Problem 3 : varying counts of predictors in R

For all possible pairwise combinations of the numbers of variables associated with outcome (`nClassVars=2` and `5`) and those not associated with the outcome (`nNoiseVars=1`, `3` and `10`) -- six pairwise combinations in total -- obtain and present graphically test errors from random forest, LDA and KNN.Choose signal magnitude (`deltaClass`) and training data sample size so that this simulation yields non-trivial results -- noticeable variability in the error rates across those six pairwise combinations of attribute counts.Describe the results: what is the impact of the increase of the number of attributes associated with the outcome on the classifier performance?What about the number of attributes not associated with outcome - does it affect classifier error rate?Are different classifier methods affected by these simulation parameters in a similar way?

The following example below illustrates the main ideas on a 3D dataset with two of the three attributes associated with the outcome:

# How many observations:

nObs <- 1000

# How many predictors are associated with outcome:

nClassVars <- 2

# How many predictors are not:

nNoiseVars <- 1

# To modulate average difference between two classes' predictor values:

deltaClass <- 1

# Simulate training and test datasets with an interaction

# between attribute levels associated with the outcome:

xyzTrain <- matrix(rnorm(nObs*(nClassVars+nNoiseVars)),nrow=nObs,ncol=nClassVars+nNoiseVars)

xyzTest <- matrix(rnorm(10*nObs*(nClassVars+nNoiseVars)),nrow=10*nObs,ncol=nClassVars+nNoiseVars)

classTrain <- 1

classTest <- 1

for ( iTmp in 1:nClassVars ) {

deltaTrain <- sample(deltaClass*c(-1,1),nObs,replace=TRUE)

xyzTrain[,iTmp] <- xyzTrain[,iTmp] + deltaTrain

classTrain <- classTrain * deltaTrain

deltaTest <- sample(deltaClass*c(-1,1),10*nObs,replace=TRUE)

xyzTest[,iTmp] <- xyzTest[,iTmp] + deltaTest

classTest <- classTest * deltaTest

}

classTrain <- factor(classTrain > 0)

table(classTrain)

# plot resulting attribute levels colored by outcome:

pairs(xyzTrain,col=as.numeric(classTrain))