Calculates the Akaike's information criterion (AIC) of the GLM model (with correction to small sample sizes).

## Syntax

**GLM_AIC**(

**Y**,

**X**,

**Betas**,

**Phi**,

**Lvk**)

**Y** is the response or the dependent variable data array (one dimensional array of cells (e.g. rows or columns)).

**X** is the independent variables data matrix, such that each column represents one variable.

**Betas** are the coefficients of the GLM model (a one dimensional array of cells (e.g. rows or columns)).

**Phi** is the GLM dispersion paramter. Phi is only meaningful for Binomial (1/batch or trial size) and for Guassian (variance).

Distribution | PHI |
---|---|

Gaussian | Variance |

Poisson | 1.0 |

Binomial | Reciprocal of the batch/trial size) |

**Lvk** is the link function that describes how the mean depends on the linear predictor (1=Identity (default), 2=Log, 3=Logit, 4=Probit, 5=Log-Log).

Link | Description |
---|---|

1 | Identity (residuals ~ Normal distribution) |

2 | Log (residuals ~ Poisson distribution) |

3 | Logit (residuals ~ Binomial distribution) |

4 | Probit(residuals ~ Binomial distribution) |

5 | Complementary log-log (residuals ~ Binomial distribution) |

## Remarks

- The underlying model is described here.
- Missng values (i.e. #N/A!) are not allowed in either the response(Y) or the explanatory input arrays.
- The number of rows in response variable (Y) must be equal to number of rows of the explanatory variables (X).
- The number of betas must equal to the number of explanatory variables (i.e. columns in X) plus one for the intercept.
- For GLM with Poisson distribution,
- The values of response variable must be non-negative integers.
- The value of the dispersion factor (Phi) must be either missing or equal to one.

- For GLM with Binomial distribution,
- The values of the response variable must be non-negative fraction between zero and one, inclusive.
- The value of the dispersion factor (Phi) must be a positive fraction (greater than zero, and less than one).

- For GLM with Guassian distribution, the dispersion factor (Phi) value must be positive.

## Files Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740

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