# GLM_AIC - Akaike's information criterion (AIC) of the GLM Model

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).
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

1. The underlying model is described here.
2. Missng values (i.e. #N/A!) are not allowed in either the response(Y) or the explanatory input arrays.
3. The number of rows in response variable (Y) must be equal to number of rows of the explanatory variables (X).
4. The number of betas must equal to the number of explanatory variables (i.e. columns in X) plus one for the intercept.
5. 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.
6. 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).
7. For GLM with Guassian distribution, the dispersion factor (Phi) value must be positive.