Analyzing Criminal Trajectory Profiles: Bridging Multilevel and Group-based Approaches Using Growth Mixture Modeling

Over the last 25 years, a life-course perspective on criminal behavior has assumed increasing prominence in the literature. This theoretical development has been accompanied by changes in the statistical models used to analyze criminological data. There are two main statistical modeling techniques currently used to model longitudinal data. These are growth curve models and latent class growth models, also known as group-based trajectory models. Using the well known Cambridge data and the Philadelphia cohort study, this article compares the two “classical” models—conventional growth curve model and group-based trajectory models. In addition, two growth mixture models are introduced that bridge the gap between conventional growth models and group-based trajectory models. For the Cambridge data, the different mixture models yield quite consistent inferences regarding the nature of the underlying trajectories of convictions. For the Philadelphia cohort study, the statistical indicators give stronger guidance on relative model fit. The main goals of this article are to contribute to the discussion about different modeling techniques for analyzing data from a life-course perspective and to provide a concrete step-by-step illustration of such an analysis and model checking.

[1]  Clifford C. Clogg,et al.  Latent Class Models for Measuring , 1988 .

[2]  R. Bosker Boekbespreking van "A.S. Bryk & S.W. Raudenbusch - Hierarchical linear models: Applications and data analysis methods" : Sage Publications, Newbury Parki, London/New Delhi 1992 , 1995 .

[3]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[4]  G. Celeux,et al.  An entropy criterion for assessing the number of clusters in a mixture model , 1996 .

[5]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[6]  J. C. Gower,et al.  Factor Analysis as a Statistical Method. 2nd ed. , 1972 .

[7]  K. Land,et al.  How Many Latent Classes of Delinquent/ Criminal Careers? Results from Mixed Poisson Regression Analyses1 , 1998, American Journal of Sociology.

[8]  R. Cook Assessment of Local Influence , 1986 .

[9]  Robert J. Sampson,et al.  Shared beginnings, divergent lives : delinquent boys to age 70 , 2007 .

[10]  D. Nagin,et al.  The long view of crime : a synthesis of longitudinal research , 2008 .

[11]  Robert J. Sampson,et al.  SEDUCTIONS OF METHOD: REJOINDER TO NAGIN AND TREMBLAY'S "DEVELOPMENTAL TRAJECTORY GROUPS: FACT OR FICTION?" , 2005 .

[12]  K. Land,et al.  AGE, CRIMINAL CAREERS, AND POPULATION HETEROGENEITY: SPECIFICATION AND ESTIMATION OF A NONPARAMETRIC, MIXED POISSON MODEL* , 1993 .

[13]  L. Wasserman,et al.  Practical Bayesian Density Estimation Using Mixtures of Normals , 1997 .

[14]  A. E. Maxwell,et al.  Factor Analysis as a Statistical Method. , 1964 .

[15]  D. Hedeker,et al.  A random-effects ordinal regression model for multilevel analysis. , 1994, Biometrics.

[16]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[17]  J. Laub Shared Beginnings, Divergent Lives , 2006 .

[18]  Kathryn Roeder,et al.  Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology , 1999 .

[19]  A. Piquero Taking Stock of Developmental Trajectories of Criminal Activity over the Life Course , 2008 .

[20]  Michael R. Gottfredson,et al.  Age and the Explanation of Crime , 1983, American Journal of Sociology.

[21]  M. Wolfgang,et al.  Delinquency Careers in Two Birth Cohorts , 1990 .

[22]  Daniel S. Nagin,et al.  Analyzing developmental trajectories: A semiparametric, group-based approach , 1999 .

[23]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[24]  Linda M. Collins,et al.  New methods for the analysis of change , 2001 .

[25]  A. Blumstein,et al.  The Criminal Career Paradigm , 2003, Crime and Justice.

[26]  W. DeSarbo,et al.  Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity , 1997 .

[27]  B. Muthén,et al.  Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study , 2007 .

[28]  T. Moffitt,et al.  LIFE-COURSE TRAJECTORIES OF DIFFERENT TYPES OF OFFENDERS* , 1995 .

[29]  T Asparouhov,et al.  Muthén, B., & Growth mixture analysis: Analysis with non-Gaussian random effects. , 2008 .

[30]  D. Hall Zero‐Inflated Poisson and Binomial Regression with Random Effects: A Case Study , 2000, Biometrics.

[31]  Stephen W. Raudenbush,et al.  How Do We Study “What Happens Next”? , 2005 .

[32]  A. Piquero,et al.  Linking juvenile and adult patterns of criminal activity in the Providence cohort of the National Collaborative Perinatal Project , 2002 .

[33]  T. Moffitt Adolescence-limited and life-course-persistent antisocial behavior: a developmental taxonomy. , 1993, Psychological review.

[34]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[35]  B. Silverman Density estimation for statistics and data analysis , 1986 .

[36]  Erkki P. Liski,et al.  Detecting influential measurements in a growth curves model , 1991 .

[37]  B. Muthén,et al.  Growth mixture modeling , 2008 .

[38]  Bengt Muthén,et al.  Latent Variable Analysis: Growth Mixture Modeling and Related Techniques for Longitudinal Data , 2004 .

[39]  B. Muthén BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .

[40]  Robert J. Sampson,et al.  A Life-Course View of the Development of Crime , 2005 .

[41]  K. Roeder,et al.  A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories , 2001 .

[42]  Daniel S. Nagin,et al.  LIFE SPAN OFFENDING TRAJECTORIES OF A DUTCH CONVICTION COHORT , 2005 .

[43]  Bengt Muthén,et al.  Statistical and substantive checking in growth mixture modeling: comment on Bauer and Curran (2003). , 2003, Psychological methods.

[44]  D. Nagin,et al.  Finite Sample Effects in Group-Based Trajectory Models , 2006 .

[45]  B. Muthén Latent Variable Mixture Modeling , 2001 .

[46]  Ed Anan Shetty,et al.  Literature , 1965, Science.

[47]  A. E. Maxwell,et al.  Factor Analysis as a Statistical Method. , 1964 .

[48]  Bengt Muthén,et al.  Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class–latent growth modeling. , 2001 .

[49]  K. Land,et al.  Sex Differences in Age Patterns of Delinquent/Criminal Careers: Results from Poisson Latent Class Analyses of the Philadelphia Cohort Study , 2002 .

[50]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[51]  D. Farrington,et al.  Criminal, penal and life histories of chronic offenders: risk and protective factors and early identification , 1993 .

[52]  David Kaplan,et al.  The Sage handbook of quantitative methodology for the social sciences , 2004 .

[53]  David P. Farrington,et al.  The Cambridge Study in Delinquent Development: A Long-Term Follow-Up of 411 London Males , 1990 .