Random Effects

Abstract

This chapter includes well-known as well as state-of-the-art statistical modeling techniques for drawing inference on correlated data, which occur in a wide variety of studies (during quality control studies of similar products made on different assembly lines, community-based studies on cancer prevention, and familial research of linkage analysis, to name a few). The first section briefly introduces statistical models that incorporate random effect terms, which are increasingly being applied to the analysis of correlated data. An effect is classified as a random effect when inferences are to be made on an entire population, and the levels of that effect represent only a sample from that population. The second section introduces the linear mixed model for clustered data, which explicitly models complex covariance structure among observations by adding random terms into the linear predictor part of the linear regression model. The third section discusses its extension – generalized linear mixed models (GLMMs) – for correlated nonnormal data. The fourth section reviews several common estimating techniques for GLMMs, including the EM and penalized quasi-likelihood approaches, Markov chain Newton-Raphson, the stochastic approximation, and the S-U algorithm. The fifth section focuses on some special topics related to hypothesis tests of random effects, including score tests for various models. The last section is a general discussion of the content of the chapter and some other topics relevant to random effects models.