PROC GENMOD: F Statistics :: SAS/STAT(R) 9.22 User's Guide

The GENMOD Procedure

F Statistics

Suppose that $\text{[math]}$ is the deviance resulting from fitting a generalized linear model and that $\text{[math]}$ is the deviance from fitting a submodel. Then, under appropriate regularity conditions, the asymptotic distribution of $\text{[math]}$ is chi-square with $\text{[math]}$ degrees of freedom, where $\text{[math]}$ is the difference in the number of parameters between the two models and $\text{[math]}$ is the dispersion parameter. If $\text{[math]}$ is unknown, and $\text{[math]}$ is an estimate of $\text{[math]}$ based on the deviance or Pearson’s chi-square divided by degrees of freedom, then, under regularity conditions, $\text{[math]}$ has an asymptotic chi-square distribution with $\text{[math]}$ degrees of freedom. Here, $\text{[math]}$ is the number of observations and $\text{[math]}$ is the number of parameters in the model that is used to estimate $\text{[math]}$ . Thus, the asymptotic distribution of

$\text{[math]}$

is the $\text{[math]}$ distribution with $\text{[math]}$ and $\text{[math]}$ degrees of freedom, assuming that $\text{[math]}$ and $\text{[math]}$ are approximately independent.

This $\text{[math]}$ statistic is computed for the Type 1 analysis, Type 3 analysis, and hypothesis tests specified in CONTRAST statements when the dispersion parameter is estimated by either the deviance or Pearson’s chi-square divided by degrees of freedom, as specified by the DSCALE or PSCALE option in the MODEL statement. In the case of a Type 1 analysis, model 0 is the higher-order model obtained by including one additional effect in model 1. For a Type 3 analysis and hypothesis tests, model 0 is the full specified model and model 1 is the submodel obtained from constraining the Type III contrast or the user-specified contrast to be 0.

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