Modeling Correlated Data

Abstract

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 hierarchical linear models (HLMs). These models take the form Y ¼ g À1 [bX] þ 1, where b is a vector of to-be-determined coefficients, X is a matrix of explanatory vari-ables, and 1 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. The nature of the relationship between the outcome variable and the coefficients depends on the specified link function g() of the GLM. In this chapter, we review popular approaches for modeling correlated data and discuss model properties, assumptions, and relative strengths. We discuss the effi-ciency gained through correct specification of correlation and the use of alternative standard errors for regression parameters for more robust inference.