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FRESA.CAD (version 2.2.0)

bootstrapVarElimination_Res: NeRI-based backwards variable elimination with bootstrapping

Description

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

Usage

bootstrapVarElimination_Res(object, pvalue = 0.05, Outcome = "Class", data, startOffset = 0, type = c("LOGIT", "LM", "COX"), testType = c("Binomial", "Wilcox", "tStudent", "Ftest"), loops = 250, fraction = 1.0, setIntersect = 1, print=TRUE, plots=TRUE, 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")
loops
The number of bootstrap loops
fraction
The fraction of data (sampled with replacement) to be used as train
setIntersect
The intersect of the model (To force a zero intersect, set this value to 0)
print
Logical. If TRUE, information will be displayed
plots
Logical. If TRUE, plots are displayed
adjsize
The number of features to be used by 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
bootCV
An object of class bootstrapValidation_Res containing the results of the bootstrap validation in the reduced model
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 beforeFSC model will have the model with the minimum bootstrap test error
beforeFSC.formula
the string formula of the model used to find the minimum bootstrap test error

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 bootstrapped residuals improvement is selected. The hypothesis: the term improves residuals is tested by checking the pvalue of average 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

bootstrapVarElimination_Bin, backVarElimination_Res, bootstrapValidation_Res

Examples

Run this code
	## 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
# 	# - Using 50 bootstrap loops
# 	reducedCancerModel <- bootstrapVarElimination_Res(object = cancerModel$final.model,
# 	                                                  pvalue = 0.005,
# 	                                                  Outcome = "pgstat",
# 	                                                  data = dataCancer,
# 	                                                  startOffset = 1,
# 	                                                  type = "COX",
# 	                                                  testType = "Wilcox",
# 	                                                  loops = 50,
# 	                                                  fraction = 1)
# 	# Shut down the graphics device driver
# 	dev.off()## End(Not run)

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