A familial longitudinal count data study

In this report, I study familial longitudinal count data with a Poisson regression model. The data is collected from individuals who are nested in families. I focus on two main issues to fit a model. The first one is the large number of excess zeros and the second one is multi-level random effects. My approach for solving these problems are to use either Zero Inflated Poisson (ZIP) or Negative Binomial (NB) models to control for the excess zeros which allow for estimation of another parameter for over dispersion while developing the model with individual and familial random effects. First, I use a Poisson regression model with only main effects. After that, I fit a ZIP model to control for the extra zeros. I provide information about general form of the exponential families and a discussion about the dispersion parameter. I also fit a Negative Binomial model instead of the ZIP model. I also build these models with only individual random effects and with both individual and familial random effects as well. I discuss the generalized estimating equation (GEE) approach to estimate the parameters of a generalized linear model with auto regressive correlation between outcomes.