Model selection and comparison

This document describes a strategy to choose between various possible count models. The computation described in this document is done in R (R Core Team, 2016) using the contributed package Countr (Kharrat and Boshnakov, 2017) and the quine data shipped with the MASS package (Venables and Ripley, 2002). The ideas used here are inspired by the demand for medical care example detailed in Cameron and Trivedi (2013, Section 6.3). 1 Prerequisites We will do the analysis of the data with package Countr, so we load it: library(Countr) library("MASS") # for glm.nb() Packages dplyr (Wickham and Francois, 2016) and xtable (Dahl, 2016) provide usefull facilities for data manipulation and presentation: library(dplyr) library(xtable) 2 Data The dataset used in this example is the quine data shipped with package MASS (Venables and Ripley, 2002) and first analysed in Aitkin (1978). The data can be loaded in the usual way: data(quine, package = "MASS") The dataset gives the number of days absent from school (Days) of 146 children in a particular school year. A number of explanatory variables are available describing the children’s ethnic background (Eth), sex (Sex), age (Age) and learner status (Lrn). The count variable Days is characterised by large overdispersion — the variance is more than 16 times larger the mean, 264.2 versus 16.46. Table 1 gives an idea about its distribution. The entries in the table were calculated as follows: breaks_ <c(0, 1, 3, 5:7, 9, 12, 15, 17, 23, 27, 32) freqtable <count_table(count = quine$Days, breaks = breaks_, formatChar = TRUE)