Tests for Overdispersion in Longitudinal Data in the Presence of Outliers∗

Frequently repeated observations of an outcome variable along with a set of covariates are recorded for each of many subjects. For example, in clinical trials, the severity of respiratory disease along with the nutritional status, age, sex and family income of children are observed once every three months for a suitable period (say for a 36 month period). Typically, the scientific interest is in the dependence of the outcome variable on the covariates. When the outcomes of a subject are count data (e.g. Poisson) or data in the form of proportions (e.g. binomial), they may exhibit overdispersion. Further, in the longitudinal setup, the outcomes of a subject are likely to be correlated. For the case when the repeated measurements of a subject are not subject to overdispersion, Liang and Zeger (1986), among others, provide a class of generalized estimating equations for the coefficient of the dependence (regression parameters) of the outcome variable on the covariates. The construction of their estimating equations is based on the assumption that the marginal probability density of an outcome belongs to a natural exponential family of distributions. Their approach takes the correlation among values for a given subject into account and provides