Mixed-Effects Regression Models with Heterogeneous Variance: Analyzing Ecological Momentary Assessment (EMA) Data of Smoking

Longitudinal studies are increasingly common in psychological and social sciences research. In these studies, subjects are measured repeatedly across time and interest often focuses on characterizing their growth or development across time. Mixed-effects regression models (MRMs) have become the method of choice for modeling of longitudinal data; variants of MRMs have been developed under a variety of names: Random-effects models. Laird and Ware (1982),variance component models (Dempster, Rubin, & Tsutakawa, 1981) , multilevel models (Goldstein, 1995), hierarchical linear models (Bryk & Raudenbush, 1992), two-stage models. Bock (1989), random coefficient models (Leeuw & Kreft, 1986), mixed models (Longford, 1987; Wolfinger, 1993), empirical Bayes models (Hui & Berger, 1983; Strenio, Weisberg, & Bryk, 1983), and random regression models (Bock, 1983b, 1983a; Gibbons, Hedeker, Waternaux, & Davis, 1988). A basic characteristic of these models is the inclusion of random subject effects into regression models in order to account for the influence of subjects on their repeated observations. These random effects reflect each person’s growth or development across time, and explain the correlational structure of the longitudinal data. Additionally, they indicate the degree of subject variation that exists in the population of subjects. There are several features that make MRMs especially useful in longitudinal research. First, subjects are not assumed to be measured on the same number of timepoints, thus, subjects with incomplete data across time are included in the