Description Usage Arguments Details Value Author(s) References Examples

This function can be used for simulations to evaluate the performance of linear model selection with independent predictors.

1 2 3 |

`n` |
sample size. |

`p.all` |
maximum model dimension, i.e., number of candidate predictors plus 1. |

`p.true` |
true model dimension, i.e., number of predictors with nonzero coefficients plus 1. |

`R2` |
coefficient of determination for the true model. |

`beta0` |
true model intercept; in some contexts this value may be arbitrary. |

`yname` |
name for the generated outcome vector. |

`xname` |
name for the generated model matrix. |

`xy`

simulates entries of a model matrix independently from the
standard normal distribution, then simulates outcomes whose mean is simply `beta0`

plus the sum of the first
`p.true - 1`

predictors. The errors are normal with mean 0 and
standard deviation chosen so as to attain the given `R2`

; see Tibshirani & Knight (1999), p. 538.

A list with components `X`

(model matrix, without intercept column) and `y`

(outcome vector).

Philip Reiss phil.reiss@nyumc.org and Lei Huang huangracer@gmail.com

Tibshirani, R., and Knight, K. (1999). The covariance inflation criterion for adaptive model selection. *Journal of the Royal Statistical Society, Series B*, 61, 529–546.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
# Generate 40 vectors of 8 candidate predictors, of which
# (the first) 2 have nonzero coefficients, along with 40 outcomes,
# with R^2=.8
tmp = xy(40, 9, 3, .8)
# As a side effect, the above created objects y5 and X59,
# equal to tmp$y and tmp$X respectively.
# The following lines can then be used to examine how different
# information criteria fare at identifying the true model as "best".
ic.min(y3, x39)
eic(y3, x39, nboot=100)
cvic(y3, x39)
``` |

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