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forward_stepwise_regression.Rmd
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forward_stepwise_regression.Rmd
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---
Title: "Arcsine Square Root Transformation, Forward Stepwise Regression"
Author: Henry Paz (henry.paz@huskers.unl.edu)
Output:
html_document:
keep_md: yes
---
The following arcsine square root transforms the test sets and performs forward stepwise regressions for average daily feed intake (ADFI), average daily gain (ADG), feed efficiency (ADG/ADFI) within heifer and steer cohort.
## Subset test sets for heifer and steer cohorts
```{r, engine='bash'}
#Subset test mapping files for heifer and steer cohorts
grep -E '#SampleID|Heifer.*No' mapping_files/mapping_file.txt > mapping_files/mapping_test_heifer.txt
grep -E '#SampleID|Steer.*No' mapping_files/mapping_file.txt > mapping_files/mapping_test_steer.txt
sed 's/#SampleID/SampleID/g' mapping_files/mapping_test_heifer.txt > r_inputs/mapping_test_heifer.txt
sed 's/#SampleID/SampleID/g' mapping_files/mapping_test_steer.txt > r_inputs/mapping_test_steer.txt
```
## Arcsine square root transformation of test sets for heifer and steer cohorts
```{r}
#Load packages
library(biom)
library(dplyr)
#Make directory
dir.create("stepwise_reg")
#Differential OTUs for heifer and steer cohorts
differential_otus_heifer <- read.table("differential_otus/heifer_differential_otus_subset.txt", sep="\t", header=F)
differential_otus_steer <- read.table("differential_otus/steer_differential_otus_subset.txt", sep="\t", header=F)
#Heifer trans arcsine transformation
otu_test_heifer <- read_biom("biom_files/otu_table_test_heifer_json.biom")
otu_test_heifer <- as.data.frame(as(biom_data(otu_test_heifer), "matrix"))
test_heifer <- sweep(otu_test_heifer, 2, colSums(otu_test_heifer), FUN = "/")
#arcsine square root transformation
trans.arcsine <- function(x){asin(sign(x) * sqrt(abs(x)))}
test_heifer[, 1:109] <- as.data.frame(lapply(test_heifer[, 1:109], FUN = function(x) {sapply(x, FUN = trans.arcsine)}))
test_heifer <- add_rownames(test_heifer, "OTUs")
test_heifer_filtered <- test_heifer[which(test_heifer$OTUs %in% differential_otus_heifer$V1),]
test_heifer_trans <- as.data.frame(t(test_heifer_filtered), stringsAsFactors=F)
colnames(test_heifer_trans) <- test_heifer_trans[1, ]
test_heifer_trans <- test_heifer_trans[-1, ]
colnames(test_heifer_trans) <- paste("OTU", colnames(test_heifer_trans), sep="")
test_heifer_final <- add_rownames(test_heifer_trans, "SampleID")
write.table(test_heifer_final, file="stepwise_reg/test_heifer_final.txt", sep="\t", col.names=T, row.names=F, quote=F)
#Steer trans arcsine transformation
otu_test_steer <- read_biom("biom_files/otu_table_test_steer_json.biom")
otu_test_steer <- as.data.frame(as(biom_data(otu_test_steer), "matrix"))
test_steer <- sweep(otu_test_steer, 2, colSums(otu_test_steer), FUN = "/")
#arcsine square root transformation
trans.arcsine <- function(x){asin(sign(x) * sqrt(abs(x)))}
test_steer[, 1:106] <- as.data.frame(lapply(test_steer[, 1:106], FUN = function(x) {sapply(x, FUN = trans.arcsine)}))
test_steer <- add_rownames(test_steer, "OTUs")
test_steer_filtered <- test_steer[which(test_steer$OTUs %in% differential_otus_steer$V1),]
test_steer_trans <- as.data.frame(t(test_steer_filtered), stringsAsFactors=F)
colnames(test_steer_trans) <- test_steer_trans[1, ]
test_steer_trans = test_steer_trans[-1, ]
colnames(test_steer_trans) <- paste("OTU", colnames(test_steer_trans), sep="")
test_steer_final <- add_rownames(test_steer_trans, "SampleID")
write.table(test_steer_final, file="stepwise_reg/test_steer_final.txt", sep="\t", col.names=T, row.names=F, quote=F)
#Heifer validation set
validation_heifer <- test_steer[which(test_steer$OTUs %in% differential_otus_heifer$V1),]
validation_heifer_trans <- as.data.frame(t(validation_heifer), stringsAsFactors=F)
colnames(validation_heifer_trans) <- validation_heifer_trans[1, ]
validation_heifer_trans = validation_heifer_trans[-1, ]
colnames(validation_heifer_trans) <- paste("OTU", colnames(validation_heifer_trans), sep="")
validation_heifer_final <- add_rownames(validation_heifer_trans, "SampleID")
write.table(validation_heifer_final, file="stepwise_reg/validation_heifer_final.txt", sep="\t", col.names=T, row.names=F, quote=F)
#Steer validation set
validation_steer <- test_heifer[which(test_heifer$OTUs %in% differential_otus_steer$V1),]
validation_steer_trans <- as.data.frame(t(validation_steer), stringsAsFactors=F)
colnames(validation_steer_trans) = validation_steer_trans[1, ]
validation_steer_trans = validation_steer_trans[-1, ]
colnames(validation_steer_trans) <- paste("OTU", colnames(validation_steer_trans), sep="")
validation_steer_final <- add_rownames(validation_steer_trans, "SampleID")
write.table(validation_steer_final, file="stepwise_reg/validation_steer_final.txt", sep="\t", col.names=T, row.names=F, quote=F)
```
#Forward stepwise regression for average daily feed intake (ADFI), average daily gain (ADG), feed efficiency (ADG/ADFI) within heifer and steer cohort
```{r}
#Load packages
library(car)
#Create data set for heifer cohort
mapping_heifer <- read.table("r_inputs/mapping_test_heifer.txt", sep="\t", header=T)
row.names(mapping_heifer) <- mapping_heifer[,1]
#Linear models for ADFI, ADG, and FE using breed composition as covariates for heifer cohort
lm_ADFI_heifer <- lm(ADFI ~ perANS + perHHS + perARS + perSHS + perBMS + perBRS + perBNS + perSGS + perBVS + perCHS + perCAS + perGVS + perLMS + perMAS + perSAS + perSMS + perHH + perAN + perSM + perCH + perM2 + perM3 + perRS + perRO, data=mapping_heifer)
ADFI_res_heifer <- as.data.frame(resid(lm_ADFI_heifer))
lm_ADG_heifer <- lm(ADG ~ perANS + perHHS + perARS + perSHS + perBMS + perBRS + perBNS + perSGS + perBVS + perCHS + perCAS + perGVS + perLMS + perMAS + perSAS + perSMS + perHH + perAN + perSM + perCH + perM2 + perM3 + perRS + perRO, data=mapping_heifer)
ADG_res_heifer <- as.data.frame(resid(lm_ADG_heifer))
lm_FE_heifer <- lm(FE ~ perANS + perHHS + perARS + perSHS + perBMS + perBRS + perBNS + perSGS + perBVS + perCHS + perCAS + perGVS + perLMS + perMAS + perSAS + perSMS + perHH + perAN + perSM + perCH + perM2 + perM3 + perRS + perRO, data=mapping_heifer)
FE_res_heifer <- as.data.frame(resid(lm_FE_heifer))
#Data sets for heifer cohort
heifer_otus <- read.table("stepwise_reg/test_heifer_final.txt", sep="\t", header=T)
row.names(heifer_otus) <- heifer_otus[,1]
heifer_otus <- heifer_otus[,-1]
heifer_ADFI <- merge(ADFI_res_heifer,heifer_otus,by="row.names")
heifer_ADFI <- heifer_ADFI[,-1]
colnames(heifer_ADFI)[1] <- "ADFI"
heifer_ADG <- merge(ADG_res_heifer,heifer_otus,by="row.names")
heifer_ADG <- heifer_ADG[,-1]
colnames(heifer_ADG)[1] <- "ADG"
heifer_FE <- merge(FE_res_heifer,heifer_otus,by="row.names")
heifer_FE <- heifer_FE[,-1]
colnames(heifer_FE)[1] <- "FE"
#Forward stepwise regression models for heifer cohort
#ADFI for heifer cohort
null_heifer_ADFI=lm(ADFI~1, data=heifer_ADFI)
#summary(null_heifer_ADFI)
full_heifer_ADFI=lm(ADFI~., data=heifer_ADFI)
#summary(full_heifer_ADFI)
step(null_heifer_ADFI, scope=list(lower=null_heifer_ADFI, upper=full_heifer_ADFI), direction="forward")
#Model ADFI
model_heifer_ADFI <- lm(formula = ADFI ~ OTU233 + OTU6532 + OTU257 + OTU2045 + OTU125 + OTU517 + OTU5323 + OTU139 + OTU216 + OTU5133, data=heifer_ADFI)
summary(model_heifer_ADFI)
#anova(model_heifer_ADFI)
#Test multi-collinearity (variance inflation factor)
vif(model_heifer_ADFI)
sqrt(vif(model_heifer_ADFI)) > 2
#Homoscedasticity & Normality
layout(matrix(c(1,2,3,4),2,2))
plot(model_heifer_ADFI)
#Extract observed and predicted values
OP_heifer_ADFI <- data.frame(Observed=heifer_ADFI$ADFI, Predicted=fitted(model_heifer_ADFI))
#Plot observed vs prediceted
par(mfrow=c(1,1))
plot(OP_heifer_ADFI$Predicted, OP_heifer_ADFI$Observed, xlab="Predicted Average Daily Feed Intake (kg/d)", ylab="Observed Average Daily Feed Intake (kg/d)")
OP=lm(Observed~Predicted, data=OP_heifer_ADFI)
#summary(OP)
abline(OP)
#ADG for heifer cohort
null_heifer_ADG=lm(ADG~1, data=heifer_ADG)
#summary(null_heifer_ADG)
full_heifer_ADG=lm(ADG~., data=heifer_ADG)
#summary(full_heifer_ADG)
step(null_heifer_ADG, scope=list(lower=null_heifer_ADG, upper=full_heifer_ADG), direction="forward")
#Model ADG
model_heifer_ADG <- lm(formula = ADG ~ OTU233 + OTU139 + OTU6532 + OTU125 + OTU2045 + OTU89, data=heifer_ADG)
summary(model_heifer_ADG)
#anova(model_heifer_ADG)
#Test multi-collinearity (variance inflation factor)
vif(model_heifer_ADG)
sqrt(vif(model_heifer_ADG)) > 2
#Homoscedasticity & Normality
layout(matrix(c(1,2,3,4),2,2))
plot(model_heifer_ADG)
#Extract observed and predicted values
OP_heifer_ADG <- data.frame(Observed = heifer_ADG$ADG, Predicted = fitted(model_heifer_ADG))
#Plot observed vs prediceted
par(mfrow=c(1,1))
plot(OP_heifer_ADG$Predicted, OP_heifer_ADG$Observed, xlab="Predicted Average Daily Gain (kg/d)", ylab="Observed Average Daily Gain (kg/d)")
OP=lm(Observed~Predicted, data=OP_heifer_ADG)
#summary(OP)
abline(OP)
#FE for heifer cohort
null_heifer_FE=lm(FE~1, data=heifer_FE)
#summary(null_heifer_FE)
full_heifer_FE=lm(FE~., data=heifer_FE)
#summary(full_heifer_FE)
step(null_heifer_FE, scope=list(lower=null_heifer_FE, upper=full_heifer_FE), direction="forward")
#Model FE
model_heifer_FE <- lm(formula = FE ~ OTU233 + OTU139 + OTU125 + OTU6532 + OTU2045 + OTU4675, data=heifer_FE)
summary(model_heifer_FE)
#anova(model_heifer_FE)
#Test multi-collinearity (variance inflation factor)
vif(model_heifer_FE)
sqrt(vif(model_heifer_FE)) > 2
#Homoscedasticity & Normality
layout(matrix(c(1,2,3,4),2,2))
plot(model_heifer_FE)
#Extract observed and predicted values
OP_heifer_FE <- data.frame(Observed = heifer_FE$FE, Predicted = fitted(model_heifer_FE))
#Plot observed vs prediceted
par(mfrow=c(1,1))
plot(OP_heifer_FE$Predicted, OP_heifer_FE$Observed, xlab="Predicted Feed Efficiency (ADG/ADFI)", ylab="Observed Feed Efficiency (ADG/ADFI)")
OP=lm(Observed~Predicted, data=OP_heifer_FE)
#summary(OP)
abline(OP)
#Create data set for steer cohort
mapping_steer <- read.table("r_inputs/mapping_test_steer.txt", header=T, sep = "\t")
row.names(mapping_steer) <- mapping_steer[,1]
#Linear models for ADFI, ADG, and FE using breed composition as covariates for steer cohort
lm_ADFI_steer <- lm(ADFI ~ perANS + perHHS + perARS + perSHS + perBMS + perBRS + perBNS + perSGS + perBVS + perCHS + perCAS + perGVS + perLMS + perMAS + perSAS + perSMS + perHH + perAN + perSM + perCH + perM2 + perM3 + perRS + perRO, data=mapping_steer)
ADFI_res_steer <- as.data.frame(resid(lm_ADFI_steer))
lm_ADG_steer <- lm(ADG ~ perANS + perHHS + perARS + perSHS + perBMS + perBRS + perBNS + perSGS + perBVS + perCHS + perCAS + perGVS + perLMS + perMAS + perSAS + perSMS + perHH + perAN + perSM + perCH + perM2 + perM3 + perRS + perRO, data=mapping_steer)
ADG_res_steer <- as.data.frame(resid(lm_ADG_steer))
lm_FE_steer <- lm(FE ~ perANS + perHHS + perARS + perSHS + perBMS + perBRS + perBNS + perSGS + perBVS + perCHS + perCAS + perGVS + perLMS + perMAS + perSAS + perSMS + perHH + perAN + perSM + perCH + perM2 + perM3 + perRS + perRO, data=mapping_steer)
FE_res_steer <- as.data.frame(resid(lm_FE_steer))
#Data sets for heifer cohort
steer_otus <- read.table("stepwise_reg/test_steer_final.txt", header=T, sep = "\t")
row.names(steer_otus) <- steer_otus[,1]
steer_otus <- steer_otus[,-1]
steer_ADFI <- merge(ADFI_res_steer,steer_otus,by="row.names")
steer_ADFI <- steer_ADFI[,-1]
colnames(steer_ADFI)[1] <- "ADFI"
steer_ADG <- merge(ADG_res_steer,steer_otus,by="row.names")
steer_ADG <- steer_ADG[,-1]
colnames(steer_ADG)[1] <- "ADG"
steer_FE <- merge(FE_res_steer,steer_otus,by="row.names")
steer_FE <- steer_FE[,-1]
colnames(steer_FE)[1] <- "FE"
#Forward stepwise regression models for steer cohort
#ADFI for seer cohort
null_steer_ADFI=lm(ADFI~1, data=steer_ADFI)
#summary(null_steer_ADFI)
full_steer_ADFI=lm(ADFI~., data=steer_ADFI)
#summary(full_steer_ADFI)
step(null_steer_ADFI, scope=list(lower=null_steer_ADFI, upper=full_steer_ADFI), direction="forward")
#Model ADFI
model_steer_ADFI <- lm(formula = ADFI ~ OTU3879 + OTU103 + OTU88 + OTU50 + OTU25 + OTU252 + OTU301 + OTU1874 + OTU41 + OTU3670 + OTU2441, data=steer_ADFI)
summary(model_steer_ADFI)
#anova(model_steer_ADFI)
#Test multi-collinearity (variance inflation factor)
vif(model_steer_ADFI)
sqrt(vif(model_steer_ADFI)) > 2
#Homoscedasticity & Normality
layout(matrix(c(1,2,3,4),2,2))
plot(model_steer_ADFI)
#Extract observed and predicted values
OP_steer_ADFI <- data.frame(Observed = steer_ADFI$ADFI, Predicted = fitted(model_steer_ADFI))
#Plot observed vs prediceted
par(mfrow=c(1,1))
plot(OP_steer_ADFI$Predicted, OP_steer_ADFI$Observed, xlab="Predicted Average Daily Feed Intake (kg/d)", ylab="Observed Average Daily Feed Intake (kg/d)")
OP=lm(Observed~Predicted, data=OP_steer_ADFI)
#summary(OP)
abline(OP)
#ADG for seer cohort
null_steer_ADG=lm(ADG~1, data=steer_ADG)
#summary(null_steer_ADG)
full_steer_ADG=lm(ADG~., data=steer_ADG)
#summary(full_steer_ADG)
step(null_steer_ADG, scope=list(lower=null_steer_ADG, upper=full_steer_ADG), direction="forward")
#Model ADG
model_steer_ADG <- lm(formula = ADG ~ OTU3081 + OTU17 + OTU14 + OTU301 + OTU2441 + OTU60 + OTU65 + OTU87 + OTU9 + OTU218 + OTU50 + OTU227 + OTU738 + OTU3879 + OTU36, data=steer_ADG)
summary(model_steer_ADG)
#anova(model_steer_ADG)
#Test multi-collinearity (variance inflation factor)
vif(model_steer_ADG)
sqrt(vif(model_steer_ADG)) > 2
#Homoscedasticity & Normality
layout(matrix(c(1,2,3,4),2,2))
plot(model_steer_ADG)
#Extract observed and predicted values
OP_steer_ADG <- data.frame(Observed = steer_ADG$ADG, Predicted = fitted(model_steer_ADG))
#Plot observed vs prediceted
par(mfrow=c(1,1))
plot(OP_steer_ADG$Predicted, OP_steer_ADG$Observed, xlab="Predicted Average Daily Gain (kg/d)", ylab="Observed Average Daily Gain (kg/d)")
OP=lm(Observed~Predicted, data=OP_steer_ADG)
#summary(OP)
abline(OP)
#FE for seer cohort
null_steer_FE=lm(FE~1, data=steer_FE)
#summary(null_steer_FE)
full_steer_FE=lm(FE~., data=steer_FE)
#summary(full_steer_FE)
step(null_steer_FE, scope=list(lower=null_steer_FE, upper=full_steer_FE), direction="forward")
#Model FE
model_steer_FE <- lm(formula = FE ~ OTU41 + OTU60 + OTU12 + OTU4409 + OTU103 + OTU25 + OTU3879 + OTU218 + OTU3081 + OTU48 + OTU168, data=steer_FE)
summary(model_steer_FE)
#anova(model_steer_FE)
#Test multi-collinearity (variance inflation factor)
vif(model_steer_FE)
sqrt(vif(model_steer_FE)) > 2
#Homoscedasticity & Normality
layout(matrix(c(1,2,3,4),2,2))
plot(model_steer_FE)
#Extract observed and predicted values
OP_steer_FE <- data.frame(Observed = steer_FE$FE, Predicted = fitted(model_steer_FE))
#Plot observed vs prediceted
par(mfrow=c(1,1))
plot(OP_steer_FE$Predicted, OP_steer_FE$Observed, xlab="Predicted Feed Efficiency (ADG/ADFI)", ylab="Observed Feed Efficiency (ADG/ADFI)")
OP=lm(Observed~Predicted, data=OP_steer_FE)
#summary(OP)
abline(OP)
#Validation heifer data sets
validation_otus_heifer <- read.table("stepwise_reg/validation_heifer_final.txt", sep="\t", header=T)
row.names(validation_otus_heifer) <- validation_otus_heifer[,1]
validation_otus_heifer <- validation_otus_heifer[,-1]
validation_heifer_ADFI <- merge(ADFI_res_steer,validation_otus_heifer,by="row.names")
validation_heifer_ADFI <- validation_heifer_ADFI[,-1]
colnames(validation_heifer_ADFI)[1] <- "ADFI"
validation_heifer_ADG <- merge(ADG_res_steer,validation_otus_heifer,by="row.names")
validation_heifer_ADG <- validation_heifer_ADG[,-1]
colnames(validation_heifer_ADG)[1] <- "ADG"
validation_heifer_FE <- merge(FE_res_steer,validation_otus_heifer,by="row.names")
validation_heifer_FE <- validation_heifer_FE[,-1]
colnames(validation_heifer_FE)[1] <- "FE"
#Validation heifer models
#Heifer ADFI
modelval_heifer_ADFI <- lm(formula = ADFI ~ OTU233 + OTU6532 + OTU257 + OTU2045 + OTU125 + OTU517 + OTU5323 + OTU139 + OTU216 + OTU5133, data=validation_heifer_ADFI)
summary(modelval_heifer_ADFI)
#Heifer ADG
modelval_heifer_ADG <- lm(formula = ADG ~ OTU233 + OTU139 + OTU6532 + OTU125 + OTU2045 + OTU89, data = validation_heifer_ADG)
summary(modelval_heifer_ADG)
#Heifer FE
modelval_heifer_FE <- lm(formula = FE ~ OTU233 + OTU139 + OTU6532 + OTU125 + OTU2045 + OTU89, data=validation_heifer_FE)
summary(modelval_heifer_FE)
#Validation steer data sets
validation_otus_steer <- read.table("stepwise_reg/validation_steer_final.txt", sep="\t", header=T)
row.names(validation_otus_steer) <- validation_otus_steer[,1]
validation_otus_steer <- validation_otus_steer[,-1]
validation_steer_ADFI <- merge(ADFI_res_heifer,validation_otus_steer,by="row.names")
validation_steer_ADFI <- validation_steer_ADFI[,-1]
colnames(validation_steer_ADFI)[1] <- "ADFI"
validation_steer_ADG <- merge(ADG_res_heifer,validation_otus_steer,by="row.names")
validation_steer_ADG <- validation_steer_ADG[,-1]
colnames(validation_steer_ADG)[1] <- "ADG"
validation_steer_FE <- merge(FE_res_heifer,validation_otus_steer,by="row.names")
validation_steer_FE <- validation_steer_FE[,-1]
colnames(validation_steer_FE)[1] <- "FE"
#Validation steer models
#steer ADFI
modelval_steer_ADFI <- lm(formula = ADFI ~ OTU3879 + OTU103 + OTU88 + OTU50 + OTU25 + OTU252 + OTU301 + OTU1874 + OTU41 + OTU3670 + OTU2441, data=validation_steer_ADFI)
summary(modelval_steer_ADFI)
#steer ADG
modelval_steer_ADG <- lm(formula = ADG ~ OTU3081 + OTU17 + OTU14 + OTU301 + OTU2441 + OTU60 + OTU65 + OTU87 + OTU9 + OTU218 + OTU50 + OTU227 + OTU738 + OTU3879 + OTU36, data=validation_steer_ADG)
summary(modelval_steer_ADG)
#steer FE
modelval_steer_FE <- lm(formula = FE ~ OTU41 + OTU60 + OTU12 + OTU4409 + OTU103 + OTU25 + OTU3879 + OTU218 + OTU3081 + OTU48 + OTU168, data=validation_steer_FE)
summary(modelval_steer_FE)
```