Introduction

Discrete data analysis such as count or binary clustered data analysis has been an important research topic over the last three decades. In general, two types of clusters are frequently encountered. First, a cluster may be formed with the responses along with associated covariates from the members of a group/family. These clustered responses are supposed to be correlated as the members of the cluster share a common random group/family effect. In this book, we refer to this type of correlation among the responses of members of same family as the familial correlation. Second, a cluster may be formed with the repeated responses along with associated covariates collected from an individual. These repeated responses from the same individual are also supposed to be correlated as there may be a dynamic relationship between the present and past responses. In this book, we refer to these correlations among the repeated responses collected from the same individual as the longitudinal correlations. It is of interest to fit a suitable parametric or semi-parametric familial and/or longitudinal correlation model primarily to analyze the means and variances of the data. Note that the familial and longitudinal correlations, however, play an important role in a respective setup to analyze the means and variances of the data efficiently.