R: Simulated Regression Data

Shao {bestglm} | R Documentation

## 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 + b[2] x2 + b[3] x3 + b[4] x4 + b[5] x5 + 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,

Experiment | b[2] | b[3] | b[4] | b[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.

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)

### Format

A data frame with 40 observations on the following 4 inputs.

`x2`

  a numeric vector

`x3`

  a numeric vector

`x4`

  a numeric vector

`x5`

  a numeric vector

### 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")

[Package bestglm version 0.36 Index]