GROWTH-CURVES OF DEVIANT-BEHAVIOR IN EARLY ADOLESCENCE - A MULTILEVELANALYSIS

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 dev iant/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 indivi dual differences in deviance (Heckman, 1981; Nagin and Paternoster, 19 91), 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-lev el growth curves. The second level treats the level 1 growth curve par ameters (e.g., slope, intercept) as outcome variables and uses time-in variant factors to explain variation in these parameters across indivi duals. We illustrate this approach by estimating a model of growth in deviance drawn from Gottfredson and Hirschi's deviant propensity theor y. An innovative feature is the assumption that adolescents' expected growth curves of deviance follow a classical Pearl-Verhulst logistic g rowth model (Pearl, 1930). The results suggest that five risk factors- parental psychiatric problems, lack of parental support, living arrang ements with zero or one parent in residence, low family income, and ma le gender-have strongly positive effects on deviant propensity. For ex ample, adolescents with no supportive parents, and no other risk facto rs, 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 c onventional structural equations models and the same explanatory varia bles.