![]() |
![]() |
The GLIMMIX Procedure |
You can add a multiplicative overdispersion parameter to a generalized linear model in the GLIMMIX procedure with the statement
random _residual_;
For models in which , this effectively lifts the constraint of the parameter. In models that already contain a
or
scale parameter—such as the normal, gamma, or negative binomial model—the statement adds a multiplicative scalar (the overdispersion parameter,
) to the variance function.
The overdispersion parameter is estimated from Pearson’s statistic after all other parameters have been determined by (restricted) maximum likelihood or quasi-likelihood. This estimate is
![]() |
where if the NOREML option is in effect, and
otherwise, and
is the sum of the frequencies. The power
is
for the gamma distribution and
otherwise.
Adding an overdispersion parameter does not alter any of the other parameter estimates. It only changes the variance-covariance matrix of the estimates by a certain factor. If overdispersion arises from correlations among the observations, then you should investigate more complex random-effects structures.
![]() |
![]() |
Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.