00000, 81.20000, 81.40000, 81.60000, 81.80000, 82.00000, 82.20000, 82.40000, 82.60000, 82.80000, 83.00000, 83.20000, 83.40000, 83.60000, 83.80000, 84.00000, 84.20000, 84.40000, 84.60000, 84.80000, 85.00000, 85.20000, 85.40000, 85.60000, 85.80000, 86.00000, 86.20000, 86.40000, 86.60000, 86.80000, 87.00000, 87.20000, 87.40000, 87.60000, 87.80000, 88.00000, 88.20000, 88.40000, 88.60000, 88.80000, 89.00000, 89.20000, 89.40000, 89.60000, 89.80000, 90.00000, 90.20000, 90.40000, 90.60000, 90.80000, 91.00000, 91.20000, 91.40000, 91.60000, 91.80000, 92.00000, 92.20000, 92.40000, 92.60000, 92.80000, 93.00000, 93.20000, 93.40000, 93.60000, 93.80000, 94.00000, 94.20000, 94.40000, 94.60000, 94.80000, 95.00000, 95.20000, 95.40000, 95.60000, 95.80000, 96.00000, 96.20000, 96.40000, 96.60000, 96.80000, 97.00000, 97.20000, 97.40000, 97.60000, 97.80000, 98.00000, 98.20000, 98.40000, 98.60000, 98.80000, 99.00000, 99.20000, 99.40000, 99.60000, 99.80000, 100.00000, 19.35974, 19.45764, 19.55595, 19.65469, 19.75386, 19.85346, 19.95350, 20.05397, 20.15488, 20.25624, 20.35805, 20.46030, 20.56302, 20.66619, 20.76982, 20.87392, 20.97848, 21.08352, 21.18904, 21.29503, 21.40151, 21.50848, 21.61593, 21.72389, 21.83234, 21.94129, 22.05075, 22.16072, 22.27121, 22.38221, 22.49374, 22.60579, 22.71837, 22.83149, 22.94515, 23.05935, 23.17411, 23.28941, 23.40527, 23.52169, 23.63868, 23.75624, 23.87437, 23.99308, 24.11238, 24.23227, 24.35275, 24.47383, 24.59551, 24.71781, 24.84071, 24.96424, 25.08839, 25.21317, 25.33859, 25.46464, 25.59134, 25.71869, 25.84670, 25.97537, 26.10470, 26.23471, 26.36540, 26.49678, 26.62884, 26.76160, 26.89507, 27.02924, 27.16413, 27.29974, 27.43608, 27.57315, 27.71096, 27.84952, 27.98883, 28.12891, 28.26975, 28.41136, 28.55376, 28.69695, 28.84093, 28.98571, 29.13130, 29.27772, 29.42495, 29.57302, 29.72193, 29.87169, 30.02230, 30.17378, 30.32613, 30.47937, 30.63349, 30.78851, 30.94443, 31.10127, 31.25904, 31.41774, 31.57737, 31.73796, 31.89952, 32.06204, 32.22554, 32.39003, 32.55551, 32.72201, 32.88953, 33.05807, 33.22766, 33.39830, 33.57000, 33.74277, 33.91662, 34.09157, 34.26763, 34.44480, 34.62311, 34.80255, 34.98315, 35.16491, 35.34785, 35.53199, 35.71733, 35.90388, 36.09167, 36.28069, 36.47098, 36.66254, 36.85539, 37.04953, 37.24499, 37.44178, 37.63992, 37.83941, 38.04028, 38.24255, 38.44622, 38.65131, 38.85785, 39.06585, 39.27532, 39.48629, 39.69876, 39.91277, 40.12832, 40.34544, 40.56415, 40.78447, 41.00641, 41.22999, 41.45525, 41.68219, 41.91084, 42.14122, 42.37336, 42.60727, 42.84298, 43.08052, 43.31990, 43.56115, 43.80431, 44.04938, 44.29640, 44.54540, 44.79640, 45.04943, 45.30452, 45.56170, 45.82099, 46.08243, 46.34604, 46.61187, 46.87993, 47.15027, 47.42292, 47.69790, 47.97526, 48.25504, 48.53726, 48.82197, 49.10920, 49.39899, 49.69139, 49.98643, 50.28416, 50.58461, 50.88784, 51.19389, 51.50280, 51.81462, 52.12940, 52.44719, 52.76804, 53.09201, 53.41914, 53.74949, 54.08312, 54.42009, 54.76045, 55.10427, 55.45161, 55.80253, 56.15710, 56.51540, 56.87748, 57.24342, 57.61331, 57.98720, 58.36519, 58.74734, 59.13376, 59.52452, 59.91971, 60.31943, 60.72377, 61.13282, 61.54669, 61.96548, 62.38931, 62.81827, 63.25250, 63.69210, 64.13720, 64.58793, 65.04443, 65.50682, 65.97525, 66.44988, 66.93084, 67.41831, 67.91245, 68.41343, 68.92143, 69.43664, 69.95925, 70.48947, 71.02750, 71.57357, 72.12791, 72.69076, 73.26238, 73.84301, 74.43295, 75.03248, 75.64191, 76.26156, 76.89175, 77.53285, 78.18523, 78.84928, 79.52541, 80.21406, 80.91570, 81.63081, 82.35991, 83.10357, 83.86235, 84.63690, 85.42787, 86.23598, 87.06199, 87.90672, 88.77104, 89.65590, 90.56233, 91.49142, 92.44435, 93.42244, 94.42710, 95.45985, 96.52240, 97.61660, 98.74451, 99.90838, 101.11074, 102.35443, 103.64260, 104.97882, 106.36717, 107.81229, 109.31953, 110.89510, 112.54630, 114.28174, 116.11178, 118.04901, 120.10898, 122.31131, 124.68127, 127.25246, 130.07109, 133.20386, 136.75336, 140.89273, 145.96033, 152.83194, 170.76289
## SMA
## 1 3.25809654, 3.33220451, 3.40119738, 3.43398720, 3.52636052, 3.55534806, 3.68887945, 3.78418963, 3.89182030, 4.02535169, 4.21950771, 4.31748811, 4.34380542, 4.35670883, 4.35670883, 4.62497281, 4.77068462, 4.77068462, 4.87519732, 4.89034913, 4.89034913, 5.02388052, 5.26269019, 5.35185813, -0.42861896, -0.31339648, -0.33213651, -0.55617481, -0.14811819, -0.25461120, -0.33213651, -0.32175055, 0.07428349, 0.22158313, -0.29549582, 0.32175055, 0.15668523, -0.07173053, 0.32175055, 0.14766754, 0.14189705, 0.17985350, -0.06461985, 0.04057135, 0.14189705, -0.02734987, 0.32175055, 0.16297034, 3.27950884, 3.56523769, 3.51876614, 2.96319572, 3.97509497, 3.71101347, 3.51876614, 3.54452124, 4.52660689, 4.89188071, 3.60962775, 5.14027599, 4.73094682, 4.16452117, 5.14027599, 4.70858475, 4.69427508, 4.78839952, 4.18215423, 4.44300749, 4.69427508, 4.27457639, 5.14027599, 4.74653264, -0.02141230, -0.23303318, -0.11756876, 0.47079149, -0.44873444, -0.15566541, 0.17011332, 0.23966840, -0.63478660, -0.86652902, 0.60987995, -0.82278787, -0.38714140, 0.19218766, -0.78356716, -0.08361194, 0.07640954, -0.01771489, 0.69304309, 0.44734164, 0.19607405, 0.74930413, 0.12241420, 0.60532549, 2.19520677, 2.55504358, 2.57756491, 2.05478431, 3.15905688, 2.92396292, 2.86524698, 2.98631226, 4.07602858, 4.57483379, 3.48673684, 5.11536549, 4.73235363, 4.17883138, 5.15458620, 4.99115895, 5.12256110, 5.21668553, 4.71495295, 4.99095800, 5.24222560, 4.95605830, 6.06056757, 5.75599216
# Austin's, sma = TRUE
# Check that even stating remove2x = FALSE it always print "remove2x = TRUE" on the summary table.
alcc(cotton, soil_test = stk, ry = ry, sufficiency = 90,
confidence = 95, summary = T, remove2x = FALSE, sma = T)## Warning: One or more original RY values exceeded 100%.
## All RY values greater than 100% have been capped to 100% for arcsine transformation.
## # A tibble: 1 x 9
## model sufficiency cstv lower_cl upper_cl confidence pvalue pearson remove2x
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 ALCC-~ 90 73.5 59.2 91.2 95 1.54e-4 0.694 TRUE
# Austin's, sma = FALSE
alcc(cotton, soil_test = stk, ry = ry, sufficiency = 90,
confidence = 95, summary = T, remove2x = FALSE, sma = F)## Warning: One or more original RY values exceeded 100%.
## All RY values greater than 100% have been capped to 100% for arcsine transformation.
## # A tibble: 1 x 9
## model sufficiency cstv lower_cl upper_cl confidence pvalue pearson remove2x
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 ALCC 90 67.5 55.9 81.5 95 8.89e-5 0.725 TRUE
## For the Austin's Code using alcc() ->
# cstv, lower & upper limit, and p=values are wrong compared to
# SMA regression as reference.
# Austin's results (REFERENCE) [ADRIAN's]:
# CSTV = 67.49 (76.89) [76.89]
# LL = 55.87 (62.36) [62.35]
# UL = 81.54 (94.79) [94.83]
# pval = 8.87e-05 (5.57e-05) [5.57e-05]
# NOW COMPARE TO MY REVISED VERSION of alcc (alcc.rev)
# Adrian's
modALCC(data = cotton, RY = ry, STV = stk, target=90, confidence = 0.95)## Warning: One or more original RY values exceeded 100%. All RY values greater
## than 100% have been capped to 100%.
## Warning: 2 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 2 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## n r target CSTV LL UL confidence p_value
## 1 24 0.7277644 90 76.89175 62.34761 94.82868 0.95 5.567174e-05
## CSTV90 n.90x2 CSTV100 n.100
## 1 76.89175 2 170.7629 2
## Curve
## 1 40.80000, 41.00000, 41.20000, 41.40000, 41.60000, 41.80000, 42.00000, 42.20000, 42.40000, 42.60000, 42.80000, 43.00000, 43.20000, 43.40000, 43.60000, 43.80000, 44.00000, 44.20000, 44.40000, 44.60000, 44.80000, 45.00000, 45.20000, 45.40000, 45.60000, 45.80000, 46.00000, 46.20000, 46.40000, 46.60000, 46.80000, 47.00000, 47.20000, 47.40000, 47.60000, 47.80000, 48.00000, 48.20000, 48.40000, 48.60000, 48.80000, 49.00000, 49.20000, 49.40000, 49.60000, 49.80000, 50.00000, 50.20000, 50.40000, 50.60000, 50.80000, 51.00000, 51.20000, 51.40000, 51.60000, 51.80000, 52.00000, 52.20000, 52.40000, 52.60000, 52.80000, 53.00000, 53.20000, 53.40000, 53.60000, 53.80000, 54.00000, 54.20000, 54.40000, 54.60000, 54.80000, 55.00000, 55.20000, 55.40000, 55.60000, 55.80000, 56.00000, 56.20000, 56.40000, 56.60000, 56.80000, 57.00000, 57.20000, 57.40000, 57.60000, 57.80000, 58.00000, 58.20000, 58.40000, 58.60000, 58.80000, 59.00000, 59.20000, 59.40000, 59.60000, 59.80000, 60.00000, 60.20000, 60.40000, 60.60000, 60.80000, 61.00000, 61.20000, 61.40000, 61.60000, 61.80000, 62.00000, 62.20000, 62.40000, 62.60000, 62.80000, 63.00000, 63.20000, 63.40000, 63.60000, 63.80000, 64.00000, 64.20000, 64.40000, 64.60000, 64.80000, 65.00000, 65.20000, 65.40000, 65.60000, 65.80000, 66.00000, 66.20000, 66.40000, 66.60000, 66.80000, 67.00000, 67.20000, 67.40000, 67.60000, 67.80000, 68.00000, 68.20000, 68.40000, 68.60000, 68.80000, 69.00000, 69.20000, 69.40000, 69.60000, 69.80000, 70.00000, 70.20000, 70.40000, 70.60000, 70.80000, 71.00000, 71.20000, 71.40000, 71.60000, 71.80000, 72.00000, 72.20000, 72.40000, 72.60000, 72.80000, 73.00000, 73.20000, 73.40000, 73.60000, 73.80000, 74.00000, 74.20000, 74.40000, 74.60000, 74.80000, 75.00000, 75.20000, 75.40000, 75.60000, 75.80000, 76.00000, 76.20000, 76.40000, 76.60000, 76.80000, 77.00000, 77.20000, 77.40000, 77.60000, 77.80000, 78.00000, 78.20000, 78.40000, 78.60000, 78.80000, 79.00000, 79.20000, 79.40000, 79.60000, 79.80000, 80.00000, 80.20000, 80.40000, 80.60000, 80.80000, 81.00000, 81.20000, 81.40000, 81.60000, 81.80000, 82.00000, 82.20000, 82.40000, 82.60000, 82.80000, 83.00000, 83.20000, 83.40000, 83.60000, 83.80000, 84.00000, 84.20000, 84.40000, 84.60000, 84.80000, 85.00000, 85.20000, 85.40000, 85.60000, 85.80000, 86.00000, 86.20000, 86.40000, 86.60000, 86.80000, 87.00000, 87.20000, 87.40000, 87.60000, 87.80000, 88.00000, 88.20000, 88.40000, 88.60000, 88.80000, 89.00000, 89.20000, 89.40000, 89.60000, 89.80000, 90.00000, 90.20000, 90.40000, 90.60000, 90.80000, 91.00000, 91.20000, 91.40000, 91.60000, 91.80000, 92.00000, 92.20000, 92.40000, 92.60000, 92.80000, 93.00000, 93.20000, 93.40000, 93.60000, 93.80000, 94.00000, 94.20000, 94.40000, 94.60000, 94.80000, 95.00000, 95.20000, 95.40000, 95.60000, 95.80000, 96.00000, 96.20000, 96.40000, 96.60000, 96.80000, 97.00000, 97.20000, 97.40000, 97.60000, 97.80000, 98.00000, 98.20000, 98.40000, 98.60000, 98.80000, 99.00000, 99.20000, 99.40000, 99.60000, 99.80000, 100.00000, 19.35974, 19.45764, 19.55595, 19.65469, 19.75386, 19.85346, 19.95350, 20.05397, 20.15488, 20.25624, 20.35805, 20.46030, 20.56302, 20.66619, 20.76982, 20.87392, 20.97848, 21.08352, 21.18904, 21.29503, 21.40151, 21.50848, 21.61593, 21.72389, 21.83234, 21.94129, 22.05075, 22.16072, 22.27121, 22.38221, 22.49374, 22.60579, 22.71837, 22.83149, 22.94515, 23.05935, 23.17411, 23.28941, 23.40527, 23.52169, 23.63868, 23.75624, 23.87437, 23.99308, 24.11238, 24.23227, 24.35275, 24.47383, 24.59551, 24.71781, 24.84071, 24.96424, 25.08839, 25.21317, 25.33859, 25.46464, 25.59134, 25.71869, 25.84670, 25.97537, 26.10470, 26.23471, 26.36540, 26.49678, 26.62884, 26.76160, 26.89507, 27.02924, 27.16413, 27.29974, 27.43608, 27.57315, 27.71096, 27.84952, 27.98883, 28.12891, 28.26975, 28.41136, 28.55376, 28.69695, 28.84093, 28.98571, 29.13130, 29.27772, 29.42495, 29.57302, 29.72193, 29.87169, 30.02230, 30.17378, 30.32613, 30.47937, 30.63349, 30.78851, 30.94443, 31.10127, 31.25904, 31.41774, 31.57737, 31.73796, 31.89952, 32.06204, 32.22554, 32.39003, 32.55551, 32.72201, 32.88953, 33.05807, 33.22766, 33.39830, 33.57000, 33.74277, 33.91662, 34.09157, 34.26763, 34.44480, 34.62311, 34.80255, 34.98315, 35.16491, 35.34785, 35.53199, 35.71733, 35.90388, 36.09167, 36.28069, 36.47098, 36.66254, 36.85539, 37.04953, 37.24499, 37.44178, 37.63992, 37.83941, 38.04028, 38.24255, 38.44622, 38.65131, 38.85785, 39.06585, 39.27532, 39.48629, 39.69876, 39.91277, 40.12832, 40.34544, 40.56415, 40.78447, 41.00641, 41.22999, 41.45525, 41.68219, 41.91084, 42.14122, 42.37336, 42.60727, 42.84298, 43.08052, 43.31990, 43.56115, 43.80431, 44.04938, 44.29640, 44.54540, 44.79640, 45.04943, 45.30452, 45.56170, 45.82099, 46.08243, 46.34604, 46.61187, 46.87993, 47.15027, 47.42292, 47.69790, 47.97526, 48.25504, 48.53726, 48.82197, 49.10920, 49.39899, 49.69139, 49.98643, 50.28416, 50.58461, 50.88784, 51.19389, 51.50280, 51.81462, 52.12940, 52.44719, 52.76804, 53.09201, 53.41914, 53.74949, 54.08312, 54.42009, 54.76045, 55.10427, 55.45161, 55.80253, 56.15710, 56.51540, 56.87748, 57.24342, 57.61331, 57.98720, 58.36519, 58.74734, 59.13376, 59.52452, 59.91971, 60.31943, 60.72377, 61.13282, 61.54669, 61.96548, 62.38931, 62.81827, 63.25250, 63.69210, 64.13720, 64.58793, 65.04443, 65.50682, 65.97525, 66.44988, 66.93084, 67.41831, 67.91245, 68.41343, 68.92143, 69.43664, 69.95925, 70.48947, 71.02750, 71.57357, 72.12791, 72.69076, 73.26238, 73.84301, 74.43295, 75.03248, 75.64191, 76.26156, 76.89175, 77.53285, 78.18523, 78.84928, 79.52541, 80.21406, 80.91570, 81.63081, 82.35991, 83.10357, 83.86235, 84.63690, 85.42787, 86.23598, 87.06199, 87.90672, 88.77104, 89.65590, 90.56233, 91.49142, 92.44435, 93.42244, 94.42710, 95.45985, 96.52240, 97.61660, 98.74451, 99.90838, 101.11074, 102.35443, 103.64260, 104.97882, 106.36717, 107.81229, 109.31953, 110.89510, 112.54630, 114.28174, 116.11178, 118.04901, 120.10898, 122.31131, 124.68127, 127.25246, 130.07109, 133.20386, 136.75336, 140.89273, 145.96033, 152.83194, 170.76289
## SMA
## 1 3.25809654, 3.33220451, 3.40119738, 3.43398720, 3.52636052, 3.55534806, 3.68887945, 3.78418963, 3.89182030, 4.02535169, 4.21950771, 4.31748811, 4.34380542, 4.35670883, 4.35670883, 4.62497281, 4.77068462, 4.77068462, 4.87519732, 4.89034913, 4.89034913, 5.02388052, 5.26269019, 5.35185813, -0.42861896, -0.31339648, -0.33213651, -0.55617481, -0.14811819, -0.25461120, -0.33213651, -0.32175055, 0.07428349, 0.22158313, -0.29549582, 0.32175055, 0.15668523, -0.07173053, 0.32175055, 0.14766754, 0.14189705, 0.17985350, -0.06461985, 0.04057135, 0.14189705, -0.02734987, 0.32175055, 0.16297034, 3.27950884, 3.56523769, 3.51876614, 2.96319572, 3.97509497, 3.71101347, 3.51876614, 3.54452124, 4.52660689, 4.89188071, 3.60962775, 5.14027599, 4.73094682, 4.16452117, 5.14027599, 4.70858475, 4.69427508, 4.78839952, 4.18215423, 4.44300749, 4.69427508, 4.27457639, 5.14027599, 4.74653264, -0.02141230, -0.23303318, -0.11756876, 0.47079149, -0.44873444, -0.15566541, 0.17011332, 0.23966840, -0.63478660, -0.86652902, 0.60987995, -0.82278787, -0.38714140, 0.19218766, -0.78356716, -0.08361194, 0.07640954, -0.01771489, 0.69304309, 0.44734164, 0.19607405, 0.74930413, 0.12241420, 0.60532549, 2.19520677, 2.55504358, 2.57756491, 2.05478431, 3.15905688, 2.92396292, 2.86524698, 2.98631226, 4.07602858, 4.57483379, 3.48673684, 5.11536549, 4.73235363, 4.17883138, 5.15458620, 4.99115895, 5.12256110, 5.21668553, 4.71495295, 4.99095800, 5.24222560, 4.95605830, 6.06056757, 5.75599216
# Revised alcc functions
alcc.rev(cotton, stv = stk, ry = ry, target = 90,
confidence = 95, summary = T, remove.leverage = "none")## Warning: One or more original RY values exceeded 100%.
## All RY values greater than 100% have been capped to 100% for arcsine transformation.
## # A tibble: 1 x 9
## n target cstv lower_cstv upper_cstv confidence pvalue r
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 24 90 76.9 62.3 94.8 95 0.0000557 0.728
## # ... with 1 more variable: remove.leverage <chr>
alcc.rev(cotton, stv = stk, ry = ry, target = 90,
confidence = 95, summary = T, remove.leverage = "cstv100")## Warning: One or more original RY values exceeded 100%.
## All RY values greater than 100% have been capped to 100% for arcsine transformation.
## # A tibble: 1 x 9
## n target cstv lower_cstv upper_cstv confidence pvalue r
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 22 90 73.5 59.2 91.2 95 0.000339 0.694
## # ... with 1 more variable: remove.leverage <chr>
alcc.rev(cotton, stv = stk, ry = ry, target = 90,
confidence = 95, summary = T, remove.leverage = "cstv90_2x")## Warning: One or more original RY values exceeded 100%.
## All RY values greater than 100% have been capped to 100% for arcsine transformation.
## # A tibble: 1 x 9
## n target cstv lower_cstv upper_cstv confidence pvalue r
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 22 90 73.5 59.2 91.2 95 0.000339 0.694
## # ... with 1 more variable: remove.leverage <chr>
# USE SMA as reference method
target = 90
cotton <- cotton %>% mutate(# Transform stv
ln_stv = log(stk),
# Cap if RY > 100
RY = ifelse(ry > 100, 100, as.double(ry)),
# Transform and center RY
arc_ry = (asin(sqrt(RY/100)) - asin(sqrt(target/100))))
# SMA model
sma.cotton <- sma(data = cotton, method = c("SMA"), formula = ln_stv ~ arc_ry)
# Print
sma.cotton## Call: sma(formula = ln_stv ~ arc_ry, data = cotton, method = c("SMA"))
##
## Fit using Standardized Major Axis
##
## ------------------------------------------------------------
## Coefficients:
## elevation slope
## estimate 4.342399 2.479801
## lower limit 4.133033 1.839335
## upper limit 4.551764 3.343281
##
## H0 : variables uncorrelated
## R-squared : 0.529641
## P-value : 5.5672e-05
# Extract intercept, its CI, and model p-value
print("CSTV from SMA")## [1] "CSTV from SMA"
exp(sma.cotton[["elevtest"]][[1]][["a"]])## [1] 76.89175
print("Lower limit")## [1] "Lower limit"
exp(sma.cotton[["elevtest"]][[1]][["a.ci"]][[1]])## [1] 62.36682
print("Upper limit")## [1] "Upper limit"
exp(sma.cotton[["elevtest"]][[1]][["a.ci"]][[2]])## [1] 94.79947
print("p-value")## [1] "p-value"
sma.cotton[["pval"]][[1]]## [1] 5.567174e-05
Data_1: The alcc() from Austin works the same than Adrian’s modALCC()
and Spreadsheet version.
Data_2: Austin’s original alcc() code fails with data_2 due to an issue with the “if_else()” used to cap RY values. The function needs to have specified the FALSE statement as.double(), otherwise it may result problematic with some datasets loaded from csv files (as data_2).
# Adrian's
fit_example_1 = modALCC(data = data_1, RY = RY, STV = STV, target=90, confidence = 0.95)## Warning: 7 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
fit_example_1## n r target CSTV LL UL confidence p_value
## 1 15 0.9682908 90 4.478476 3.947041 5.081463 0.95 3.296044e-09
## CSTV90 n.90x2 CSTV100 n.100
## 1 4.478476 7 19.15054 0
## Curve
## 1 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 1.097927, 1.108379, 1.118944, 1.129625, 1.140423, 1.151339, 1.162376, 1.173535, 1.184817, 1.196225, 1.207760, 1.219425, 1.231221, 1.243150, 1.255214, 1.267415, 1.279755, 1.292236, 1.304860, 1.317630, 1.330548, 1.343616, 1.356836, 1.370210, 1.383742, 1.397433, 1.411286, 1.425303, 1.439488, 1.453842, 1.468369, 1.483071, 1.497951, 1.513012, 1.528257, 1.543689, 1.559311, 1.575127, 1.591138, 1.607350, 1.623765, 1.640386, 1.657217, 1.674262, 1.691525, 1.709008, 1.726717, 1.744655, 1.762826, 1.781234, 1.799883, 1.818779, 1.837924, 1.857325, 1.876985, 1.896910, 1.917103, 1.937572, 1.958319, 1.979352, 2.000675, 2.022293, 2.044214, 2.066441, 2.088983, 2.111844, 2.135031, 2.158551, 2.182410, 2.206616, 2.231175, 2.256095, 2.281384, 2.307048, 2.333097, 2.359537, 2.386379, 2.413629, 2.441298, 2.469395, 2.497929, 2.526910, 2.556347, 2.586252, 2.616636, 2.647508, 2.678882, 2.710768, 2.743179, 2.776127, 2.809626, 2.843690, 2.878331, 2.913565, 2.949407, 2.985872, 3.022976, 3.060736, 3.099169, 3.138294, 3.178128, 3.218691, 3.260004, 3.302086, 3.344960, 3.388649, 3.433176, 3.478564, 3.524841, 3.572032, 3.620165, 3.669269, 3.719374, 3.770512, 3.822716, 3.876020, 3.930460, 3.986075, 4.042904, 4.100988, 4.160372, 4.221100, 4.283223, 4.346790, 4.411856, 4.478476, 4.546710, 4.616622, 4.688278, 4.761749, 4.837110, 4.914440, 4.993823, 5.075351, 5.159117, 5.245225, 5.333784, 5.424910, 5.518728, 5.615374, 5.714992, 5.817737, 5.923779, 6.033299, 6.146495, 6.263582, 6.384794, 6.510388, 6.640644, 6.775870, 6.916408, 7.062634, 7.214969, 7.373879, 7.539891, 7.713596, 7.895664, 8.086860, 8.288063, 8.500287, 8.724716, 8.962742, 9.216022, 9.486552, 9.776766, 10.089688, 10.429142, 10.800084, 11.209119, 11.665380, 12.182103, 12.779738, 13.492946, 14.389790, 15.647308, 19.150544
## SMA
## 1 0.00000000, 0.69314718, 1.09861229, 1.38629436, 1.60943791, 1.79175947, 1.94591015, 2.07944154, 2.19722458, 2.30258509, 2.39789527, 2.48490665, 2.56494936, 2.63905733, 2.70805020, -0.31130128, -0.14189705, -0.07594886, -0.03199105, 0.00000000, 0.07428349, 0.05398723, 0.12039263, 0.14766754, 0.09623715, 0.17985350, 0.32175055, 0.22158313, 0.22158313, 0.32175055, 0.09342397, 0.85846552, 1.15629226, 1.35480886, 1.49928272, 1.83475226, 1.74309289, 2.04298443, 2.16615987, 1.93389654, 2.31151393, 2.95233114, 2.49996793, 2.49996793, 2.95233114, -0.09342397, -0.16531834, -0.05767997, 0.03148550, 0.11015519, -0.04299279, 0.20281726, 0.03645711, 0.03106471, 0.36868855, 0.08638134, -0.46742449, 0.06498143, 0.13908940, -0.24428093, -1.40585875, 0.05232998, 0.75562183, 1.24182049, 1.60943791, 2.12722900, 2.18972031, 2.62314325, 2.86410172, 2.73719891, 3.21012648, 3.93795506, 3.56563456, 3.63974254, 4.16109861
# Austin's
alcc(data_1, soil_test = STV, ry = RY, sufficiency = 90,
confidence = 95, summary = T, remove2x = FALSE, sma = TRUE)## model sufficiency cstv lower_cl upper_cl confidence pvalue
## 1 ALCC-SMA 90 4.478476 3.947041 5.081463 95 6.469298e-10
## pearson remove2x
## 1 0.9682908 TRUE
# Fixed alcc.rev
alcc.rev(data_1, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "none")## n target cstv lower_cstv upper_cstv confidence pvalue r
## 1 15 90 4.478476 3.947041 5.081463 95 3.296044e-09 0.9682908
## remove.leverage
## 1 none
# plot
alcc_plot.rev(data_1, stv = STV, ry = RY, target = 90,
confidence = 95, remove.leverage = "cstv90_2x")
# Using dataframe
# Alternative using the vectors
# fit_example_1 = modALCC(Y = data_1$RY,STV = data_1$STV, target=90,confidence = 0.95)
# Adrian's
fit_example_2 = modALCC(data = data_2, RY = RY, STV = STV, target=90, confidence = 0.95)## Warning: 9 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 22 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
fit_example_2## n r target CSTV LL UL confidence p_value
## 1 137 0.7164928 90 23.25457 21.57156 25.06888 0.95 7.314913e-23
## CSTV90 n.90x2 CSTV100 n.100
## 1 23.25457 22 53.10299 9
## Curve
## 1 12.000000, 12.200000, 12.400000, 12.600000, 12.800000, 13.000000, 13.200000, 13.400000, 13.600000, 13.800000, 14.000000, 14.200000, 14.400000, 14.600000, 14.800000, 15.000000, 15.200000, 15.400000, 15.600000, 15.800000, 16.000000, 16.200000, 16.400000, 16.600000, 16.800000, 17.000000, 17.200000, 17.400000, 17.600000, 17.800000, 18.000000, 18.200000, 18.400000, 18.600000, 18.800000, 19.000000, 19.200000, 19.400000, 19.600000, 19.800000, 20.000000, 20.200000, 20.400000, 20.600000, 20.800000, 21.000000, 21.200000, 21.400000, 21.600000, 21.800000, 22.000000, 22.200000, 22.400000, 22.600000, 22.800000, 23.000000, 23.200000, 23.400000, 23.600000, 23.800000, 24.000000, 24.200000, 24.400000, 24.600000, 24.800000, 25.000000, 25.200000, 25.400000, 25.600000, 25.800000, 26.000000, 26.200000, 26.400000, 26.600000, 26.800000, 27.000000, 27.200000, 27.400000, 27.600000, 27.800000, 28.000000, 28.200000, 28.400000, 28.600000, 28.800000, 29.000000, 29.200000, 29.400000, 29.600000, 29.800000, 30.000000, 30.200000, 30.400000, 30.600000, 30.800000, 31.000000, 31.200000, 31.400000, 31.600000, 31.800000, 32.000000, 32.200000, 32.400000, 32.600000, 32.800000, 33.000000, 33.200000, 33.400000, 33.600000, 33.800000, 34.000000, 34.200000, 34.400000, 34.600000, 34.800000, 35.000000, 35.200000, 35.400000, 35.600000, 35.800000, 36.000000, 36.200000, 36.400000, 36.600000, 36.800000, 37.000000, 37.200000, 37.400000, 37.600000, 37.800000, 38.000000, 38.200000, 38.400000, 38.600000, 38.800000, 39.000000, 39.200000, 39.400000, 39.600000, 39.800000, 40.000000, 40.200000, 40.400000, 40.600000, 40.800000, 41.000000, 41.200000, 41.400000, 41.600000, 41.800000, 42.000000, 42.200000, 42.400000, 42.600000, 42.800000, 43.000000, 43.200000, 43.400000, 43.600000, 43.800000, 44.000000, 44.200000, 44.400000, 44.600000, 44.800000, 45.000000, 45.200000, 45.400000, 45.600000, 45.800000, 46.000000, 46.200000, 46.400000, 46.600000, 46.800000, 47.000000, 47.200000, 47.400000, 47.600000, 47.800000, 48.000000, 48.200000, 48.400000, 48.600000, 48.800000, 49.000000, 49.200000, 49.400000, 49.600000, 49.800000, 50.000000, 50.200000, 50.400000, 50.600000, 50.800000, 51.000000, 51.200000, 51.400000, 51.600000, 51.800000, 52.000000, 52.200000, 52.400000, 52.600000, 52.800000, 53.000000, 53.200000, 53.400000, 53.600000, 53.800000, 54.000000, 54.200000, 54.400000, 54.600000, 54.800000, 55.000000, 55.200000, 55.400000, 55.600000, 55.800000, 56.000000, 56.200000, 56.400000, 56.600000, 56.800000, 57.000000, 57.200000, 57.400000, 57.600000, 57.800000, 58.000000, 58.200000, 58.400000, 58.600000, 58.800000, 59.000000, 59.200000, 59.400000, 59.600000, 59.800000, 60.000000, 60.200000, 60.400000, 60.600000, 60.800000, 61.000000, 61.200000, 61.400000, 61.600000, 61.800000, 62.000000, 62.200000, 62.400000, 62.600000, 62.800000, 63.000000, 63.200000, 63.400000, 63.600000, 63.800000, 64.000000, 64.200000, 64.400000, 64.600000, 64.800000, 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 2.336883, 2.355345, 2.373822, 2.392314, 2.410824, 2.429353, 2.447902, 2.466472, 2.485066, 2.503683, 2.522326, 2.540994, 2.559691, 2.578416, 2.597171, 2.615957, 2.634775, 2.653625, 2.672510, 2.691430, 2.710385, 2.729377, 2.748407, 2.767476, 2.786584, 2.805733, 2.824922, 2.844155, 2.863430, 2.882748, 2.902112, 2.921521, 2.940976, 2.960478, 2.980028, 2.999627, 3.019275, 3.038973, 3.058722, 3.078522, 3.098374, 3.118280, 3.138239, 3.158253, 3.178322, 3.198446, 3.218628, 3.238866, 3.259162, 3.279517, 3.299931, 3.320405, 3.340940, 3.361536, 3.382194, 3.402915, 3.423698, 3.444546, 3.465459, 3.486436, 3.507480, 3.528590, 3.549767, 3.571012, 3.592326, 3.613709, 3.635161, 3.656685, 3.678279, 3.699945, 3.721683, 3.743495, 3.765380, 3.787340, 3.809375, 3.831485, 3.853672, 3.875936, 3.898277, 3.920697, 3.943195, 3.965774, 3.988432, 4.011172, 4.033993, 4.056896, 4.079883, 4.102953, 4.126107, 4.149347, 4.172672, 4.196083, 4.219582, 4.243168, 4.266843, 4.290606, 4.314460, 4.338404, 4.362439, 4.386567, 4.410787, 4.435100, 4.459507, 4.484009, 4.508607, 4.533301, 4.558092, 4.582980, 4.607967, 4.633054, 4.658240, 4.683527, 4.708916, 4.734406, 4.760000, 4.785698, 4.811500, 4.837408, 4.863422, 4.889542, 4.915771, 4.942108, 4.968555, 4.995111, 5.021779, 5.048559, 5.075451, 5.102457, 5.129578, 5.156813, 5.184165, 5.211634, 5.239220, 5.266926, 5.294751, 5.322696, 5.350763, 5.378953, 5.407266, 5.435703, 5.464265, 5.492953, 5.521768, 5.550712, 5.579784, 5.608986, 5.638319, 5.667784, 5.697382, 5.727114, 5.756981, 5.786984, 5.817124, 5.847402, 5.877819, 5.908377, 5.939075, 5.969916, 6.000901, 6.032030, 6.063304, 6.094726, 6.126295, 6.158014, 6.189883, 6.221903, 6.254076, 6.286402, 6.318884, 6.351522, 6.384317, 6.417271, 6.450385, 6.483660, 6.517098, 6.550699, 6.584466, 6.618399, 6.652499, 6.686769, 6.721209, 6.755821, 6.790607, 6.825566, 6.860702, 6.896016, 6.931508, 6.967181, 7.003035, 7.039073, 7.075296, 7.111705, 7.148302, 7.185089, 7.222066, 7.259237, 7.296601, 7.334162, 7.371920, 7.409878, 7.448036, 7.486397, 7.524963, 7.563734, 7.602714, 7.641903, 7.681304, 7.720918, 7.760747, 7.800794, 7.841059, 7.881546, 7.922255, 7.963189, 8.004350, 8.045739, 8.087360, 8.129213, 8.171302, 8.213628, 8.256193, 8.298999, 8.342049, 8.385345, 8.428890, 8.472684, 8.516732, 8.561034, 8.605594, 8.650414, 8.695497, 8.740844, 8.786458, 8.832342, 8.878499, 8.924930, 8.971640, 9.018629, 9.065902, 9.113461, 9.161308, 9.209446, 9.257879, 9.306609, 9.355639, 9.404972, 9.454611, 9.504560, 9.554821, 9.605397, 9.656292, 9.707509, 9.759051, 9.810922, 9.863125, 9.915663, 9.968541, 10.021761, 10.075327, 10.129242, 10.183511, 10.238138, 10.293126, 10.348478, 10.404200, 10.460295, 10.516766, 10.573619, 10.630857, 10.688485, 10.746507, 10.804928, 10.863751, 10.922982, 10.982625, 11.042685, 11.103166, 11.164074, 11.225413, 11.287189, 11.349407, 11.412071, 11.475188, 11.538762, 11.602799, 11.667304, 11.732284, 11.797744, 11.863690, 11.930128, 11.997064, 12.064504, 12.132455, 12.200922, 12.269914, 12.339435, 12.409494, 12.480096, 12.551250, 12.622962, 12.695240, 12.768091, 12.841522, 12.915543, 12.990159, 13.065381, 13.141215, 13.217670, 13.294756, 13.372480, 13.450851, 13.529880, 13.609574, 13.689945, 13.771001, 13.852752, 13.935209, 14.018381, 14.102280, 14.186917, 14.272302, 14.358448, 14.445364, 14.533064, 14.621560, 14.710863, 14.800987, 14.891945, 14.983749, 15.076415, 15.169955, 15.264384, 15.359717, 15.455968, 15.553154, 15.651289, 15.750391, 15.850475, 15.951559, 16.053661, 16.156798, 16.260989, 16.366253, 16.472609, 16.580077, 16.688679, 16.798434, 16.909365, 17.021495, 17.134845, 17.249441, 17.365306, 17.482466, 17.600946, 17.720773, 17.841975, 17.964580, 18.088618, 18.214118, 18.341112, 18.469631, 18.599711, 18.731384, 18.864686, 18.999655, 19.136328, 19.274745, 19.414946, 19.556974, 19.700873, 19.846689, 19.994468, 20.144260, 20.296115, 20.450087, 20.606231, 20.764604, 20.925266, 21.088278, 21.253707, 21.421618, 21.592084, 21.765177, 21.940974, 22.119557, 22.301010, 22.485420, 22.672882, 22.863491, 23.057350, 23.254567, 23.455255, 23.659532, 23.867524, 24.079364, 24.295192, 24.515156, 24.739412, 24.968128, 25.201479, 25.439655, 25.682855, 25.931293, 26.185196, 26.444810, 26.710396, 26.982235, 27.260631, 27.545908, 27.838422, 28.138553, 28.446718, 28.763369, 29.089000, 29.424154, 29.769426, 30.125473, 30.493024, 30.872890, 31.265974, 31.673293, 32.095997, 32.535388, 32.992958, 33.470424, 33.969784, 34.493376, 35.043972, 35.624899, 36.240199, 36.894871, 37.595217, 38.349366, 39.168111, 40.066313, 41.065417, 42.198418, 43.520998, 45.142004, 47.343203, 53.102988
## SMA
## 1 1.386294361, 1.609437912, 1.791759469, 1.791759469, 1.945910149, 1.945910149, 2.197224577, 2.197224577, 2.302585093, 2.302585093, 2.302585093, 2.302585093, 2.397895273, 2.397895273, 2.484906650, 2.564949357, 2.564949357, 2.564949357, 2.564949357, 2.564949357, 2.639057330, 2.639057330, 2.639057330, 2.639057330, 2.639057330, 2.708050201, 2.708050201, 2.708050201, 2.708050201, 2.708050201, 2.772588722, 2.772588722, 2.772588722, 2.772588722, 2.772588722, 2.833213344, 2.833213344, 2.833213344, 2.833213344, 2.890371758, 2.890371758, 2.890371758, 2.890371758, 2.944438979, 2.944438979, 2.944438979, 2.944438979, 2.995732274, 2.995732274, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.044522438, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.091042453, 3.135494216, 3.135494216, 3.135494216, 3.178053830, 3.178053830, 3.178053830, 3.218875825, 3.218875825, 3.218875825, 3.218875825, 3.258096538, 3.258096538, 3.295836866, 3.295836866, 3.295836866, 3.295836866, 3.332204510, 3.332204510, 3.332204510, 3.367295830, 3.401197382, 3.401197382, 3.433987204, 3.433987204, 3.526360525, 3.555348061, 3.555348061, 3.555348061, 3.583518938, 3.583518938, 3.583518938, 3.610917913, 3.610917913, 3.610917913, 3.610917913, 3.637586160, 3.637586160, 3.663561646, 3.663561646, 3.713572067, 3.713572067, 3.713572067, 3.713572067, 3.737669618, 3.737669618, 3.737669618, 3.737669618, 3.737669618, 3.761200116, 3.784189634, 3.784189634, 3.806662490, 3.806662490, 3.828641396, 3.850147602, 3.850147602, 3.871201011, 3.871201011, 3.891820298, 3.912023005, 3.912023005, 3.912023005, 3.912023005, 3.912023005, 3.931825633, 3.931825633, 3.951243719, 3.988984047, 3.988984047, 3.988984047, 3.988984047, 4.007333185, 4.007333185, 4.007333185, 4.025351691, 4.025351691, -0.895304167, -0.473648276, -0.246924949, -0.413563898, -0.061746450, -0.311301282, -0.016314700, -0.103238229, -0.154283264, -0.141897055, -0.141897055, -0.075948861, -0.383302283, -0.554140835, 0.017057900, -0.257889186, -0.235848272, -0.190222134, -0.311301282, -0.031991051, -0.047112430, -0.463647609, -0.178429054, -0.201848221, -0.075948861, -0.332136508, -0.116398476, -0.246924949, -0.213320253, -0.178429054, -0.103238229, 0.000000000, -0.089766292, -0.383302283, -0.166454709, 0.321750554, -0.213320253, -0.047112430, -0.154283264, -0.141897055, 0.017057900, -0.089766292, -0.224650010, 0.221583133, -0.075948861, -0.190222134, 0.179853500, -0.178429054, -0.342464683, 0.120392634, -0.166454709, 0.096237148, -0.352740374, -0.047112430, 0.321750554, -0.075948861, -0.129276257, -0.047112430, -0.332136508, 0.017057900, 0.321750554, 0.179853500, -0.268749461, 0.321750554, 0.321750554, 0.221583133, 0.321750554, -0.116398476, 0.000000000, 0.017057900, -0.129276257, -0.075948861, 0.147667544, 0.321750554, 0.321750554, 0.221583133, 0.053987227, 0.120392634, 0.034994002, -0.089766292, 0.147667544, 0.321750554, 0.120392634, 0.321750554, 0.074283491, 0.179853500, 0.321750554, 0.034994002, 0.120392634, 0.221583133, 0.147667544, 0.017057900, 0.221583133, 0.074283491, 0.179853500, -0.031991051, 0.074283491, 0.034994002, 0.179853500, 0.053987227, 0.179853500, 0.321750554, 0.321750554, 0.179853500, 0.321750554, 0.179853500, -0.031991051, 0.321750554, 0.074283491, 0.221583133, 0.179853500, 0.074283491, -0.031991051, 0.120392634, -0.047112430, 0.096237148, 0.096237148, 0.120392634, 0.053987227, 0.096237148, 0.321750554, 0.321750554, 0.321750554, 0.179853500, 0.321750554, 0.321750554, 0.321750554, 0.034994002, 0.321750554, 0.147667544, 0.221583133, 0.179853500, 0.321750554, 0.147667544, 0.034994002, 0.321750554, 0.179853500, 0.848817889, 1.930943814, 2.512800241, 2.085142686, 2.988037180, 2.347586614, 3.104631955, 2.881553835, 2.750553280, 2.782340901, 2.782340901, 2.951588508, 2.162805253, 1.724369955, 3.190278467, 2.484661929, 2.541227115, 2.658320765, 2.347586614, 3.064400604, 3.025593520, 1.956609247, 2.688586196, 2.628483898, 2.951588508, 2.294115672, 2.847779742, 2.512800241, 2.599042396, 2.688586196, 2.881553835, 3.146501547, 2.916127838, 2.162805253, 2.719316822, 3.972233202, 2.599042396, 3.025593520, 2.750553280, 2.782340901, 3.190278467, 2.916127838, 2.569966024, 3.715166324, 2.951588508, 2.658320765, 3.608072556, 2.688586196, 2.267609729, 3.455473846, 2.719316822, 3.393481883, 2.241238484, 3.025593520, 3.972233202, 2.951588508, 2.814730564, 3.025593520, 2.294115672, 3.190278467, 3.972233202, 3.608072556, 2.456790422, 3.972233202, 3.972233202, 3.715166324, 3.972233202, 2.847779742, 3.146501547, 3.190278467, 2.814730564, 2.951588508, 3.525471415, 3.972233202, 3.972233202, 3.715166324, 3.285052862, 3.455473846, 3.236309179, 2.916127838, 3.525471415, 3.972233202, 3.455473846, 3.972233202, 3.337140628, 3.608072556, 3.972233202, 3.236309179, 3.455473846, 3.715166324, 3.525471415, 3.190278467, 3.715166324, 3.337140628, 3.608072556, 3.064400604, 3.337140628, 3.236309179, 3.608072556, 3.285052862, 3.608072556, 3.972233202, 3.972233202, 3.608072556, 3.972233202, 3.608072556, 3.064400604, 3.972233202, 3.337140628, 3.715166324, 3.608072556, 3.337140628, 3.064400604, 3.455473846, 3.025593520, 3.393481883, 3.393481883, 3.455473846, 3.285052862, 3.393481883, 3.972233202, 3.972233202, 3.972233202, 3.608072556, 3.972233202, 3.972233202, 3.972233202, 3.236309179, 3.972233202, 3.525471415, 3.715166324, 3.608072556, 3.972233202, 3.525471415, 3.236309179, 3.972233202, 3.608072556, 0.537476472, -0.321505902, -0.721040772, -0.293383216, -1.042127031, -0.401676465, -0.907407377, -0.684329258, -0.447968187, -0.479755808, -0.479755808, -0.649003415, 0.235090020, 0.673525318, -0.705371817, 0.080287429, 0.023722242, -0.093371408, 0.217362743, -0.499451247, -0.386536191, 0.682448083, -0.049528866, 0.010573431, -0.312531178, 0.413934529, -0.139729541, 0.195249960, 0.109007805, 0.019464006, -0.108965113, -0.373912825, -0.143539116, 0.609783469, 0.053271901, -1.139019858, 0.234170948, -0.192380176, 0.082660064, 0.108030857, -0.299906709, -0.025756080, 0.320405734, -0.770727345, -0.007149529, 0.286118214, -0.663633577, 0.307146078, 0.728122544, -0.410951409, 0.325205616, -0.348959445, 0.803283954, 0.018928917, -0.927710764, 0.139453945, 0.276311890, 0.065448933, 0.796926781, -0.099236014, -0.881190748, -0.472578340, 0.678703794, -0.836738986, -0.794179371, -0.537112494, -0.794179371, 0.371096083, 0.072374278, 0.028597358, 0.404145261, 0.306508030, -0.267374877, -0.676396336, -0.676396336, -0.419329458, 0.010784004, -0.123269336, 0.095895331, 0.416076672, -0.158175585, -0.571035820, -0.054276465, -0.538245997, 0.096846576, -0.081712031, -0.416885140, 0.319038883, 0.099874215, -0.131647386, 0.058047523, 0.393240471, -0.104248411, 0.273777284, 0.002845357, 0.546517308, 0.300445531, 0.401276981, 0.055489090, 0.378508784, 0.105499511, -0.258661135, -0.258661135, 0.105499511, -0.234563583, 0.129597062, 0.673269014, -0.234563583, 0.400528990, 0.046033792, 0.176117078, 0.447049005, 0.742261885, 0.351188644, 0.803047876, 0.456665719, 0.456665719, 0.415727165, 0.586148149, 0.498338416, -0.060210196, -0.060210196, -0.060210196, 0.303950450, -0.060210196, -0.040407569, -0.040407569, 0.714934540, 0.016750845, 0.463512631, 0.273817723, 0.380911491, 0.035099984, 0.481861770, 0.771024006, 0.053118489, 0.417279135, -0.911389297, 0.393880180, 1.158058163, 0.730400608, 1.787445782, 1.146995216, 2.155354985, 1.932276865, 1.906636826, 1.938424447, 1.938424447, 2.107672054, 1.414198979, 0.975763681, 2.528683570, 1.903109739, 1.959674925, 2.076768576, 1.766034424, 2.482848415, 2.518149303, 1.449165029, 2.181141978, 2.121039681, 2.444144290, 1.855664326, 2.409328396, 2.074348895, 2.160591050, 2.250134850, 2.507641010, 2.772588722, 2.542215013, 1.788892428, 2.345403997, 3.658944999, 2.285754193, 2.712305317, 2.437265077, 2.526211112, 2.934148678, 2.659998049, 2.313836235, 3.513103756, 2.749525940, 2.456258197, 3.406009988, 2.537816922, 2.116840456, 3.353494737, 2.617337712, 3.291502773, 2.139259375, 2.923614411, 3.870254092, 2.896129414, 2.759271470, 2.970134427, 2.238656578, 3.134819373, 3.916774108, 3.597065225, 2.445783091, 3.961225870, 4.003785485, 3.746718607, 4.003785485, 2.920154020, 3.218875825, 3.262652745, 2.887104841, 3.063183499, 3.637066406, 4.121568521, 4.121568521, 3.864501643, 3.434388181, 3.641176809, 3.422012142, 3.101830801, 3.746265698, 4.226929036, 3.710169681, 4.259718859, 3.624626286, 3.987931533, 4.381079716, 3.645155693, 3.864320361, 4.152183715, 3.962488807, 3.627295859, 4.179582690, 3.801556994, 4.072488921, 3.528816970, 3.828225241, 3.727393792, 4.125132655, 3.802112961, 4.175143075, 4.539303721, 4.539303721, 4.175143075, 4.563401273, 4.199240627, 3.655568675, 4.563401273, 3.928308700, 4.329864893, 4.245760643, 3.974828715, 3.724561547, 4.115634789, 3.707733370, 4.097127937, 4.097127937, 4.180173310, 4.009752326, 4.138800634, 4.737754660, 4.737754660, 4.737754660, 4.373594014, 4.737754660, 4.757557287, 4.757557287, 4.041051350, 4.814715701, 4.367953915, 4.557648823, 4.450555055, 4.833064840, 4.386303054, 4.097140817, 4.851083345, 4.486922699
# Revised alcc.rev
#
# remove.leverage = "none"
alcc.rev(data_2, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "none")## n target cstv lower_cstv upper_cstv confidence pvalue r
## 1 137 90 23.25457 21.57156 25.06888 95 7.314913e-23 0.7164928
## remove.leverage
## 1 none
# plot
alcc_plot.rev(data_2, stv = STV, ry = RY, target = 90,
confidence = 95, remove.leverage = "none")
# remove.leverage = "cstv100"
alcc.rev(data_2, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "cstv100")## n target cstv lower_cstv upper_cstv confidence pvalue r
## 1 128 90 22.74894 21.07941 24.5507 95 1.722875e-20 0.7044885
## remove.leverage
## 1 cstv100
# plot
alcc_plot.rev(data_2, stv = STV, ry = RY, target = 90,
confidence = 95, remove.leverage = "cstv100")
# remove.leverage = "cstv90_2x"
alcc.rev(data_2, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "cstv90_2x")## n target cstv lower_cstv upper_cstv confidence pvalue r
## 1 115 90 21.98504 20.32021 23.78626 95 5.322914e-17 0.6813117
## remove.leverage
## 1 cstv90_2x
# plot
alcc_plot.rev(data_2, stv = STV, ry = RY, target = 90,
confidence = 95, remove.leverage = "cstv90_2x")
# Austin's original alcc() fails with data_2
# alcc(data_2, soil_test = STV, ry = RY, sufficiency = 90, confidence = 95, summary = T, remove2x = FALSE, sma = TRUE)Data_3: Austin’s alcc() does not produce the same results than the
modALCC() or the Spreadsheet version. Again, this is related to the fact
that Austin’s alcc() always remove points STV > CSTV100 when present,
so it produces different results than Adrian’s modALCC().
Using the Adrian’s revised alcc.rev() functions, Austin’s alcc() is equivalent to use the alcc.rev(remove.leverage = ‘cstv100’).
# Example 3 dataframe. Imported from xlsx file
data_3 = readxl::read_xlsx(path ="data_3.xlsx", sheet = 1)
# Adrian's modALCC()
modALCC(data = data_3, RY = RY, STV = STV, target=90, confidence = 0.95)## Warning: 3 STV points exceeded the CSTV for 100%.
## Risk of leverage. You may consider a sensitivity analysis by removing extreme points,
## re-run the modALCC(), and check results.
## Warning: 3 STV points exceeded two-times (2x)
## the CSTV for 90%. Risk of leverage. You may consider a sensitivity analysis by
## removing extreme points, re-run the modALCC(), and check results.
## n r target CSTV LL UL confidence p_value
## 1 107 0.3735166 90 21.76416 19.35018 24.47929 0.95 7.410056e-05
## CSTV90 n.90x2 CSTV100 n.100
## 1 21.76416 3 38.7896 3
## Curve
## 1 25.000000, 25.200000, 25.400000, 25.600000, 25.800000, 26.000000, 26.200000, 26.400000, 26.600000, 26.800000, 27.000000, 27.200000, 27.400000, 27.600000, 27.800000, 28.000000, 28.200000, 28.400000, 28.600000, 28.800000, 29.000000, 29.200000, 29.400000, 29.600000, 29.800000, 30.000000, 30.200000, 30.400000, 30.600000, 30.800000, 31.000000, 31.200000, 31.400000, 31.600000, 31.800000, 32.000000, 32.200000, 32.400000, 32.600000, 32.800000, 33.000000, 33.200000, 33.400000, 33.600000, 33.800000, 34.000000, 34.200000, 34.400000, 34.600000, 34.800000, 35.000000, 35.200000, 35.400000, 35.600000, 35.800000, 36.000000, 36.200000, 36.400000, 36.600000, 36.800000, 37.000000, 37.200000, 37.400000, 37.600000, 37.800000, 38.000000, 38.200000, 38.400000, 38.600000, 38.800000, 39.000000, 39.200000, 39.400000, 39.600000, 39.800000, 40.000000, 40.200000, 40.400000, 40.600000, 40.800000, 41.000000, 41.200000, 41.400000, 41.600000, 41.800000, 42.000000, 42.200000, 42.400000, 42.600000, 42.800000, 43.000000, 43.200000, 43.400000, 43.600000, 43.800000, 44.000000, 44.200000, 44.400000, 44.600000, 44.800000, 45.000000, 45.200000, 45.400000, 45.600000, 45.800000, 46.000000, 46.200000, 46.400000, 46.600000, 46.800000, 47.000000, 47.200000, 47.400000, 47.600000, 47.800000, 48.000000, 48.200000, 48.400000, 48.600000, 48.800000, 49.000000, 49.200000, 49.400000, 49.600000, 49.800000, 50.000000, 50.200000, 50.400000, 50.600000, 50.800000, 51.000000, 51.200000, 51.400000, 51.600000, 51.800000, 52.000000, 52.200000, 52.400000, 52.600000, 52.800000, 53.000000, 53.200000, 53.400000, 53.600000, 53.800000, 54.000000, 54.200000, 54.400000, 54.600000, 54.800000, 55.000000, 55.200000, 55.400000, 55.600000, 55.800000, 56.000000, 56.200000, 56.400000, 56.600000, 56.800000, 57.000000, 57.200000, 57.400000, 57.600000, 57.800000, 58.000000, 58.200000, 58.400000, 58.600000, 58.800000, 59.000000, 59.200000, 59.400000, 59.600000, 59.800000, 60.000000, 60.200000, 60.400000, 60.600000, 60.800000, 61.000000, 61.200000, 61.400000, 61.600000, 61.800000, 62.000000, 62.200000, 62.400000, 62.600000, 62.800000, 63.000000, 63.200000, 63.400000, 63.600000, 63.800000, 64.000000, 64.200000, 64.400000, 64.600000, 64.800000, 65.000000, 65.200000, 65.400000, 65.600000, 65.800000, 66.000000, 66.200000, 66.400000, 66.600000, 66.800000, 67.000000, 67.200000, 67.400000, 67.600000, 67.800000, 68.000000, 68.200000, 68.400000, 68.600000, 68.800000, 69.000000, 69.200000, 69.400000, 69.600000, 69.800000, 70.000000, 70.200000, 70.400000, 70.600000, 70.800000, 71.000000, 71.200000, 71.400000, 71.600000, 71.800000, 72.000000, 72.200000, 72.400000, 72.600000, 72.800000, 73.000000, 73.200000, 73.400000, 73.600000, 73.800000, 74.000000, 74.200000, 74.400000, 74.600000, 74.800000, 75.000000, 75.200000, 75.400000, 75.600000, 75.800000, 76.000000, 76.200000, 76.400000, 76.600000, 76.800000, 77.000000, 77.200000, 77.400000, 77.600000, 77.800000, 78.000000, 78.200000, 78.400000, 78.600000, 78.800000, 79.000000, 79.200000, 79.400000, 79.600000, 79.800000, 80.000000, 80.200000, 80.400000, 80.600000, 80.800000, 81.000000, 81.200000, 81.400000, 81.600000, 81.800000, 82.000000, 82.200000, 82.400000, 82.600000, 82.800000, 83.000000, 83.200000, 83.400000, 83.600000, 83.800000, 84.000000, 84.200000, 84.400000, 84.600000, 84.800000, 85.000000, 85.200000, 85.400000, 85.600000, 85.800000, 86.000000, 86.200000, 86.400000, 86.600000, 86.800000, 87.000000, 87.200000, 87.400000, 87.600000, 87.800000, 88.000000, 88.200000, 88.400000, 88.600000, 88.800000, 89.000000, 89.200000, 89.400000, 89.600000, 89.800000, 90.000000, 90.200000, 90.400000, 90.600000, 90.800000, 91.000000, 91.200000, 91.400000, 91.600000, 91.800000, 92.000000, 92.200000, 92.400000, 92.600000, 92.800000, 93.000000, 93.200000, 93.400000, 93.600000, 93.800000, 94.000000, 94.200000, 94.400000, 94.600000, 94.800000, 95.000000, 95.200000, 95.400000, 95.600000, 95.800000, 96.000000, 96.200000, 96.400000, 96.600000, 96.800000, 97.000000, 97.200000, 97.400000, 97.600000, 97.800000, 98.000000, 98.200000, 98.400000, 98.600000, 98.800000, 99.000000, 99.200000, 99.400000, 99.600000, 99.800000, 100.000000, 5.913921, 5.938470, 5.963055, 5.987678, 6.012339, 6.037039, 6.061779, 6.086559, 6.111380, 6.136242, 6.161146, 6.186093, 6.211083, 6.236117, 6.261195, 6.286319, 6.311488, 6.336704, 6.361966, 6.387276, 6.412635, 6.438041, 6.463498, 6.489003, 6.514560, 6.540167, 6.565827, 6.591538, 6.617302, 6.643120, 6.668991, 6.694917, 6.720899, 6.746936, 6.773029, 6.799179, 6.825387, 6.851653, 6.877977, 6.904361, 6.930804, 6.957308, 6.983873, 7.010500, 7.037188, 7.063940, 7.090755, 7.117633, 7.144577, 7.171585, 7.198659, 7.225800, 7.253007, 7.280282, 7.307625, 7.335037, 7.362518, 7.390069, 7.417691, 7.445384, 7.473148, 7.500985, 7.528895, 7.556879, 7.584937, 7.613070, 7.641278, 7.669563, 7.697925, 7.726364, 7.754881, 7.783476, 7.812151, 7.840907, 7.869743, 7.898660, 7.927659, 7.956741, 7.985907, 8.015156, 8.044490, 8.073910, 8.103416, 8.133008, 8.162688, 8.192457, 8.222314, 8.252260, 8.282298, 8.312426, 8.342646, 8.372958, 8.403364, 8.433864, 8.464458, 8.495148, 8.525934, 8.556817, 8.587798, 8.618878, 8.650057, 8.681336, 8.712716, 8.744197, 8.775781, 8.807469, 8.839260, 8.871157, 8.903160, 8.935269, 8.967485, 8.999810, 9.032244, 9.064789, 9.097444, 9.130211, 9.163091, 9.196084, 9.229192, 9.262416, 9.295756, 9.329213, 9.362788, 9.396483, 9.430298, 9.464234, 9.498292, 9.532473, 9.566779, 9.601209, 9.635766, 9.670449, 9.705261, 9.740203, 9.775274, 9.810477, 9.845812, 9.881281, 9.916885, 9.952624, 9.988500, 10.024514, 10.060667, 10.096961, 10.133396, 10.169974, 10.206695, 10.243562, 10.280575, 10.317736, 10.355045, 10.392504, 10.430115, 10.467879, 10.505796, 10.543869, 10.582098, 10.620485, 10.659032, 10.697739, 10.736609, 10.775642, 10.814840, 10.854205, 10.893737, 10.933439, 10.973312, 11.013357, 11.053576, 11.093971, 11.134543, 11.175294, 11.216225, 11.257338, 11.298635, 11.340117, 11.381786, 11.423644, 11.465692, 11.507933, 11.550368, 11.592999, 11.635828, 11.678856, 11.722086, 11.765520, 11.809159, 11.853005, 11.897061, 11.941328, 11.985809, 12.030505, 12.075419, 12.120553, 12.165909, 12.211490, 12.257296, 12.303332, 12.349599, 12.396099, 12.442835, 12.489809, 12.537024, 12.584482, 12.632185, 12.680137, 12.728340, 12.776796, 12.825509, 12.874480, 12.923713, 12.973210, 13.022975, 13.073010, 13.123318, 13.173903, 13.224766, 13.275912, 13.327344, 13.379064, 13.431076, 13.483383, 13.535988, 13.588896, 13.642110, 13.695632, 13.749467, 13.803618, 13.858089, 13.912884, 13.968007, 14.023461, 14.079251, 14.135381, 14.191855, 14.248676, 14.305850, 14.363381, 14.421274, 14.479531, 14.538160, 14.597164, 14.656547, 14.716316, 14.776475, 14.837028, 14.897983, 14.959342, 15.021113, 15.083301, 15.145911, 15.208949, 15.272421, 15.336333, 15.400691, 15.465502, 15.530772, 15.596507, 15.662715, 15.729402, 15.796574, 15.864241, 15.932407, 16.001082, 16.070273, 16.139988, 16.210234, 16.281021, 16.352355, 16.424248, 16.496706, 16.569739, 16.643357, 16.717568, 16.792384, 16.867813, 16.943866, 17.020554, 17.097888, 17.175878, 17.254537, 17.333875, 17.413906, 17.494641, 17.576093, 17.658275, 17.741202, 17.824886, 17.909343, 17.994586, 18.080632, 18.167495, 18.255192, 18.343740, 18.433156, 18.523457, 18.614662, 18.706790, 18.799859, 18.893892, 18.988907, 19.084928, 19.181976, 19.280074, 19.379246, 19.479518, 19.580915, 19.683463, 19.787191, 19.892127, 19.998301, 20.105744, 20.214490, 20.324570, 20.436021, 20.548879, 20.663183, 20.778971, 20.896287, 21.015172, 21.135673, 21.257837, 21.381715, 21.507357, 21.634821, 21.764162, 21.895441, 22.028724, 22.164075, 22.301567, 22.441275, 22.583277, 22.727657, 22.874504, 23.023912, 23.175981, 23.330817, 23.488535, 23.649255, 23.813106, 23.980228, 24.150769, 24.324889, 24.502761, 24.684571, 24.870521, 25.060830, 25.255736, 25.455500, 25.660405, 25.870765, 26.086925, 26.309266, 26.538212, 26.774237, 27.017872, 27.269717, 27.530450, 27.800851, 28.081811, 28.374371, 28.679745, 28.999371, 29.334975, 29.688650, 30.062983, 30.461232, 30.887593, 31.347636, 31.849016, 32.402775, 33.025879, 33.746927, 34.621766, 35.794793, 38.789595
## SMA
## 1 1.6094379124, 1.7917594692, 1.7917594692, 1.9459101491, 1.9459101491, 2.0794415417, 2.0794415417, 2.1972245773, 2.1972245773, 2.1972245773, 2.1972245773, 2.1972245773, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3025850930, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.3978952728, 2.4849066498, 2.4849066498, 2.4849066498, 2.5649493575, 2.5649493575, 2.5649493575, 2.5649493575, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.6390573296, 2.7080502011, 2.7080502011, 2.7080502011, 2.7080502011, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.7725887222, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8332133441, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.8903717579, 2.9444389792, 2.9444389792, 2.9444389792, 2.9444389792, 2.9444389792, 2.9957322736, 2.9957322736, 2.9957322736, 3.0445224377, 3.0445224377, 3.0910424534, 3.0910424534, 3.1354942159, 3.1780538303, 3.1780538303, 3.1780538303, 3.2188758249, 3.2188758249, 3.2580965380, 3.2580965380, 3.2580965380, 3.2580965380, 3.2958368660, 3.2958368660, 3.3322045102, 3.3322045102, 3.3322045102, 3.3672958300, 3.4011973817, 3.4339872045, 3.4339872045, 3.4339872045, 3.4965075615, 3.4965075615, 3.4965075615, 3.5553480615, 3.8918202981, 4.0073331852, 4.1896547420, -0.4035026678, -0.6055446636, -0.3934169016, -0.0897662917, 0.3217505544, -0.5439929355, -0.5439929355, -0.3424646835, 0.0539872272, -0.2687494608, -0.1902221337, -0.5137313196, -0.2901891602, -0.1418970546, -0.3527403738, -0.2018482212, -0.5643265694, -0.2133202528, -0.2469249490, -0.5439929355, -0.1032382286, -0.3321365075, -0.1418970546, -0.0319910515, -0.3424646835, -0.3007828654, -0.3113012820, -0.0163147004, -0.7254469968, -0.4135638984, -0.1418970546, -0.1542832637, -0.0897662917, -0.1664547090, -0.1292762574, 0.3217505544, 0.1476675438, -0.4636476090, -0.3007828654, 0.0349940022, -0.2687494608, 0.3217505544, -0.1784290543, 0.1476675438, -0.1784290543, -0.3934169016, -0.0617464495, -0.2795136623, 0.1476675438, -0.3833022825, -0.5745548442, -0.4636476090, -0.2133202528, -0.1418970546, 0.0962371485, -0.0471124298, -0.1542832637, -0.3007828654, 0.0962371485, 0.3217505544, -0.2246500097, 0.0742834912, -0.4736482758, -0.0163147004, -0.0759488607, -0.0897662917, -0.2133202528, -0.3629686486, -0.6803702690, 0.3217505544, -0.4736482758, -0.1542832637, 0.0349940022, 0.1203926336, -0.0759488607, -0.2469249490, -0.3217505544, 0.0962371485, -0.3113012820, 0.0962371485, -0.0617464495, 0.3217505544, 0.3217505544, -0.3217505544, -0.2246500097, -0.4636476090, -0.0319910515, -0.3629686486, 0.0349940022, -0.4035026678, 0.1203926336, -0.1664547090, -0.0319910515, 0.1798534998, -0.2133202528, -0.2578891860, 0.3217505544, -0.1902221337, -0.1418970546, -0.0617464495, 0.3217505544, 0.3217505544, -0.3629686486, -0.5643265694, 0.3217505544, 0.1798534998, 0.3217505544, 2.3555445368, 1.9926624244, 2.3736593061, 2.9190378763, 3.6581520481, 2.1032138028, 2.1032138028, 2.4651731940, 3.1772296468, 2.5975710929, 2.7386118812, 2.1575658649, 2.5590638341, 2.8254072363, 2.4467173073, 2.7177305827, 2.0666931181, 2.6971259800, 2.6367695027, 2.1032138028, 2.8948412982, 2.4837233488, 2.8254072363, 3.0228064077, 2.4651731940, 2.5400367695, 2.5211449286, 3.0509622740, 1.7773091174, 2.3374738352, 2.8254072363, 2.8031607043, 2.9190378763, 2.7812999037, 2.8480751055, 3.6581520481, 3.3454863056, 2.2475198501, 2.5400367695, 3.1431164338, 2.5975710929, 3.6581520481, 2.7597931090, 3.3454863056, 2.7597931090, 2.3736593061, 2.9693635497, 2.5782378045, 3.3454863056, 2.3918258973, 2.0483223929, 2.2475198501, 2.6971259800, 2.8254072363, 3.2531135768, 2.9956473130, 2.8031607043, 2.5400367695, 3.2531135768, 3.6581520481, 2.6767769129, 3.2136832124, 2.2295579255, 3.0509622740, 2.9438549868, 2.9190378763, 2.6971259800, 2.4283465821, 1.8582701974, 3.6581520481, 2.2295579255, 2.8031607043, 3.1431164338, 3.2964985841, 2.9438549868, 2.6367695027, 2.5023772757, 3.2531135768, 2.5211449286, 3.2531135768, 2.9693635497, 3.6581520481, 3.6581520481, 2.5023772757, 2.6767769129, 2.2475198501, 3.0228064077, 2.4283465821, 3.1431164338, 2.3555445368, 3.2964985841, 2.7812999037, 3.0228064077, 3.4032946224, 2.6971259800, 2.6170769360, 3.6581520481, 2.7386118812, 2.8254072363, 2.9693635497, 3.6581520481, 3.6581520481, 2.4283465821, 2.0666931181, 3.6581520481, 3.4032946224, 3.6581520481, -0.7461066244, -0.2009029552, -0.5818998369, -0.9731277272, -1.7122418990, -0.0237722611, -0.0237722611, -0.2679486167, -0.9800050694, -0.4003465156, -0.5413873038, 0.0396587124, -0.2564787411, -0.5228221433, -0.1441322143, -0.4151454897, 0.2358919749, -0.3945408870, -0.3341844097, 0.2946814700, -0.4969460254, -0.0858280760, -0.4275119635, -0.6249111349, -0.0672779212, -0.1421414967, -0.0362382788, -0.5660556242, 0.7075975324, 0.2274755222, -0.2604578788, -0.2382113469, -0.3540885188, -0.1422425741, -0.2090177759, -1.0190947185, -0.7064289759, 0.3915374795, 0.0990205601, -0.4350662327, 0.1104791082, -0.9501018470, -0.0517429079, -0.5728975833, 0.0127956132, 0.3989294162, -0.1967748275, 0.1943509178, -0.5728975833, 0.3807628249, 0.7242663294, 0.5856934940, 0.1360873641, 0.0078061078, -0.4199002327, -0.1624339689, 0.0300526397, 0.2931765745, -0.4199002327, -0.7677802902, 0.2135948450, -0.3233114545, 0.6608138324, -0.1605905161, -0.0534832289, -0.0286661184, 0.1932457779, 0.4620251758, 1.0861687817, -0.7137130689, 0.7148810537, 0.1412782748, -0.1986774546, -0.3007663106, 0.0518772868, 0.3589627709, 0.5421451620, -0.2085911391, 0.5698975248, -0.1620711234, 0.1661306662, -0.4800982177, -0.4800982177, 0.6756765546, 0.5420989120, 0.9713559748, 0.2352901303, 0.8297499560, 0.1149801042, 0.9025520012, -0.0006617181, 0.5145369623, 0.3093981024, -0.0710901123, 0.6350785302, 0.7502188940, 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# Austin's alcc()
alcc(data_3, soil_test = STV, ry = RY, sufficiency = 90,
confidence = 95, summary = T, remove2x = FALSE, sma = TRUE)## # A tibble: 1 x 9
## model sufficiency cstv lower_cl upper_cl confidence pvalue pearson remove2x
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 ALCC-~ 90 21.1 18.7 23.7 95 0.00136 0.291 TRUE
# Fixed alcc.rev(remove.leverage = "none")
alcc.rev(data_3, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "none")## # A tibble: 1 x 9
## n target cstv lower_cstv upper_cstv confidence pvalue r
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 107 90 21.8 19.4 24.5 95 0.0000741 0.374
## # ... with 1 more variable: remove.leverage <chr>
# Fixed alcc.rev(remove.leverage = "cstv100")
alcc.rev(data_3, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "cstv100")## # A tibble: 1 x 9
## n target cstv lower_cstv upper_cstv confidence pvalue r
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 104 90 21.1 18.7 23.7 95 0.00272 0.291
## # ... with 1 more variable: remove.leverage <chr>
# Fixed alcc.rev(remove.leverage = "cstv90_2x")
alcc.rev(data_3, stv = STV, ry = RY, target = 90,
confidence = 95, summary = T, remove.leverage = "cstv90_2x")## # A tibble: 1 x 9
## n target cstv lower_cstv upper_cstv confidence pvalue r
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 104 90 21.1 18.7 23.7 95 0.00272 0.291
## # ... with 1 more variable: remove.leverage <chr>
# plot
alcc_plot.rev(data_3, stv = STV, ry = RY, target = 90,
confidence = 95, remove.leverage = "none")
alcc_plot.rev(data_3, stv = STV, ry = RY, target = 90,
confidence = 95, remove.leverage = "cstv100")