## F Statistics

Suppose that *D*_{0} is the deviance resulting
from fitting a generalized linear model and that
*D*_{1} is the deviance from fitting a submodel.
Then, under appropriate regularity conditions, the
asymptotic distribution of is
chi-square with *r* degrees of freedom, where *r*
is the difference in the number of parameters between
the two models and is the dispersion parameter.
If is unknown, and is an estimate
of based on the deviance or Pearson's chi-square
divided by degrees of freedom, then, under regularity
conditions, has an asymptotic
chi-square distribution with *n*-*p* degrees of freedom.
Here, *n* is the number of observations and *p* is the number
of parameters in the model that is used to estimate .Thus, the asymptotic distribution of

is the *F* distribution
with *r* and *n*-*p* degrees of freedom, assuming
that and are approximately independent.
This *F* 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
sub-model obtained from constraining the Type III
contrast or the user-specified contrast to be 0.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.