VAIC procedure

Calculates the Akaike and Schwarz information coefficients for REML (R.W. Payne).

Options

PRINT = strings

Controls printed output (deviance, aic, sic, dffixed, dfrandom); default aic

INCLUDE = strings

Which constants to include that depend only on the fixed model (determinant, pi); default pi

DMETHOD = string

Method to use to calculate log(determinant(X′X)) (choleski, lrv); default chol

Parameters

DEVIANCE = scalars

Saves the deviance

AIC = scalars

Saves the Akaike information coefficient;

SIC = scalars

Saves the Schwarz information coefficient

DFFIXED = scalars

Saves the number of parameters fitted in the fixed model

DFRANDOM = scalars

saves the number of parameters fitted in the random model (and any covariance models)

SAVE = REML save structure

Save structure for wich to calculate the coefficients; default uses the save structure from the most recent REML

Description

The Akaike and Schwarz information coefficients are often used to assess the appropriateness of random (and covariance) models in REML. They are calculated from the deviance (which can be printed by REML):

aic = deviance + 2 × r

sic = deviance + log(n - p) × r

where n is the total number of usable units in the analysis, r is the number of parameters fitted in the random model (and any covariance models), and p is the number of parameters fitted in the fixed model.

An additional consideration is that the deviance provided by REML omits some constants that depend on the fixed model. In fact the full deviance is given by

full-deviance = REML-deviance + (n-p)*log(2π) - log(det(X′X))

where X is the design matrix of the fixed model. Other software systems tend to include the first term, involving π, but omit the log-determinant term which is more time-consuming to calculate. The inclusion of these terms in the calculation is controlled by the INCLUDE option, with settings

determinant

-log(det(X′X))

+(n-p)*log(2π)

The DMETHOD option controls how -log(det(X′X)) is calculated when this is included. However, the default is INCLUDE=pi.

Printed output is controlled by the PRINT option, with settings:

deviance

prints the deviance (adding the extra terms specified by INCLUDE);

aic

prints the Akaike information coefficient;

sic

prints the Schwarz information coefficient;

dffixed

prints the number of parameters fitted in the fixed model;

dfrandom

prints the number of parameters fitted in the random model (and any covariance models).

These can all be saved using the DEVIANCE, AIC, SIC, DFFIXED and DFRANDOM parameters. By default VAIC prints just the Akaike information coefficient.

Usually the coefficients are calculated for the most recent REML analysis. However, you can use the SAVE parameter to specify the SAVE structure from an earlier analysis.

Options: PRINT, INCLUDE, DMETHOD.

Parameter: DEVIANCE, AIC, SIC, DFFIXED, DFRANDOM, SAVE.