One way of correcting overdispersion is to multiply the covariance matrix by a dispersion parameter. You can supply the value of the dispersion parameter directly, or you can estimate the dispersion parameter based on either the Pearson’s chisquare statistic or the deviance for the fitted model.
The Pearson’s chisquare statistic and the deviance are defined in the section LackofFit Tests. If the SCALE= option is specified in the MODEL statement, the dispersion parameter is estimated by

In order for the Pearson’s statistic and the deviance to be distributed as chisquare, there must be sufficient replication within the subpopulations. When this is not true, the data are sparse, and the pvalues for these statistics are not valid and should be ignored. Similarly, these statistics, divided by their degrees of freedom, cannot serve as indicators of overdispersion. A large difference between the Pearson’s statistic and the deviance provides some evidence that the data are too sparse to use either statistic.
You can use the AGGREGATE (or AGGREGATE=) option to define the subpopulation profiles. If you do not specify this option, each observation is regarded as coming from a separate subpopulation. For events/trials syntax, each observation represents n Bernoulli trials, where n is the value of the trials variable; for singletrial syntax, each observation represents a single trial. Without the AGGREGATE (or AGGREGATE=) option, the Pearson’s chisquare statistic and the deviance are calculated only for events/trials syntax.
Note that the parameter estimates are not changed by this method. However, their standard errors are adjusted for overdispersion, affecting their significance tests.