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 (a 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).
Value **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).
Value Lvk 1 Identity (residuals ~ Normal distribution) ( **default**).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.
- Missing values (i.e., #N/A!) are not allowed in either the response(Y) or the explanatory input arrays.
- The number of rows in the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
- The number of betas must be 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 the 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 a 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 Gaussian distribution, the dispersion factor (Phi) value must be positive.

## Files Examples

## Related Links

## 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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