bestglm (version 0.13)

Shao: Simulated Regression Data

Description

Data a simulation study reported by Shao (1993, Table 1). The linear regression model Shao (1993, Table 2) reported 4 simulation experiments using 4 different values for the regression coefficients:

$$y = 2 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \beta_5 x_5 + e,$$ where $e$ is an independent normal error with unit variance.

The four regression coefficients for the four experiments are shown in the table below,

crrrr{ Experiment $\beta_2$ $\beta_3$ $\beta_4$ $\beta_5$ 1 0 0 4 0 2 0 0 4 8 3 9 0 4 8 4 9 6 4 8}

The table below summarizes the probability of correct model selection in the experiment reported by Shao (1993, Table 2). Three model selection methods are compared: LOOCV (leave-one-out CV), CV(d=25) or the delete-d method with d=25 and APCV which is a very efficient computation CV method but specialized to the case of linear regression.

rlll{ Experiment LOOCV CV(d=25) APCV 1 0.484 0.934 0.501 2 0.641 0.947 0.651 3 0.801 0.965 0.818 4 0.985 0.948 0.999 }

The CV(d=25) outperforms LOOCV in all cases and it also outforms APCV by a large margin in Experiments 1, 2 and 3 but in case 4 APCV is slightly better.

Usage

data(Shao)

source

Shao, Jun (1993). Linear Model Selection by Cross-Validation. Journal of the American Statistical Assocation 88, 486-494.

Examples

#In this example BICq(q=0.25) selects the correct model but BIC does not
data(Shao)
X<-as.matrix.data.frame(Shao)
b<-c(0,0,4,0)
set.seed(123321123)
#Note: matrix multiplication must be escaped in Rd file
y<-X%*%b+rnorm(40)
Xy<-data.frame(Shao, y=y)
bestglm(Xy)
bestglm(Xy, IC="BICq")