Modeling Hierarchical Data, Allowing for Overdispersion and Zero Inflation, in Particular Excess Zeros

Abstract

In a lot of applied research, binary and count outcome frequently appear, next to continuous data. Statistical modeling of such data lies within the framework of exponential family distributions (McCullagh and Nelder, 1989; Agresti, 2002; Molenberghs and Verbeke, 2005). The resulting generalized linear models (GLMs) contain three components: a random component that identifies a vector of observations of the outcome and its probability distribution; a systematic component, i.e., a specification for the mean vector in terms of a vector of fixed unknown parameters and known covariate values; and a link function which specifies the function of expectation that the model equates to the systematic component with known link functions, such as the logit and log functions for binary and count data, respectively. ...