Description Usage Arguments Value Author(s) References Examples

Given an outcome vector and model matrix, this function finds the submodel(s) minimizing the Akaike (1973, 1974) information criterion (AIC), a corrected version thereof (Sugiura, 1978; Hurvich and Tsai, 1989), and the Bayesian information criterion (BIC; Schwarz, 1978).

1 |

`y` |
outcome vector |

`X` |
model matrix. This should not include an intercept column; such a column is added by the function. |

`pvec` |
vector of possible dimensions of the model to consider: by default, ranges from 1 (intercept only) to |

A list with components

`nlogsig2hat` |
value of the first (non-penalty) term of the criterion, i.e., sample size times log of MLE of the variance, for best model of each dimension in |

`aic` |
lowest AIC for models of each dimension. |

`aicc` |
lowest corrected AIC for models of each dimension. |

`bic` |
lowest BIC for models of each dimension. |

`best.aic, best.aicc, best.bic` |
vectors of logicals indicating which columns of the model matrix are included in the model minimizing AIC, corrected AIC, or BIC. |

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

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In *Second International Symposium on Information Theory* (eds. B. N. Petrov and F. Csaki), pp. 267–281. Budapest: Akademiai Kiado.

Akaike, H. (1974). A new look at the statistical model identification. *IEEE Transactions on Automatic Control*, 19, 716–723.

Hurvich, C. M., and Tsai, C.-L. (1989). Regression and time series model selection in small samples. *Biometrika*, 76, 297–307.

Schwarz, G. (1978). Estimating the dimension of a model. *Annals of Statistics*, 6, 461–464.

Sugiura, N. (1978). Further analysis of the data by Akaike's information criterion and the finite corrections. *Communications in Statistics: Theory & Methods*, 7, 13–26.

1 2 3 |

```
Loading required package: leaps
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.
$nlogsig2hat
[1] 236.3452 209.0421 196.1834 185.2882 179.8606 178.6913
$aic
[1] 238.3452 213.0421 202.1834 193.2882 189.8606 190.6913
$aicc
[1] 287.6180 262.6002 252.1358 243.7516 240.9606 242.5631
$bic
[1] 240.1954 216.7424 207.7339 200.6888 199.1114 201.7922
$best.aic
1 2 3 4 5
TRUE FALSE TRUE TRUE TRUE
$best.aicc
1 2 3 4 5
TRUE FALSE TRUE TRUE TRUE
$best.bic
1 2 3 4 5
TRUE FALSE TRUE TRUE TRUE
```

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