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 (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

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

Files Examples

Related Links

• Wikipedia - Akaike's Information Criterion (AIC).
• Wikipedia - Generalized linear model.

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.