Preface

The main goal of this material is to provide a technical support for the students attending the course ’’Regression models for count data: beyond the Poisson model“, given as part of the XV Brazilian School of Regression models - March/2017 in Goiânia, Goiás, Brazil.

The main goal of this course is to present a wide range of statistical models to deal with count data. We focus on parametric and second-moment specified models. We shall present the model specification along with strategies for model fitting and associated R(R Core Team 2015) code. Furthermore, this book-course and supplementary materials, such as R code and data sets are available for the students on the web page http://cursos.leg.ufpr.br/rmcd.

We intend to keep the course in a level suitable for bachelor students who already attended a course on generalized linear models (Nelder and Wedderburn 1972). However, since the course also covers updated topics, it can be of interest of postgraduate students and researches in general.

We designed the course for three hours of tuition. In the first part of the course, we shall present the analysis of count data based on fully parametric models. After a brief introduction and motivation on count data, we present the Poisson, Gamma-Count, Poisson-Tweedie and COM-Poisson distributions. We explore their properties through a consideration of dispersion, zero-inflated and heavy tail indexes. Furthermore, the estimation and inference for these models based on the likelihood paradigm is discussed along with the associated R code and worked examples.

In the second part of the course, we provide a brief introduction to the estimating function approach (Jørgensen and Knudsen 2004 ; Bonat and Jørgensen 2016) and discuss models based on second-moment assumptions in the style of Wedderburn (1974). In particular, we focus on the recently proposed Extended Poisson-Tweedie model (Bonat et al. 2016) and its special case the quasi-Poisson model. The estimating function approach adopted for estimation and inference is presented along with R code and data examples. The use of the R package mcglm (Bonat 2016) is discussed for fitting the extended Poisson-Tweedie model.

We acknowledge our gratitude to the scientific committee of XV Brazilian regression model school for this opportunity.

Department of Statistics, Paraná Federal University, Curitiba, PR, Brazil.

March 27, 2017.