The following statements fit the Poisson model with a scale parameter estimated using the Pearson statistic. Without the NOSCALE option, the specified value is used only as a starting value for the scale parameter in the fitting process and it is then allowed to change over the iterations. If a specific value is desired, specify SCALE= value and the NOSCALE option in the MODEL statement. The scale parameter can be estimated using either the Pearson statistic (SCALE=PEARSON) or the deviance statistic (SCALE=DEVIANCE). One approach to adjusting for overdispersion is to introduce a scale parameter into the Poisson distribution which ordinarily does not have one. Notice that, in several populations, the variance is considerably greater than the mean suggesting overdispersion.Īnalysis Of Maximum Likelihood Parameter Estimates The following statements estimate the mean and variance in each population, where a population is defined as a Dose value. The colony count is observed at three replicates, plates, at each drug level. The count response, SALM, is a count of Salmonella colonies observed at six doses of the drug quinoline.

The following data set is used to illustrate the various models for overdispersion. There are many possible causes and alternative approaches for modeling such data as mentioned in this note and illustrated in the examples that follow. Underdispersion can also occur when there is less variability than expected under the Poisson distribution. Count data is often considered to have a Poisson distribution and Poisson regression is commonly used to model count data, but such data often exhibits more variability than expected under that distribution.

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