Common Errors in Statistics (and How to Avoid Them), 4th Edition

Chapter 14

Modeling Counts and Correlated Data

While inexact models may mislead, attempting to allow for every contingency a priori is impractical. Thus models must be built by an iterative feedback process in which an initial parsimonious model may be modified when diagnostic checks applied to residuals indicate the need.

—G. E. P. Box

TODAY, STATISTICAL SOFTWARE INCORPORATES ADVANCED ALGORITHMS FOR THE analysis of generalized linear models (GLMs)¹ and extensions to panel data settings, including fixed-, random-, and mixed-effects models, logistic, Poisson, and negative-binomial regression, generalized estimating equation models (GEEs), and hierarichical linear models (HLMs). These models take the form

where the nature of the relationship between the outcome variable and the coefficients depend on the specified link function g() of the GLM, β is a vector of to-be-determined coefficients, X is a matrix of explanatory variables, and ε is a vector of identically distributed random variables. These variables may follow the normal, gamma, Poisson, or some other distribution depending on the specified variance function of the GLM.

In this chapter, we consider first the use of GLMs to model counts, then survival data, finish by reviewing popular approaches for modeling correlated data, and discuss model properties, assumptions, and relative strengths. We discuss the efficiency gained ...