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## Contributions: Abstract
Longitudinal studies of behavioral outcomes frequently deal with outcomes whose distributions are inherently non-normal, such as count data or ordered categorical responses. Especially for rare events, these responses have a preponderance of low or zero values that need to be modeled correctly. A typical example is the number of juvenile arrests where many observations are recorded with very few or no arrests. When considering criminal behavior over time, a substantive researcher may be interested in modeling trajectory classes (Nagin, 1999). Using a well-known data set (Farrington & West, 1990), this talk will evaluate the applicability of recently developed growth modeling techniques. Using the Growth Mixture Modeling framework (Muthen & Shedden, 1999), we consider individual differences in development over time with continuous latent variables, and capture more fundamental forms of unobserved heterogeneity in the trajectories using categorical latent variables. The classes of the categorical latent variable can represent latent trajectory classes, for example adolescent-limited versus life-course persistent antisocial behavior (Moffitt, 1993). An important part of Generalized Growth Mixture Modeling is the estimation of class membership probabilities from covariates and the inclusion of distal outcomes predicted by latent classes. The estimated prediction of class membership and its predictive power for distal outcomes is a key feature in examining hypothesis derived from substantive theories. As in criminological application, researchers are not only interested in different developmental trajectories and covariates that can help predict the criminal development but ultimately how these trajectories and covariates predict their criminal status at a later point in time. Thus far, Growth Mixture Modeling has only dealt with continuous outcomes. Extensions to other outcomes will be illustrated in this talk facilitated by a new technique introduced by Asparouhov and MuthÃ©n (2004) using maximum-likelihood estimation based on an EM algorithm with numerical integration. These extensions can be classified in two ways. First, models may be distinguished based on how the dependent variable is treated. For example, new random effects versions of zero-inflated Poisson (ZIP) modeling of counts will be considered. ZIP modeling allows for two classes of individuals: those who during a given time period are not engaged in the behavior at all versus those who are engaged in the behavior but happen to have zero outcome at the time of measurement. Second, models can be distinguished based on how they handle the heterogeneity in the development over time. Mixture models, random effects models, and models with random effects within latent classes will be compared regarding their identifiability, interpretability and predictive power for distal outcomes. |