Daniel S. Nagin

A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories

This article introduces a new SAS procedure written by the authors that analyzes longitudinal data (developmental trajectories) by fitting a mixture model. The TRAJ procedure fits semiparametric (discrete) mixtures of censored normal, Poisson, zero-inflated Poisson, and Bernoulli distributions to longitudinal data. Applications to psychometric scale data, offense counts, and a dichotomous prevalence measure in violence research are illustrated. In addition, the use of the Bayesian information criterion to address the problem of model selection, including the estimation of the number of components in the mixture, is demonstrated.

Trajectories of Boys' Physical Aggression, Opposition, and Hyperactivity on the Path to Physically Violent and Nonviolent Juvenile Delinquency

A semi-parametric mixture model was used with a sample of 1,037 boys assessed repeatedly from 6 to 15 years of age to approximate a continuous distribution of developmental trajectories for three externalizing behaviors. Regression models were then used to determine which trajectories best predicted physically violent and nonviolent juvenile delinquency up to 17 years of age. Four developmental trajectories were identified for the physical aggression, opposition, and hyperactivity externalizing behavior dimensions: a chronic problem trajectory, a high level near-desister trajectory, a moderate level desister trajectory, and a no problem trajectory. Boys who followed a given trajectory for one type of externalizing problem behavior did not necessarily follow the same trajectory for the two other types of behavior problem. The different developmental trajectories of problem behavior also led to different types of juvenile delinquency. A chronic oppositional trajectory, with the physical aggression and hyperactivity trajectories being held constant, led to covert delinquency (theft) only, while a chronic physical aggression trajectory, with the oppositional and hyperactivity trajectories being held constant, led to overt delinquency (physical violence) and to the most serious delinquent acts.

Developmental Trajectories of Childhood Disruptive Behaviors and Adolescent Delinquency: A Six-Site, Cross-National Study

This study used data from 6 sites and 3 countries to examine the developmental course of physical aggression in childhood and to analyze its linkage to violent and nonviolent offending outcomes in adolescence. The results indicate that among boys there is continuity in problem behavior from childhood to adolescence and that such continuity is especially acute when early problem behavior takes the form of physical aggression. Chronic physical aggression during the elementary school years specifically increases the risk for continued physical violence as well as other nonviolent forms of delinquency during adolescence. However, this conclusion is reserved primarily for boys, because the results indicate no clear linkage between childhood physical aggression and adolescent offending among female samples despite notable similarities across male and female samples in the developmental course of physical aggression in childhood.

Trajectories of change in criminal offending : Good marriages and the desistance process

Building on R. J. Sampson and J. H. Laub, the authors draw an analogy between changes in criminal offending spurred by the formation of social bonds and an investment process. This conceptualization suggests that because investment in social relationships is gradual and cumulative, resulting desistance will be gradual and cumulative. Using a dynamic statistical model developed by D. S. Nagin and K. C. Land, they test their ideas about change using yearly longitudinal data from S. and E. Glueck and Gluecks classic study of criminal careers. Their results show that desistance from crime is facilitated by the development of quality marital bonds, and that this influence is gradual and cumulative over time

Advances in Group-Based Trajectory Modeling and an SAS Procedure for Estimating Them

This article is a follow-up to Jones, Nagin, and Roeder (2001), which described an SAS procedure for estimating group-based trajectory models. Group-based trajectory is a specialized application of finite mixture modeling and is designed to identify clusters of individuals following similar progressions of some behavior or outcome over age or time. This article has two purposes. One is to summarize extensions of the methodology and of the SAS procedure that have been developed since Jones et al. The other is to illustrate how group-based trajectory modeling lends itself to presentation of findings in the form of easily understood graphical and tabular data summaries.

Enduring individual differences and rational choice theories of crime

In explaining crime, some criminological theories emphasize time-stable individual differences in propensity to offend while others emphasize more proximate and situational factors. Using scenario data from a sample of college undergraduates the AA. have found evidence to support both positions. A measure of criminal propensity (poor self-control) was found to be significantly related to self-reported decisions to commit 3 offenses (drunk driving, theft, and sexual assault). Even after considering differences in self-control, there was evidence to suggest that the attractiveness of the crime target, the ease of committing the crime with minimum risk, and perceptions of the costs and benefits of committing the crime were all significantly related to offending decisions.

Group-Based Trajectory Modeling in Clinical Research

Group-based trajectory models are increasingly being applied in clinical research to map the developmental course of symptoms and assess heterogeneity in response to clinical interventions. In this review, we provide a nontechnical overview of group-based trajectory and growth mixture modeling alongside a sampling of how these models have been applied in clinical research. We discuss the challenges associated with the application of both types of group-based models and propose a set of preliminary guidelines for applied researchers to follow when reporting model results. Future directions in group-based modeling applications are discussed, including the use of trajectory models to facilitate causal inference when random assignment to treatment condition is not possible.

Criminal Deterrence Research at the Outset of the Twenty-First Century

Evidence for a substantial deterrent effect is much firmer than it was two decades ago. However, large gaps in knowledge on the links between policy actions and behavior make it difficult to assess the effectiveness of policy options for deterring crime. There are four major impediments. First, analyses must estimate not only short-term consequences but also calibrate long-term effects. Some policies that are effective in preventing crime in the short term may be ineffective or even criminogenic in the long run because they may erode the foundation of the deterrent effect-fear of stigmatization. Second, knowledge about the relationship of sanction risk perceptions to policy is virtually nonexistent; such knowledge would be invaluable in designing effective crime-deterrent policies. Third, estimates of deterrent effects based on data from multiple governmental units measure a policys average effectiveness across unit. It is important to understand better the sources of variation in response across place and time. Fourth, research on the links between intended and actual policy is fragmentary; a more complete understanding of the technology of sanction generation is necessary for identifying the boundaries of feasible policy.

Analyzing developmental trajectories of distinct but related behaviors: a group-based method.

This article presents a group-based method to jointly estimate developmental trajectories of 2 distinct but theoretically related measurement series. The method will aid the analysis of comorbidity and heterotypic continuity. Three key outputs of the model are (a) for both measurement series, the form of the trajectory of distinctive subpopulations; (b) the probability of membership in each such trajectory group; and (c) the joint probability of membership in trajectory groups across behaviors. This final output offers 2 novel features. First, the joint probabilities can characterize the linkage in the developmental course of distinct but related behaviors. Second, the joint probabilities can measure differences within the population in the magnitude of this linkage. Two examples are presented to illustrate the application of the method.

Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology

Abstract Social scientists are commonly interested in relating a latent trait (e.g., criminal tendency) to measurable individual covariates (e.g., poor parenting) to understand what defines or perhaps causes the latent trait. In this article we develop an efficient and convenient method for answering such questions. The basic model presumes that two types of variables have been measured: Response variables (possibly longitudinal) that partially determine the latent class membership, and covariates or risk factors that we wish to relate to these latent class variables. The model assumes that these observable variables are conditionally independent, given the latent class variable. We use a mixture model for the joint distribution of the observables. We apply this model to a longitudinal dataset assembled as part of the Cambridge Study of Delinquent Development to test a fundamental theory of criminal development. This theory holds that crime is committed by two distinct groups within the population: Adoles...