Growth curves of deviant behavior in early adolescence: A multilevel analysis

Multilevel growth curve models provide a means of analyzing individual differences in the growth of deviance, allow a number of theories to be integrated in a single model, and can help to unify research on deviant/delinquent/criminal careers at different stages of the life cycle. Building on the distinction between population heterogeneity and state dependence as alternative explanations of persistent individual differences in deviance (Heckman, 1981; Nagin and Paternoster, 1991), we show that models with two levels can be used to represent and analyze a variety of criminological theories. The first level (level 1) uses repeated measurements on individuals to estimate individual-level growth curves. The second level treats the level 1 growth curve parameters (e.g., slope, intercept) as outcome variables and uses time-invariant factors to explain variation in these parameters across individuals. We illustrate this approach by estimating a model of growth in deviance drawn from Gottfredson and Hirschi's deviant propensity theory. An innovative feature is the assumption that adolescents' expected growth curves of deviance follow a classical Pearl-Verhulst logistic growth model (Pearl, 1930). The results suggest that five risk factors—parental psychiatric problems, lack of parental support, living arrangements with zero or one parent in residence, low family income, and male gender—have strongly positive effects on deviant propensity. For example, adolescents with no supportive parents, and no other risk factors, have expected asymptotic levels of deviance (peak levels attained at about age 18) that are about twice as high as those of adolescents with no risk factors. Yet more than two-thirds of the individual-level variability in growth curves is unexplained by the five risk factors. This unobserved heterogeneity would remain hidden in analyses using conventional structural equations models and the same explanatory variables.