bestsetNoise: Best Subset Selection Applied to Noise

Description

Best subset selection applied to completely random noise. This function demonstrates how variable selection techniques in regression can often err in suggesting that more variables be included in a regression model than necessary.

Usage

bestsetNoise(m=100, n=40, method="exhaustive", nvmax=3, print.summary = TRUE)

bestset.noise(m=100, n=40, method="exhaustive", nvmax=3, print.summary = TRUE)

bsnCV(m = 100, n = 40, method = "exhaustive", nvmax = 3, 
      nfolds = 2, print.summary = TRUE)

Arguments

the number of observations to be simulated.

the number of predictor variables in the simulated model.

method

Use exhaustive search, or backward selection, or forward selection, or sequential replacement.

nvmax

maximum number of explanatory variables in model.

nfolds

For splitting the data into training and text sets, the number of folds.

print.summary

Should summary information be printed

Value

bestsetNoise returns the lm model object for the "best" model. bsnCV returns as many models as there are folds.

Details

A set of n predictor variables are simulated as independent standard normal variates, in addition to a response variable which is also independent of the predictors. The best model with nvmax variables is selected using the regsubsets() function from the leaps package. (The leaps package must be installed for this function to work.) The function bsnCV splits the data (randomly) into nfolds (2 or more) parts. It puts each part aside in turn for use to fit the model (effectively, test data), with the remaining data used for selecting the variables that will be used for fitting. One model fit is returned for each of the nfolds parts.

Examples

Run this code

leaps.out <- try(require(leaps, quietly=TRUE))
leaps.out.log <- is.logical(leaps.out)
if ((leaps.out.log==TRUE)&(leaps.out==TRUE)){
bestsetNoise(20,6) # `best' 3-variable regression for 20 simulated observations 
                   # on 7 unrelated variables (including the response)
bsnCV(20,6) # `best' 3-variable regressions (one for each fold) for 20 
                   # simulated observations on 7 unrelated variables
                   # (including the response)
}