A basic assumption in the construction of models from likelihood theory is that observations in the model are independent. This is a reasonable assumption for perhaps the majority of studies. However, for longitudinal studies this assumption is not feasible; nor does it hold when data are clustered. For example, observations from a study on student drop-out can be clustered by the type of schools sampled. If the study is related to intervention strategies, schools in affluent suburban, middle-class suburban, middle-class urban, and below poverty level schools have more highly correlated strategies within the school type than between types or groups. Likewise, if we have study data taken on a group of individual patients over time (e.g., treatment results obtained once per month for a year), the data related to individuals in the various time periods are likely to be more highly correlated than are treatment results between patients. Any time the data can be grouped into clusters, or panels, of correlated groups, we must adjust the likelihood-based model (based on independent observations) to account for the extra-correlation.

We have previously employed robust variance estimators and bootstrapped standard errors when faced with overdispersed count data. Overdispersed Poisson models were adjusted by using different types of negative binomial models, or by extending the basic Poisson model by adjusting the variance or by designing a new log-likelihood function to account for the specific cause of the overdispersion.