A regime-switching longitudinal model of alcohol lapse-relapse
Year: 2014
Type: book-chapter
Abstract: Contemporary general linear models assume that continuous changes in the predictor variables result in proportionate amounts of (linear) change in the outcome variable. Empirical evidence from the alcohol treatment literature, however, favors the application of nonlinear dynamic models over the general linear model in their ability to capture sudden, discontinuous jumps in individuals’ drinking tendency. One example of such nonlinear models is the cusp catastrophe model, used by Witkiewitz and Marlatt (2004) to represent the complex interplay between different risk factors in triggering sudden shifts in individuals’ tendency to drink. Although the cusp catastrophe model has been promising in capturing some aspects of alcohol use dynamics, current approaches of fitting variations of this model do not address several practical data analytic problems commonly seen in empirical data, including the presence of incomplete data, measurement and/or process noise, the lagged effects of previous drinking on current alcohol use, heterogeneous timing of lapse-relapse within and across subjects, and the large number of abstainers at any given time—commonly referred to as the “zeroinflation” phenomenon. We propose a mixture structural equation model with regime-switching as an alternative approach to account for these data analytic issues while retaining some of the key features of the cusp catastrophe model. The proposed model is illustrated using longitudinal drinking data from the COMBINE study (COMBINE Study Research Group, 2003). REGIME-SWITCHING MODEL OF ALCOHOL LAPSE-RELAPSE 2 The Cusp Catastrophe Model Over the last few decades, some researchers’ initial enthusiasm toward nonlinear dynamical systems has gone through various periods of wax and wane. Since the pioneering work of Poincare (1892) and Lorenz’s (1963) computer simulation of a “chaotic” weather system (for a introduction see Alligood, Sauer, & Yorke, 1996; Gleick, 1987; Hilborn, 1994), some of the properties of nonlinear dynamical systems have continued to intrigue social and behavioral scientists. In particular, the idea that a small difference in initial conditions could lead to drastically discrepant outcomes as time progresses, or the existence of models, broadly classified as catastrophe models, that can capture discontinuous jumps in various systems’ change trajectories, have great conceptual appeal to social scientists (see e.g., Vallacher & Nowak, 1994). Catastrophe theory (Thom, 1975, 1993) is the study of the many ways in which continuous changes in a system’s parameters can result in discontinuous changes in an outcome variable of interest. Various catastrophe models have been used to represent sudden jumps manifested, for instance, in individuals’ driving speed (Cobb, 1981; Poston & Stewart, 1978; Zeeman, 1976), attitude (Wimmers, Savelsbergh, & Kamp, 1998), affective states (Allen & Carifo, 1995; Strahan & Conger, 1999), alcohol use (Clair, 1999; Witkiewitz & Marlatt, 2004), paranormal beliefs (Lange & Houran, 2000) and human development in discrete stages (Byrne, Mazanov, & Gregson, 2001; Preece, 1980; Molenaar & Nesselroade, 2000, in press; Van der Maas & Molenaar, 1992). Among the seven possible catastrophe models considered by Thom, the cusp catastrophe is one of the simplest and most commonly applied forms in the social sciences. The model posits that changes in the values of an outcome variable (often termed the behavioral parameter) depend on two control parameters: a splitting parameter and a normal parameter (Gilmore, 1981; Stewart & Peregoy, 1983). In practice, these parameters are often expressed as linear, fixed functions of one or more covariates (e.g., Cobb & Zacks, 1985; Grasman, Van der Maas, & Wagenmakers, 2009; Guastello, 1984; Van der Maas & Molenaar, 1992). Thus, they are sometimes referred to as the splitting and normal variables. Several approaches have been used to fit various catastrophe models. Cobb (Cobb, 1981; Cobb, Koppstein, & Chen, 1983) formulated the cusp catastrophe model as a stochastic partial differential equation model and used a likelihood approach to estimate the parameters. As an alternative to Cobb’s method, Guastello (1982, 1992) presented a simpler approach of using polynomial regression to estimate the parameters in a catastrophe model. This estimation technique has been applied by researchers such as Hufford, Witkiewitz, Shields, Kodva, and Caruso (2003) in modeling the relapse process of alcohol use. Alexander, Herbert, DeShon, and Hanges (1992) pointed out some problems associated with Guastello’s approach and suggested the use of Olivas (1987) multivariate confirmatory Funding for this study was provided by a grant from NSF (BCS-0826844). We are grateful to Peter Molenaar and Han van der Maas, whose work on catastrophe systems has inspired us to undertake the modeling work in the present chapter. We are also grateful to the comments of R. Shane Hutton in the early stages of model building and to the help of Zhaowei Hua and Ruixin Guo in organizing data from the COMBINE study. Correspondence concerning this article can be addressed to Sy-Miin Chow, University of North Carolina, CB#3270 Davie Hall, Chapel Hill, NC 27599-3270 or by email to [email protected]. REGIME-SWITCHING MODEL OF ALCOHOL LAPSE-RELAPSE 3 approach as an alternative. In particular, Guastello (1982) and Brown (1995), in a different approach, both used empirical difference scores as the dependent variable in estimating the parameters for a cusp catastrophe model. Brown (1995) used nonlinear least squares together with a Runge-Kutta integration procedure to obtain iterative estimates of the parameters in a model, whereas Guastello (1982) reformulated the cusp catastrophe model into a polynomial regression model and used ordinary least squares to estimate the corresponding parameters. For the purpose of this chapter, suffice it to say that difference score has a long history of controversy in psychology. In some cases the use of difference score is totally justifiable (e.g., Nesselroade & Cable, 1974; Nesselroade & Bartsch, 1977; Hummel-Rossi & Weinberg, 1975; Maxwell & Howard, 1981), but in others, not necessarily so (Bereiter, 1963; Cronbach & Furby, 1970; Harris, 1963; Horn, 1963; Lord, 1956). Methodological advances in the past few decades have enabled researchers to formulate difference score-related approaches within a latent variable framework, which helps strengthen the appeal of such approaches when used with noisy data (e.g., McArdle & Hamagami, 2001; Molenaar & Newell, 2003). This feature has not be incorporated into the modeling approaches summarized above. One other issue pertaining to these approaches is that transformation functions are typically used to reparameterize the cusp catastrophe model into a simpler form (e.g., polynomial regression model) to facilitate model fitting. However, when the transformation functions are not explicitly specified as constraints in the model specification, there is no guarantee that the fitted, simpler model corresponds in anyway to the original model (for a discussion of this issue in the context of stochastic differential equation modeling see Singer, 1992, 1993). More importantly, while some of the features of catastrophe models have proven useful across a wide range of applications, they impose several assumptions that may be overly restrictive in empirical applications. The goal of this study is to present a mixture structural equation model with regime-switching as an alternative approach to account for some of the known data analytic issues associated with the cusp catastrophe model. While the new proposed model only retains some of the features of the original model thought to be particularly pertinent to the modeling of alcohol use dynamics, it provides more flexibility than the cusp catastrophe model in a number of ways. Some of these advantages include: (1) it is suited for use with longitudinal panel data with multiple subjects, (2) missing data can be readily accommodated, (3) model fitting can be performed at the latent variable level if needed, (4) the new model allows researchers to test multivariate extensions involving lagged effects, (5) predictions encompass a greater range of drinking behaviors, including light and moderate drinking levels, as opposed to focusing on the two extreme modes of alcohol use, namely, complete abstinence and heavy drinking, (6) the new approach helps capture heterogeneous timing of relapse within and across subjects and (7) the presence of a large number of abstainers at any given time point—referred to as the zero-inflation phenomenon in statistics—is represented more flexibly using mixture modeling techniques. The proposed model is illustrated using a set of longitudinal drinking data from the COMBINE study (Anton et al., 2006). REGIME-SWITCHING MODEL OF ALCOHOL LAPSE-RELAPSE 4 Mathematical Background of the Cusp Catastrophe System Consider a dynamical system whose changes over time are governed by the following deterministic equation:
Language: English
Subfield: Epidemiology
Field: Medicine
Domain: Health Sciences
Open Access status: green
OpenAlex ID: W2192051752