/
Griffing.R
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Griffing.R
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#' @name Griffing
#' @aliases Griffing
#' @title Diallel Analysis using Griffing Approach
#' @description \code{Griffing} is used for performing Diallel Analysis using Griffing's Approach.
#' @param y Numeric Response Vector
#' @param Rep Replicate as factor
#' @param Cross1 Cross 1 as factor
#' @param Cross2 Cross 2 as factor
#' @param data A \code{data.frame}
#' @param Method Method for Diallel Analysis using Griffing's approach.
#' It can take \strong{1}, \strong{2}, \strong{3}, or \strong{4}
#' as argument depending on the method being used.
#' \enumerate{
#' \item Method-I (Parents + \eqn{F_{1}}'s + reciprocals);
#' \item Method-II (Parents and one set of \eqn{F_{1}}'s);
#' \item Method-III (One set of \eqn{F_{1}}'s and reciprocals);
#' \item Method-IV (One set of \eqn{F_{1}}'s only).
#' }
#' @param Model Model for Diallel Analysis using Griffing's approach.
#' It can take \strong{1} or \strong{2} as arguments depending on the model being used.
#' \enumerate{
#' \item Fixed Effects Model;
#' \item Random Effects Model.
#' }
#' @details Diallel Analysis using Griffing's approach.
#' @return Means Means
#' @return ANOVA Analysis of Variance (ANOVA) table
#' @return Genetic.Components Genetic Components
#' @return Effects Effects of Crosses
#' @return StdErr Standard Errors of Crosses
#' @author Muhammad Yaseen (\email{myaseen208@@gmail.com})
#' @references \enumerate{
#' \item Griffing, B. (1956) Concept of General and Specific Combining Ability
#' in relation to Diallel Crossing Systems. \emph{Australian Journal of Biological Sciences},
#' \strong{9(4)}, 463--493.
#' \item Singh, R. K. and Chaudhary, B. D. (2004) \emph{Biometrical Methods in Quantitative Genetic Analysis}.
#' New Delhi: Kalyani.
#' }
#' @seealso
#' \code{\link{Hayman}}
#' , \code{\link{GriffingData1}}
#' , \code{\link{GriffingData2}}
#' , \code{\link{GriffingData3}}
#' , \code{\link{GriffingData4}}
#' @import ggplot2 stats
#' @export
#' @examples
#' #-------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 1 & Model 1
#' #-------------------------------------------------------------
#' Griffing1Data1 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData1
#' , Method = 1
#' , Model = 1
#' )
#' names(Griffing1Data1)
#' Griffing1Data1
#' Griffing1Data1Means <- Griffing1Data1$Means
#' Griffing1Data1ANOVA <- Griffing1Data1$ANOVA
#' Griffing1Data1Genetic.Components <- Griffing1Data1$Genetic.Components
#' Griffing1Data1Effects <- Griffing1Data1$Effects
#' Griffing1Data1StdErr <- as.matrix(Griffing1Data1$StdErr)
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 1 & Model 2
#' #--------------------------------------------------------------
#' Griffing2Data1 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData1
#' , Method = 1
#' , Model = 2
#' )
#' names(Griffing2Data1)
#' Griffing2Data1
#' Griffing2Data1Means <- Griffing2Data1$Means
#' Griffing2Data1ANOVA <- Griffing2Data1$ANOVA
#' Griffing2Data1Genetic.Components <- Griffing2Data1$Genetic.Components
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 2 & Model 1
#' #--------------------------------------------------------------
#' Griffing1Data2 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData2
#' , Method = 2
#' , Model = 1
#' )
#' names(Griffing1Data2)
#' Griffing1Data2
#' Griffing1Data2Means <- Griffing1Data2$Means
#' Griffing1Data2ANOVA <- Griffing1Data2$ANOVA
#' Griffing1Data2Genetic.Components <- Griffing1Data2$Genetic.Components
#' Griffing1Data2Effects <- Griffing1Data2$Effects
#' Griffing1Data2StdErr <- as.matrix(Griffing1Data2$StdErr)
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 2 & Model 2
#' #--------------------------------------------------------------
#' Griffing2Data2 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData2
#' , Method = 2
#' , Model = 2
#' )
#' names(Griffing2Data2)
#' Griffing2Data2
#' Griffing2Data2Means <- Griffing2Data2$Means
#' Griffing2Data2ANOVA <- Griffing2Data2$ANOVA
#' Griffing2Data2Genetic.Components <- Griffing2Data2$Genetic.Components
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 3 & Model 1
#' #--------------------------------------------------------------
#' Griffing1Data3 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData3
#' , Method = 3
#' , Model = 1
#' )
#' names(Griffing1Data3)
#' Griffing1Data3
#' Griffing1Data3Means <- Griffing1Data3$Means
#' Griffing1Data3ANOVA <- Griffing1Data3$ANOVA
#' Griffing1Data3Genetic.Components <- Griffing1Data3$Genetic.Components
#' Griffing1Data3Effects <- Griffing1Data3$Effects
#' Griffing1Data3StdErr <- as.matrix(Griffing1Data3$StdErr)
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 3 & Model 2
#' #--------------------------------------------------------------
#' Griffing2Data3 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData3
#' , Method = 3
#' , Model = 2
#' )
#' names(Griffing2Data3)
#' Griffing2Data3
#' Griffing2Data3Means <- Griffing2Data3$Means
#' Griffing2Data3ANOVA <- Griffing2Data3$ANOVA
#' Griffing2Data3Genetic.Components <- Griffing2Data3$Genetic.Components
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 4 & Model 1
#' #--------------------------------------------------------------
#' Griffing1Data4 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData4
#' , Method = 4
#' , Model = 1
#' )
#' names(Griffing1Data4)
#' Griffing1Data4
#' Griffing1Data4Means <- Griffing1Data4$Means
#' Griffing1Data4ANOVA <- Griffing1Data4$ANOVA
#' Griffing1Data4Genetic.Components <- Griffing1Data4$Genetic.Components
#' Griffing1Data4Effects <- Griffing1Data4$Effects
#' Griffing1Data4StdErr <- as.matrix(Griffing1Data4$StdErr)
#'
#'
#' #--------------------------------------------------------------
#' ## Diallel Analysis with Griffing's Aproach Method 4 & Model 2
#' #--------------------------------------------------------------
#' Griffing2Data4 <-
#' Griffing(
#' y = Yield
#' , Rep = Rep
#' , Cross1 = Cross1
#' , Cross2 = Cross2
#' , data = GriffingData4
#' , Method = 4
#' , Model = 2
#' )
#' names(Griffing2Data4)
#' Griffing2Data4
#' Griffing2Data4Means <- Griffing2Data4$Means
#' Griffing2Data4ANOVA <- Griffing2Data4$ANOVA
#' Griffing2Data4Genetic.Components <- Griffing2Data4$Genetic.Components
Griffing <-
function(y, Rep, Cross1, Cross2, data, Method, Model) {
if(Method > 4 | Model > 2) {
stop ("Either Method No. or Model No. is incorrect: \n Method=1, 2, 3, or 4 and Model=1, or 2:")
}
else if(Method==1 & Model==1)
{
#-----------------------------------------------------------------------------
# Method-I(Parents + F1's + reciprocals)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-I (Fixed Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
DataTotals <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
n <- nrow(DataTotals)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((colSums(Means)+rowSums(Means))^2))/(2*n)-(2*(sum(colSums(Means)))^2)/n^2)
SS.sca <- (sum(Means*(Means+t(Means)))/2-(sum((colSums(Means)+rowSums(Means))^2))/(2*n)+(sum(colSums(Means)))^2/n^2)
SS.reciprocals <- sum((Means-t(Means))^2)/4
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-1)/2
, n*(n-1)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, SS.reciprocals
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[-4]/MS[4], NA)
P.Value <- c(pf(F.Test[-4], df[-4], df[4], lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "reciprocals"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-MS[4])/(2*n)
sca.v <- (MS[2]-MS[4])
r.v <- (MS[3]-MS[4])/2
gca.v.to.sca.v <- gca.v/sca.v
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, r.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "Reciprocal", "gca/sca"))
#-----------------------------------------------------------------------------
# General Combining Ability (gca) Effects
#-----------------------------------------------------------------------------
G <- diag((colSums(Means)+rowSums(Means))/(2*n)-(sum(colSums(Means)))/n^2)
#-----------------------------------------------------------------------------
# Specific Combining Ability (sca) Effects
#-----------------------------------------------------------------------------
S <- matrix(NA, nrow=n, ncol=n, byrow=TRUE)
for(i in 1:n)
{
for(j in 1:n)
{
if (i >= j)
{
S[i, j] <- 0
}
else
{
S[i, j] <- (Means[i, j] + Means[j, i])/2-(rowSums(Means)[i] + colSums(Means)[i] + rowSums(Means)[j] + colSums(Means)[j])/(2*n) + (sum(colSums(Means)))/n^2
}
}
}
#-----------------------------------------------------------------------------
# Reciprocal Effects
#-----------------------------------------------------------------------------
R <- t(Means-t(Means))/2
R[upper.tri(R)] <- 0
Effects <- G + S + R
#-----------------------------------------------------------------------------
# Standard Errors
#-----------------------------------------------------------------------------
MSE <- Simple.ANOVA["Rep", "Mean Sq"]
SE.gi <- sqrt((n-1)/(2*n^2)*MSE/r)
SE.sii <- sqrt((n-1)^2/n^2*MSE/r)
SE.sij <- sqrt((n^2-2*n+2)/(2*n^2)*MSE/r)
SE.rij <- sqrt(1/2*MSE/r)
SE.gi.gj <- sqrt(1/n*MSE/r)
SE.sii.sji <- sqrt(2*(n-2)/n*MSE/r)
SE.sii.sij <- sqrt((3*n-2)/(2*n)*MSE/r)
SE.sii.sjk <- sqrt(3*(n-2)/(2*n)*MSE/r)
SE.sij.sik <- sqrt((n-1)/n*MSE/r)
SE.sij.skl <- sqrt((n-2)/n*MSE/r)
SE.rij.rkl <- sqrt(MSE/r)
StdErr <-
c(
SE.gi
, SE.sii
, SE.sij
, SE.rij
, SE.gi.gj
, SE.sii.sji
, SE.sii.sij
, SE.sii.sjk
, SE.sij.sik
, SE.sij.skl
, SE.rij.rkl
)
list(
Means = Means
, ANOVA = ANOVA
, Genetic.Components = Genetic.Components
, Effects = Effects
, StdErr = StdErr
)
#-----------------------------------------------------------------------------
}
else
if(Method==1 & Model==2)
{
#-----------------------------------------------------------------------------
# Method-I(Parents + F1's + reciprocals)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-II (Random Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
DataTotals <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
n <- nrow(DataTotals)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((colSums(Means)+rowSums(Means))^2))/(2*n)-(2*(sum(colSums(Means)))^2)/n^2)
SS.sca <- (sum(Means*(Means+t(Means)))/2-(sum((colSums(Means)+rowSums(Means))^2))/(2*n)+(sum(colSums(Means)))^2/n^2)
SS.reciprocals <- sum((Means-t(Means))^2)/4
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-1)/2
, n*(n-1)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, SS.reciprocals
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[1]/MS[2], MS[2:3]/MS[4], NA)
P.Value <- c(pf(F.Test[-4], c(df[1], df[2:3]), c(df[2], df[4]), lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "reciprocals"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-(MS[4]+n*(n-1)*MS[2])/(n^2-n+1))/(2*n)
sca.v <- (MS[2]-MS[4])*(n^2)/(2*(n^2-n+1))
r.v <- (MS[3]-MS[4])/2
e.v <- MS[4]
A.v <- 2*gca.v
D.v <- sca.v
gca.v.to.sca.v <- gca.v/sca.v
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, r.v, e.v,
A.v, D.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "Reciprocal", "Error",
"Additive", "Dominant", "gca/sca"))
list(
Means = Means
, ANOVA = ANOVA
, Genetic.Components = Genetic.Components
)
#-----------------------------------------------------------------------------
}
else
if(Method==2 & Model==1)
{
#-----------------------------------------------------------------------------
# Method-II (Parents and one set of F1's)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-I (Fixed Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
Means1 <- Means
Means1[lower.tri(Means1)] <- 0
Means2 <- Means1 + t(Means1) - diag(diag(Means1))
n <- nrow(Means2)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((rowSums(Means2) + diag(Means2))^2)-(4*(sum(rowSums(Means1)))^2)/n)/(n+2))
SS.sca <- sum((Means1)^2)-sum((rowSums(Means2)+diag(Means2))^2)/(n+2)+(2*(sum(rowSums(Means1)))^2)/((n+1)*(n+2))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-1)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[-3]/MS[3], NA)
P.Value <- c(pf(F.Test[-3], df[-3], df[3], lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-MS[3])/(n+2)
sca.v <- (MS[2]-MS[3])
gca.v.to.sca.v <- ((MS[1]-MS[3])/(n+2))/(MS[2]-MS[3])
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "gca/sca"))
#-----------------------------------------------------------------------------
# General Combining Ability (gca) Effects
#-----------------------------------------------------------------------------
G <- diag(((rowSums(Means2)+diag(Means2))-(2*(sum(rowSums(Means1))))/n)/(n+2))
#-----------------------------------------------------------------------------
# Specific Combining Ability (sca) Effects
#-----------------------------------------------------------------------------
S <- matrix(NA, nrow=n, ncol=n, byrow=TRUE)
for(i in 1:n)
{
for(j in 1:n)
{
if (i>=j)
{
S[i, j] <- 0
}
else
{
S[i, j] <- Means[i, j]-(rowSums(Means2)[i] + diag(Means2)[i] + rowSums(Means2)[j] + diag(Means2)[j])/(n+2) + (2*sum(rowSums(Means1)))/((n+1)*(n+2))
}
}
}
Effects <- G+S
Effects[lower.tri(Effects)] <- NA
dimnames(Effects) <- dimnames(Means)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Standard Errors
#-----------------------------------------------------------------------------
MSE <- Simple.ANOVA["Rep", "Mean Sq"]
SE.gi <- sqrt((n-1)/(n*(n+2))*MSE/r)
SE.sii <- sqrt((n^2+n+2)/((n+1)*(n+2))*MSE/r)
SE.sij <- sqrt(n*(n-1)/((n+1)*(n+2))*MSE/r)
SE.gi.gj <- sqrt(2/(n+2)*MSE/r)
SE.sii.sjj <- sqrt(2*(n-2)/(n+2)*MSE/r)
SE.sij.sik <- sqrt(2*(n+1)/(n+2)*MSE/r)
SE.sij.skl <- sqrt(2*n/(n+2)*MSE/r)
StdErr <-
c(
SE.gi
, SE.sii
, SE.sij
, SE.gi.gj
, SE.sii.sjj
, SE.sij.sik
, SE.sij.skl
)
#-----------------------------------------------------------------------------
list(
Means = Means
, ANOVA = ANOVA
, Genetic.Components = Genetic.Components
, Effects = Effects
, StdErr = StdErr
)
#-----------------------------------------------------------------------------
}
else
if(Method==2 & Model==2)
{
#-----------------------------------------------------------------------------
# Method-II (Parents and one set of F1's)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-II (Random Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
Means1 <- Means
Means1[lower.tri(Means1)] <- 0
Means2 <- Means1 + t(Means1) - diag(diag(Means1))
n <- nrow(Means2)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((rowSums(Means2)+diag(Means2))^2)-(4*(sum(rowSums(Means1)))^2)/n)/(n+2))
SS.sca <- sum((Means1)^2)-sum((rowSums(Means2)+diag(Means2))^2)/(n+2)+(2*(sum(rowSums(Means1)))^2)/((n+1)*(n+2))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-1)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[1]/MS[2], MS[2]/MS[3], NA)
P.Value <- c(pf(F.Test[-3], c(df[1], df[2]), c(df[2], df[3]), lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-MS[2])/(n+2)
sca.v <- (MS[2]-MS[3])
e.v <- MS[3]
A.v <- 2*gca.v
D.v <- sca.v
gca.v.to.sca.v <- gca.v/sca.v
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, e.v, A.v, D.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "Error", "Additive", "Dominance", "gca/sca"))
#-----------------------------------------------------------------------------
list(
Means = Means
, ANOVA = ANOVA
, Genetic.Components = Genetic.Components
)
#-----------------------------------------------------------------------------
}
else
if(Method==3 & Model==1)
{
#-----------------------------------------------------------------------------
# Method-III (One set of F1's and reciprocals)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-I (Fixed Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
Means1 <- Means
diag(Means1) <- 0
n <- nrow(Means1)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
# dimnames(Means1) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((rowSums(Means1) + colSums(Means1))^2))/(2*(n-2))-(2*(sum(colSums(Means1)))^2)/(n*(n-2)))
SS.sca <- (sum(((Means1 + t(Means1))^2)/2)/2-(sum((rowSums(Means1) + colSums(Means1))^2))/(2*(n-2)) + (sum(colSums(Means1)))^2/((n-1)*(n-2)))
SS.reciprocals <- sum((Means1 - t(Means1))^2)/4
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-3)/2
, n*(n-1)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, SS.reciprocals
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[-4]/MS[4], NA)
P.Value <- c(pf(F.Test[-4], df[-4], df[4], lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "reciprocals"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-MS[4])/(2*(n-2))
sca.v <- (MS[2]-MS[4])/2
r.v <- (MS[3]-MS[4])/2
gca.v.to.sca.v <- ((MS[1]-MS[4])/(2*(n-2)))/((MS[2]-MS[4])/2)
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, r.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "Reciprocal", "gca/sca"))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# General Combining Ability (gca) Effects
#-----------------------------------------------------------------------------
G <- diag((n*(colSums(Means1) + rowSums(Means1)) - (2*sum(colSums(Means1))))/(2*n*(n-2)))
#-----------------------------------------------------------------------------
# Specific Combining Ability (sca) Effects
#-----------------------------------------------------------------------------
S <- matrix(NA, nrow=n, ncol=n, byrow=TRUE)
for(i in 1:n)
{
for(j in 1:n)
{
if (i>=j)
{
S[i, j] <- 0
}
else
{
S[i, j] <- (Means1[i, j] + Means1[j, i])/2-(rowSums(Means1)[i] + colSums(Means1)[i] + rowSums(Means1)[j] + colSums(Means1)[j])/(2*(n-2)) + (sum(colSums(Means1)))/((n-1)*(n-2))
}
}
}
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Reciprocal Effects
#-----------------------------------------------------------------------------
R <- t(Means1-t(Means1))/2
R[upper.tri(R)] <- 0
Effects <- G + S + R
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Standard Errors
#-----------------------------------------------------------------------------
MSE <- Simple.ANOVA["Rep", "Mean Sq"]
SE.gi <- sqrt((n-1)/(2*n*(n-2))*MSE/r)
SE.sii <- sqrt((n-3)/(2*(n-1))*MSE/r)
SE.rij <- sqrt(1/2*MSE/r)
SE.gi.gj <- sqrt(1/(n-2)*MSE/r)
SE.sij.sik <- sqrt((n-3)/(n-2)*MSE/r)
SE.sij.skl <- sqrt((n-4)/(n-2)*MSE/r)
StdErr <-
c(
SE.gi
, SE.sii
, SE.rij
, SE.gi.gj
, SE.sij.sik
, SE.sij.skl
)
#-----------------------------------------------------------------------------
list(
Means = Means
, ANOVA = ANOVA
, Genetic.Components = Genetic.Components
, Effects = Effects
, StdErr = StdErr
)
#-----------------------------------------------------------------------------
}
else
if(Method==3 & Model==2)
{
#-----------------------------------------------------------------------------
# Method-III (One set of F1's and reciprocals)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-II (Random Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
Means1 <- Means
diag(Means1) <- 0
n <- nrow(Means1)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
# dimnames(Means1) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((rowSums(Means1) + colSums(Means1))^2))/(2*(n-2))-(2*(sum(colSums(Means1)))^2)/(n*(n-2)))
SS.sca <- (sum(((Means1 + t(Means1))^2)/2)/2-(sum((rowSums(Means1)+colSums(Means1))^2))/(2*(n-2))+(sum(colSums(Means1)))^2/((n-1)*(n-2)))
SS.reciprocals <- sum((Means1 - t(Means1))^2)/4
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-3)/2
, n*(n-1)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, SS.reciprocals
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[1]/MS[2], MS[2:3]/MS[4], NA)
P.Value <- c(pf(F.Test[-4], c(df[1], df[2:3]), c(df[2], df[4]), lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "reciprocals"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-MS[2])/(2*(n-2))
sca.v <- (MS[2]-MS[4])/2
r.v <- (MS[3]-MS[4])/2
e.v <- MS[4]
A.v <- 2*gca.v
D.v <- sca.v
gca.v.to.sca.v <- gca.v/sca.v
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, r.v, e.v,
A.v, D.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "Reciprocal", "Error",
"Additive", "Dominant", "gca/sca"))
#-----------------------------------------------------------------------------
list(
Means = Means
, ANOVA = ANOVA
, Genetic.Components = Genetic.Components
)
#-----------------------------------------------------------------------------
}
else
if(Method==4 & Model==1)
{
#-----------------------------------------------------------------------------
# Method-IV (One set of F1's only)
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Model-I (Fixed Effects Model)
#-----------------------------------------------------------------------------
data$Trt <- paste(data[[deparse(substitute(Cross1))]], data[[deparse(substitute(Cross2))]], sep="-")
y <- deparse(substitute(y))
Rep <- deparse(substitute(Rep))
Cross1 <- deparse(substitute(Cross1))
Cross2 <- deparse(substitute(Cross2))
Trt <- deparse(substitute(Trt))
Simple.ANOVA <- summary(aov(data[[y]] ~ as.factor(data[[Rep]]) + data[[Trt]]), data=data)[[1]]
rownames(Simple.ANOVA) <- c("Rep", "Trt", "Residuals")
Means <- tapply(X= data[[y]], INDEX = list(data[[Cross1]], data[[Cross2]]), FUN = mean, na.rm = T)
Means1 <- rbind(cbind(rep(NA, ncol(Means)), Means), rep(NA, ncol(Means) + 1))
Means1[lower.tri(Means1, diag=TRUE)] <- 0
Means2 <- Means1 + t(Means1) - diag(diag(Means1))
n <- ncol(Means2)
r <- length(levels(as.factor(data[[Rep]])))
# dimnames(Means) <- list(paste0("Cross", 2:n), paste0("Cross", 2:n))
# dimnames(Means1) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
# dimnames(Means2) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
SS.gca <- ((sum((rowSums(Means2))^2))/(n-2)-(4*(sum(rowSums(Means2))/2)^2)/(n*(n-2)))
SS.sca <- (sum((Means2)^2))/2-(sum((rowSums(Means2))^2))/(n-2)+(2*(sum(rowSums(Means2))/2)^2)/((n-1)*(n-2))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# ANOVA Table
#-----------------------------------------------------------------------------
df <-
c(
n-1
, n*(n-3)/2
, Simple.ANOVA["Residuals","Df"]
)
SS <-
c(
SS.gca
, SS.sca
, Simple.ANOVA["Residuals", "Sum Sq"]/r
)
MS <- SS/df
F.Test <- c(MS[-3]/MS[3], NA)
P.Value <- c(pf(F.Test[-3], df[-3], df[3], lower.tail = FALSE, log.p = FALSE), NA)
ANOVA <- data.frame(`Df` = df, `Sum Sq` = SS, `Mean Sq` = MS,
`F value` = F.Test, `Pr(>F)` = P.Value, check.names = FALSE)
rownames(ANOVA) <-
c(
"gca"
, "sca"
, "Error"
)
class(ANOVA) <- c("anova", "data.frame")
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Genetic Components
#-----------------------------------------------------------------------------
gca.v <- (MS[1]-MS[3])/(n-2)
sca.v <- (MS[2]-MS[3])
gca.v.to.sca.v <- gca.v/sca.v
Genetic.Components <- data.frame("Components"=c(gca.v, sca.v, gca.v.to.sca.v),
row.names=list("gca", "sca", "gca/sca"))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# General Combining Ability (gca) Effects
#-----------------------------------------------------------------------------
G <- diag((n*rowSums(Means2)-2*(sum(rowSums(Means2))/2))/(n*(n-2)))
#-----------------------------------------------------------------------------
# Specific Combining Ability (sca) Effects
#-----------------------------------------------------------------------------
S <- matrix(NA, nrow=n, ncol=n, byrow=TRUE)
for(i in 1:n)
{
for(j in 1:n)
{
if (i>=j)
{
S[i, j] <- 0
}
else
{
S[i, j] <- Means2[i, j]-(rowSums(Means2)[i]+colSums(Means2)[j])/(n-2)+(2*sum(rowSums(Means2))/2)/((n-1)*(n-2))
}
}
}
#-----------------------------------------------------------------------------
Effects <- G + S
Effects[lower.tri(Effects)] <- NA
# dimnames(Effects) <- list(paste0("Cross", 1:n), paste0("Cross", 1:n))
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
# Standard Errors
#-----------------------------------------------------------------------------
MSE <- Simple.ANOVA["Rep", "Mean Sq"]
SE.gi <- sqrt((n-1)/(n*(n-2))*MSE/r)
SE.sii <- sqrt((n-3)/(n-1)*MSE/r)
SE.sij <- sqrt((n^2-2*n+2)/(2*n^2)*MSE/r)
SE.gi.gj <- sqrt(2/(n-2)*MSE/r)
SE.sij.sik <- sqrt(2*(n-3)/(n-2)*MSE/r)
SE.sij.skl <- sqrt(2*(n-4)/(n-2)*MSE/r)
StdErr <-
c(
SE.gi