Detection of outliers in longitudinal count data via overdispersion

Count data are usually modeled using the Poisson generalized linear model. The Poisson model requires that the variance be a deterministic function of the mean. This assumption may not be met for a particular data set, that is, the model may not adequately capture the variability in the data. The extra-variability in the data may be accommodated using overdispersion models, such as the negative binomial distribution. In addition to the overdispersion outliers may be present in the data as indicated by the model residuals or some functions of the model residuals. A variance shift outlier model (VSOM) for count data is introduced. The model is used to detect potential outliers in the data, and to down-weight them in the analysis if desired. In this model the overdispersion is modeled using an observation-specific random effect. The status of a given observation as an outlier is indicated by the size of the associated shift in variance for that observation. The model is then extended to longitudinal count data for the detection of outliers at the subject level. We illustrate the methodology using a real data set taken from the literature. Extensions of the VSOM for count data to other non-normal responses are discussed.