FRESA.CAD (version 2.2.0)

backVarElimination_Res: NeRI-based backwards variable elimination

Description

This function removes model terms that do not significantly improve the "net residual" (NeRI)

Usage

backVarElimination_Res(object,
	                       pvalue = 0.05,
	                       Outcome = "Class",
	                       data,
	                       startOffset = 0, 
	                       type = c("LOGIT", "LM", "COX"),
	                       testType = c("Binomial", "Wilcox", "tStudent", "Ftest"),
	                       setIntersect = 1,
						   adjsize= 1)

Arguments

object

An object of class lm, glm, or coxph containing the model to be analyzed

pvalue

The maximum p-value, associated to the NeRI, allowed for a term in the model

Outcome

The name of the column in data that stores the variable to be predicted by the model

data

A data frame where all variables are stored in different columns

startOffset

Only terms whose position in the model is larger than the startOffset are candidates to be removed

type

Fit type: Logistic ("LOGIT"), linear ("LM"), or Cox proportional hazards ("COX")

testType

Type of non-parametric test to be evaluated by the improvedResiduals function: Binomial test ("Binomial"), Wilcoxon rank-sum test ("Wilcox"), Student's t-test ("tStudent"), or F-test ("Ftest")

setIntersect

The intersect of the model (To force a zero intersect, set this value to 0)

adjsize

The number of features to be used in the BH FSR correction

Value

back.model

An object of the same class as object containing the reduced model

loops

The number of loops it took for the model to stabilize

reclas.info

A list with the NeRI statistics of the reduced model, as given by the getVar.Res function

back.formula

An object of class formula with the formula used to fit the reduced model

lastRemoved

The name of the last term that was removed (-1 if all terms were removed)

beforeFSC.model

the model with before the FSR procedure. Coefficients are bagged

beforeFSC.formula

the string formula of the the FSR procedure

Details

For each model term $x_i$, the residuals are computed for the Full model and the reduced model( where the term $x_i$ removed). The term whose removal results in the smallest drop in residuals improvement is selected. The hypothesis: the term improves residuals is tested by checking the pvalue of improvement. If $p(residuals better than reduced residuals)>pvalue$, then the term is removed. In other words, only model terms that significantly aid in improving residuals are kept. The procedure is repeated until no term fulfils the removal criterion. The p-values of improvement can be computed via a sign-test (Binomial) a paired Wilcoxon test, paired t-test or f-test. The first three tests compare the absolute values of the residuals, while the f-test test if the variance of the residuals is improved significantly.

See Also

backVarElimination_Bin, bootstrapVarElimination_Bin bootstrapVarElimination_Res

Examples

	## Not run: 
# 	# Start the graphics device driver to save all plots in a pdf format
# 	pdf(file = "Example.pdf")
# 	# Get the stage C prostate cancer data from the rpart package
# 	library(rpart)
# 	data(stagec)
# 	# Split the stages into several columns
# 	dataCancer <- cbind(stagec[,c(1:3,5:6)],
# 	                    gleason4 = 1*(stagec[,7] == 4),
# 	                    gleason5 = 1*(stagec[,7] == 5),
# 	                    gleason6 = 1*(stagec[,7] == 6),
# 	                    gleason7 = 1*(stagec[,7] == 7),
# 	                    gleason8 = 1*(stagec[,7] == 8),
# 	                    gleason910 = 1*(stagec[,7] >= 9),
# 	                    eet = 1*(stagec[,4] == 2),
# 	                    diploid = 1*(stagec[,8] == "diploid"),
# 	                    tetraploid = 1*(stagec[,8] == "tetraploid"),
# 	                    notAneuploid = 1-1*(stagec[,8] == "aneuploid"))
# 	# Remove the incomplete cases
# 	dataCancer <- dataCancer[complete.cases(dataCancer),]
# 	# Load a pre-stablished data frame with the names and descriptions of all variables
# 	data(cancerVarNames)
# 	# Get a Cox proportional hazards model using:
# 	# - A lax p-value
# 	# - 10 bootstrap loops
# 	# - Age as a covariate
# 	# - The Wilcoxon rank-sum test as the feature inclusion criterion
# 	cancerModel <- ForwardSelection.Model.Res(pvalue = 0.1,
# 	                                    loops = 10,
# 	                                    covariates = "1 + age",
# 	                                    Outcome = "pgstat",
# 	                                    variableList = cancerVarNames,
# 	                                    data = dataCancer,
# 	                                    type = "COX",
# 	                                    testType= "Wilcox",
# 	                                    timeOutcome = "pgtime")
# 	# Remove not significant variables from the previous model:
# 	# - Using a strict p-value
# 	# - Excluding the covariate as a candidate for feature removal 
# 	# - Using the Wilcoxon rank-sum test as the feature removal criterion
# 	reducedCancerModel <- backVarElimination_Res(object = cancerModel$final.model,
# 	                                             pvalue = 0.005,
# 	                                             Outcome = "pgstat",
# 	                                             data = dataCancer,
# 	                                             startOffset = 1,
# 	                                             type = "COX",
# 	                                             testType = "Wilcox")
# 	# Shut down the graphics device driver
# 	dev.off()## End(Not run)