Factors Affecting the Adequacy and Preferability of Semiparametric Groups-Based Approximations of Continuous Growth Trajectories

REFERENCES

• Achenbach , T. M. 1991 . Manual for the Child Behavior Checklist 4–18 and 1991 profile Burlington , VT : University of Vermont, Department of Psychiatry. .
   Google Scholar
• Achenbach , T. M. 1992 . Manual for the Child Behavior Checklist 2–3 and 1992 profile Burlington , VT : University of Vermont, Department of Psychiatry. .
   Google Scholar
• Agresti , A. , Caffo , B. and Ohman-Strickland , P. 2004 . Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies . Computational Statistics & Data Analysis , 47 : 639 – 653 .
   Web of Science ®Google Scholar
• Bauer , D. J. 2007 . Observations on the use of growth mixture models in psychological research . Multivariate Behavioral Research , 42 : 757 – 786 .
   Web of Science ®Google Scholar
• Bauer , D. J. , Goldfield , B. A. and Reznick , J. S. 2002 . Alternative approaches to analyzing individual differences in the rate of early vocabulary development . Applied Psycholinguistics , 23 : 313 – 335 .
   Web of Science ®Google Scholar
• Beyers , W. and Seiffge-Krenke , I. 2007 . Are friends and romantic partners the “best medicine”? How the quality of other close relations mediates the impact of changing family relationships on adjustment . International Journal of Behavioral Development , 31 : 559 – 568 .
   Web of Science ®Google Scholar
• Bobo , J. K. , Klepinger , D. H. and Dong , F. B. 2007 . Identifying social drinkers likely to consume alcohol during pregnancy: Findings from a prospective cohort study . Psychological Reports , 101 : 857 – 870 .
   PubMed Web of Science ®Google Scholar
• Brame , R. , Nagin , D. S. and Tremblay , R. E. 2001 . Developmental trajectories of physical aggression from school entry to late adolescence . Journal of Child Psychology and Psychiatry , 42 : 503 – 512 .
   PubMed Web of Science ®Google Scholar
• Brame , R. , Nagin , D. S. and Wasserman , L. 2006 . Exploring some analytical characteristics of finite mixture models . Journal of Quantitative Criminology , 22 : 31 – 59 .
   Web of Science ®Google Scholar
• Bryk , A. and Raudenbush , S. W. 1987 . Application of hierarchical linear models to assessing change . Psychological Bulletin , 101 : 147 – 158 .
   Web of Science ®Google Scholar
• Butler , S. M. and Louis , T. A. 1992 . Random effects models with non-parametric priors . Statistics in Medicine , 11 : 1981 – 2000 .
   PubMed Web of Science ®Google Scholar
• Carrig , M. , Wirth , R. J. and Curran , P. J. 2004 . A SAS Macro for estimating and visualizing individual growth curves . Structural Equation Modeling , 11 : 132 – 149 .
   Web of Science ®Google Scholar
• Curran , P. J. Comparing three modern approaches to longitudinal data analysis: An examination of a single developmental sample . Symposium presented at the biennial meeting of the Society for Research in Child Development . Washington , DC . April .
   Google Scholar
• Delucchi , K. L. , Matzger , H. and Weisner , C. 2004 . Dependent and problem drinking over 5 years: A latent class analysis . Drug and Alcohol Dependence , 74 : 235 – 244 .
   PubMed Web of Science ®Google Scholar
• Eggleston , E. P. , Laub , J. H. and Sampson , R. J. 2004 . Methodological sensitivities to latent class analysis of long-term criminal trajectories . Journal of Quantitative Criminology , 20 : 1 – 26 .
   Web of Science ®Google Scholar
• Falck , R. S. , Wang , J. and Carlson , R. G. 2007 . Crack cocaine trajectories among users in a midwestern American city . Addiction , 102 : 1421 – 1431 .
   PubMed Web of Science ®Google Scholar
• Feldman , B. J. , Masyn , K. E. and Conger , R. D. 2009 . New approaches to studying problem behaviors: A comparison of methods for modeling longitudinal, categorical adolescent drinking data . Developmental Psychology , 45 : 652 – 676 .
   PubMed Web of Science ®Google Scholar
• Fitzmaurice , G. , Laird , N. and Ware , J. 2011 . Applied longitudinal analysis, , 2nd ed. Hoboken , NJ : Wiley. .
   Google Scholar
• Follmann , D. A. and Lambert , D. 1989 . Generalizing logistic regression by nonparametric mixing . Journal of the American Statistical Association , 84 : 295 – 300 .
   Web of Science ®Google Scholar
• Fontaine , N. , Carbonneau , R. , Vitaro , F. , Barker , E. D. and Tremblay , R. E. 2009 . Research review: A critical review of studies on the developmental trajectories of antisocial behavior in females . Journal of Child Psychology and Psychiatry , 50 : 363 – 385 .
   PubMed Web of Science ®Google Scholar
• Galindo-Garre , F. and Vermunt , J. K. 2006 . Avoiding boundary estimates in latent class analysis by Bayesian posterior mode estimation . Behaviormetrika , 33 : 43 – 59 .
   Google Scholar
• Goldstein , H. 1986 . Multilevel mixed linear model analysis using iterative generalized least squares . Biometrika , 73 : 43 – 56 .
   Web of Science ®Google Scholar
• Gross , H. E. , Shaw , D. S. , Burwell , R. A. and Nagin , D. S. 2009 . Transactional processes in child disruptive behavior and maternal depression: A longitudinal study from early childhood to adolescence . Development and Psychopathology , 21 : 139 – 156 .
   PubMed Web of Science ®Google Scholar
• Hadzi , D. 2009 . Finding patterns and groupings I: Introduction to latent class analysis . Acta Neuropsychiatrica , 21 : 312 – 313 .
   Web of Science ®Google Scholar
• Heckman , J. and Singer , B. 1984 . A method for minimizing the impact of distributional assumptions in econometric models for duration data . Econometrica , 52 : 271 – 320 .
   Web of Science ®Google Scholar
• Hedeker , D. and Gibbons , R. D. 2006 . Longitudinal data analysis New York , NY : Wiley. .
   Google Scholar
• Hill , K. G. , White , H. R. , Chung , I. , Hawkins , D. and Catalano , R. 2000 . Early adult outcomes of adolescent binge drinking: Person- and variable-centered analyses of binge drinking trajectories . Alcoholism: Clinical and Experimental Research , 24 : 892 – 901 .
   PubMed Web of Science ®Google Scholar
• Hipp , J. R. and Bauer , D. J. 2006 . Local solutions in the estimation of growth mixture models . Psychological Methods , 11 : 36 – 53 .
   PubMed Web of Science ®Google Scholar
• Horn , J. L. 2000 . Comments on integrating person-centered and variable-centered research on problems associated with the use of alcohol . Alcoholism: Clinical and Experimental Research , 24 : 924 – 930 .
   PubMed Web of Science ®Google Scholar
• Huang , X. 2011 . Detecting random-effects model misspecification via coarsened data . Computational Statistics and Data Analysis , 55 : 703 – 714 .
   Web of Science ®Google Scholar
• Jackson , K. M. and Sher , K. J. 2008 . Comparison of longitudinal phenotypes based on alternate heavy drinking cut scores: A systematic comparison of trajectory approaches III . Psychology of Addictive Behaviors , 22 : 198 – 209 .
   PubMed Web of Science ®Google Scholar
• Jones , B. , Nagin , D. and Roeder , K. 2001 . A SAS procedure based on mixture models for estimating developmental trajectories . Sociology Methods and Research , 29 : 374 – 393 .
   Web of Science ®Google Scholar
• Jones , D. J. , Runyan , D. K. , Lewis , T. , Litrownik , A. , Black , M. , Wiley , T. and Nagin , D. S. 2010 . Trajectories of childhood sexual abuse and early adolescent HIV/AIDS risk behaviors: The role of other maltreatment, witnessed violence, and child gender. . Journal of Clinical Child & Adolescent Psychology , 39 : 667 – 680 .
   PubMed Web of Science ®Google Scholar
• Kreuter , F. and Muthén , B. 2008 . Analyzing criminal trajectory profiles: Bridging multilevel and group-based approaches using growth mixture modeling . Journal of Quantitative Criminology , 24 : 1 – 31 .
   Web of Science ®Google Scholar
• Krueger , R. , Markon , K. , Patrick , C. and Iacono , W. 2005 . Externalizing psychopathology in adulthood: A dimensional-spectrum conceptualization and its implications for DSM-IV . Journal of Abnormal Psychology , 114 : 537 – 550 .
   PubMed Web of Science ®Google Scholar
• Lacourse , E. , Nagin , D. , Tremblay , R. E. , Vitaro , F. and Claes , M. 2003 . Developmental trajectories of boys' delinquent group membership and facilitation of violent behaviors during adolescence . Development and Psychopathology , 15 : 183 – 197 .
   PubMed Web of Science ®Google Scholar
• Laird , N. 1978 . Nonparametric maximum likelihood estimation of a mixing distribution . Journal of the American Statistical Association , 73 : 805 – 811 .
   Web of Science ®Google Scholar
• Laird , N. M. and Ware , J. H. 1982 . Random effects models for longitudinal data . Biometrics , 38 : 963 – 974 .
   PubMed Web of Science ®Google Scholar
• Leroux , B. G. 1992 . Consistent estimation of a mixing distribution . The Annals of Statistics , 20 : 1350 – 1360 .
   Web of Science ®Google Scholar
• Lindsay , B. G. Mixture models: Theory, geometry and applications . Volume 5 of NSF-CBMS Regional Conference Series in Probability and Statistics . Hayward , CA : Institute of Mathematical Statistics. .
   Google Scholar
• Litiere , S. , Alonso , A. and Molenberghs , G. 2008 . The impact of a misspecified random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models . Statistics in Medicine , 27 : 3125 – 3144 .
   PubMed Web of Science ®Google Scholar
• Losoya , S. , Knight , G. , Chassin , L. , Little , M. , Vargas-Chanes , O. , Mauricio , A. and Piquero , A. 2008 . Trajectories of acculturation and enculturation in relation to heavy episodic drinking and marijuana use in a sample of Mexican American serious juvenile offenders . Journal of Drug Issues , 1 : 171 – 198 .
   Google Scholar
• Louvet , B. , Gaudreau , P. , Menaut , A. , Genty , J. and Deneuve , P. 2007 . Longitudinal patterns of stability and change in coping across three competitions: A latent class growth analysis . Journal of Sport & Exercise Psychology , 29 : 100 – 117 .
   PubMed Web of Science ®Google Scholar
• Maggi , S. , Hertzman , C. and Vaillancourt , T. 2007 . Changes in smoking behaviors from late childhood to adolescence: Insights from the Canadian national longitudinal survey of children and youth . Health Psychology , 26 : 232 – 240 .
   PubMed Web of Science ®Google Scholar
• Magidson , J. and Vermunt , J. K. 2001 . Latent class factor and cluster models, bi-plots and related graphical displays . Sociological Methodology , 31 : 223 – 264 .
   Web of Science ®Google Scholar
• Mazza , J. J. , Fleming , C. B. , Abbott , R. D. , Haggerty , K. P. and Catalano , R. 2010 . Identifying trajectories of adolescents' depressive phenomena: An examination of early risk factors . Journal of Youth and Adolescence , 39 : 579 – 593 .
   PubMed Web of Science ®Google Scholar
• McCulloch , C. E. , Searle , S. R. and Neuhaus , J. M. 2008 . Generalized, linear, and mixed models. Hoboken , NJ : Wiley. .
   Google Scholar
• McLachlan , G. and Peel , D. 2000 . Finite mixture models New York , NJ : Wiley. .
   Google Scholar
• Murphy , D. A. , Brecht , M. L. , Herbeck , D. M. and Huang , D. 2009 . Trajectories of HIV risk behavior from age 15 to 25 in the National Longitudinal Survey of Youth sample . Journal of Youth Adolescence , 38 : 1226 – 1239 .
   PubMed Web of Science ®Google Scholar
• Muthén , B. O. 2004 . “ Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. ” . In Handbook of quantitative methodology for the social sciences , Edited by: Kaplan , D. 345 – 368 . Newbury Park , CA : Sage. .
   Google Scholar
• Muthén , B. O. 2008 . “ Latent variable hybrids: Overview of new and old models. ” . In Advances in latent variable mixture models , Edited by: Hancock , G. and Samuelson , K. 1 – 24 . Charlotte , NC : Information Age. .
   Google Scholar
• Muthén , B. and Asparouhov , T. 2008 . “ Growth mixture modeling: Analysis with non-Gaussian random effects. ” . In Longitudinal data analysis , Edited by: Davidian , F. G. , Verbeke , M. G. and Molenberghs , G. 143 – 165 . Boca Raton , FL : Chapman & Hall/CRC Press. .
   Google Scholar
• Muthén , L. K. and Muthén , B. O. 1998–2010 . Mplus users' guide, , 5th ed. , Los Angeles , CA : Author. .
   Google Scholar
• Muthén , L. K. and Muthén , B. O. 2002 . How to use a Monte Carlo study to decide on sample size and determine power . Structural Equation Modeling , 9 : 599 – 620 .
   Web of Science ®Google Scholar
• Nagin , D. S. 1999 . Analyzing developmental trajectories: A semi-parametric, group-based approach . Psychological Methods , 4 : 139 – 157 .
   Web of Science ®Google Scholar
• Nagin , D. S. 2004 . Response to “Methodological sensitivities to latent class analysis of long-term criminal trajectories.” . Journal of Quantitative Criminology , 20 : 27 – 35 .
   Web of Science ®Google Scholar
• Nagin , D. S. 2005 . Group-based modeling of development Cambridge , MA : Harvard University Press. .
   Google Scholar
• Nagin , D. S. and Land , K. C. 1993 . Age, criminal careers, and population heterogeneity: Specification and estimation of a nonparametric, mixed Poisson model . Criminology , 31 : 327 – 362 .
   Web of Science ®Google Scholar
• Nagin , D. S. and Tremblay , R. E. 1999 . Trajectories of boys' physical aggression, opposition, and hyperactivity on the path to physically violent and nonviolent juvenile delinquency . Child Development , 70 : 1181 – 1196 .
   PubMed Web of Science ®Google Scholar
• Nagin , D. S. and Tremblay , R. E. 2001 . Analyzing developmental trajectories of distinct but related behaviors: A group-based method . Psychological Methods , 6 : 18 – 34 .
   PubMed Web of Science ®Google Scholar
• Nagin , D. S. and Tremblay , R. E. 2005a . Developmental trajectory groups: Fact or a useful statistical fiction? . Criminology , 43 : 873 – 904 .
   Web of Science ®Google Scholar
• Nagin , D. S. and Tremblay , R. E. 2005b . From seduction to passion: A response to Sampson and Laub . Criminology , 43 : 915 – 918 .
   Web of Science ®Google Scholar
• Nagin , D. S. and Tremblay , R. E. 2005c . What has been learned from group-based trajectory modeling? Examples from physical aggression and other problem behaviors . Annals of the American Academy of Political and Social Science , 602 : 82 – 117 .
   Web of Science ®Google Scholar
• Nagin , D. S. and Tremblay , R. E. 2005d . Further reflections on modeling and analyzing developmental trajectories: A response to Raudenbush and Maughan . Annals of the American Academy of Political and Social Science , 602 : 145 – 154 .
   Web of Science ®Google Scholar
• Nash , J. K. and Kim , J. S. 2007 . Patterns of change over time in beliefs legitimizing aggression in adolescents and young adults: Risk trajectories and their relationship with serious aggression . Social Work Research , 31 : 231 – 240 .
   Web of Science ®Google Scholar
• Neuhaus , J. M. , Hauck , W. W. and Kalbfleisch , J. D. 1992 . The effects of mixture distribution misspecification when fitting mixed-effects logistic models . Biometrika , 79 : 755 – 762 .
   Web of Science ®Google Scholar
• NICHD Early Child Care Research Network . 2004 . Trajectories of physical aggression from toddlerhood to middle childhood . Monographs of the Society for Research in Child Development , 69
   Google Scholar
• Nylund , K. L. , Asparouhov , T. and Muthén , B. O. 2007 . Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study . Structural Equation Modeling , 14 : 535 – 569 .
   Web of Science ®Google Scholar
• Obradovic , J. , Burt , K. B. and Masten , A. S. 2006 . Pathways of adaptation from adolescence to young adulthood antecedents and correlates . Annals of the New York Academy of Sciences , 1094 : 340 – 344 .
   PubMed Web of Science ®Google Scholar
• Otten , R. , Wanner , B. , Vitaro , F. and Engels , R. 2008 . Own and friends' smoking attitudes and social preference as early predictors of adolescent smoking . Journal of Clinical Child & Adolescent Psychology , 37 : 808 – 819 .
   PubMed Web of Science ®Google Scholar
• Petitclerc , A. , Boivin , M. , Dionne , G. , Zoccolillo , M. and Tremblay , R. 2009 . Disregard for rules: The early development and predictors of a specific dimension of disruptive behavior disorders . Journal of Child Psychology and Psychiatry , 50 : 1477 – 1484 .
   PubMed Web of Science ®Google Scholar
• Piquero , A. R. , Fagan , J. , Mulvey , E. P. , Steinberg , L. and Odgers , C. 2005 . Developmental trajectories of legal socialization among serious adolescent offenders . Journal of Criminal Law and Criminology , 96 : 267 – 298 .
   PubMed Web of Science ®Google Scholar
• Rabe-Hesketh , S. , Pickles , A. and Skrondal , A. 2003 . Correcting for covariate measurement error in logistic regression using nonparametric maximum likelihood estimation . Statistical Modelling , 3 : 215 – 232 .
   Web of Science ®Google Scholar
• Raudenbush , S. W. and Bryk , A. S. 2002 . Hierarchical linear models: Applications and data analysis methods, , 2nd ed. Newbury Park , CA : Sage. .
   Google Scholar
• Rodriguez-Zas , S. , Southey , B. , Whitfield , C. and Robinson , G. 2006 . Semiparametric approach to characterize unique gene expression trajectories over time . BMC Genomics , 7 : 233 – 240 .
   PubMed Web of Science ®Google Scholar
• Roeder , K. and Wasserman , L. 1997 . Practical Bayesian density estimation using mixtures of normals . Journal of the American Statistical Association , 92 : 894 – 902 .
   Web of Science ®Google Scholar
• Ruscio , J. and Kaczetow , W. 2008 . Simulating multivariate nonnormal data using an iterative algorithm . Multivariate Behavioral Research , 43 : 355 – 381 .
   PubMed Web of Science ®Google Scholar
• Sampson , R. J. and Laub , J. H. 2003 . Life course desisters? Trajectories of crime among delinquent boys followed to age 70 . Criminology , 41 : 555 – 592 .
   Web of Science ®Google Scholar
• Sampson , R. J. and Laub , J. H. 2005 . Seductions of method: Rejoinder to Nagin and Tremblay's “Developmental trajectory groups: Fact or fiction?” . Criminology , 43 : 905 – 913 .
   Web of Science ®Google Scholar
• Sampson , R. J. , Laub , J. H. and Eggleston , E. P. 2004 . On the robustness and validity of groups . Journal of Quantitative Criminology , 20 : 37 – 42 .
   Web of Science ®Google Scholar
• Schafer , D. W. 2001 . Semiparametric maximum likelihood for measurement error model regression . Biometrics , 57 : 53 – 61 .
   PubMed Web of Science ®Google Scholar
• Segawa , E. , Ngwe , J. E. , Li , Y. and Flay, B., & Coinvestigators . 2005 . Evaluation of the effects of the Aban Aya Youth Project in reducing violence among African American adolescent males using latent class growth mixture modeling techniques . Evaluation Review , 29 : 128 – 148 .
   PubMed Web of Science ®Google Scholar
• Sher , K. J. , Gotham , H. J. and Watson , A. L. 2004 . Trajectories of dynamic predictors of disorder: Their meanings and implications . Development and Psychopathology , 16 : 825 – 856 .
   PubMed Web of Science ®Google Scholar
• Singer , J. D. and Willett , J. B. 2003 . Applied longitudinal data analysis: Modeling change and event occurrence. New York , NY : Oxford University Press. .
   Google Scholar
• Skardhamar , T. 2009 . Reconsidering the theory on adolescent-limited and life-course persistent antisocial behavior . British Journal of Criminology , 49 : 863 – 878 .
   Web of Science ®Google Scholar
• Skardhamar , T. 2010 . Distinguishing facts and artifacts in group-based modeling . Criminology , 48 : 295 – 320 .
   Web of Science ®Google Scholar
• Skrondal , A. and Rabe-Hesketh , S. 2004 . Generalized latent variable modeling: Multilevel, longitudinal and structural equation models Boca Raton , FL : Chapman & Hall/CRC. .
   Google Scholar
• Snijders , T. and Bosker , R. 1999 . Multilevel analysis: An introduction to basic and advanced multilevel modeling. London , , UK : Sage. .
   Google Scholar
• Sterba , S. K. and Bauer , D. J. 2010 . Matching method with theory in person-oriented developmental psychopathology research . Development & Psychopathology , 22 : 239 – 254 .
   PubMed Web of Science ®Google Scholar
• Sterba , S. K. , Mathiowetz , R. E. and Bauer , D. J. 2008 . Abstract: Adequacy of semiparametric approximations for growth models with nonnormal random effects . Multivariate Behavioral Research , 43 : 658 – 659 .
   PubMed Web of Science ®Google Scholar
• Sterba , S. , Prinstein , M. J. , Bauer , D. J. and Cox , M. J. November 2005 . “ Unpacking heterotypic continuity: Gender and developmental factors differentiating latent trajectories of homotypic vs. heterotypic symptoms from 2–11 years. ” . In Association for the Advancement of Cognitive and Behavioral Therapy November , New Orleans , LA
   Google Scholar
• Titterington , D. M. , Smith , A. F. M. and Makov , U. E. 1985 . Statistical analysis of finite mixture distributions New York , NY : Wiley. .
   Google Scholar
• Tofighi , D. and Enders , C. K. 2007 . “ Identifying the correct number of classes in growth mixture models. ” . In Advances in latent variable mixture models , Edited by: Hancock , G. R. and Samuelsen , K. M. 317 – 341 . Greenwich , CT : Information Age. .
   Google Scholar
• van den Oord , E. , Pickles , A. and Waldman , I. D. 2003 . Normal variation and abnormality: An empirical study of the liability distributions underlying depression and delinquency . Journal of Child Psychology and Psychiatry , 44 : 180 – 192 .
   PubMed Web of Science ®Google Scholar
• van der Vorst , H. , Vermulst , A. , Meeus , W. , Dekovic , M. and Engels , R. 2009 . Identification and prediction of drinking trajectories in early and mid-adolescence . Journal of Clinical Child and Adolescent Psychology , 38 : 329 – 341 .
   PubMed Web of Science ®Google Scholar
• van Dulmen , M. , Goncy , E. , Vest , A. and Flannery , D. 2009 . “ Group-based trajectory modeling of externalizing behavior problems from childhood through adulthood: Exploring discrepancies in the empirical findings. ” . In The development of persistent criminology. Edited by: Savage , J. Oxford Scholarship Online Monographs. .
   Google Scholar
• van Ryzin , M. , Chatham , M. , Kryzer , E. , Kertes , D. and Gunnar , M. 2009 . Identifying atypical cortisol patterns in young children: The benefits of group-based trajectory modeling . Psychoneuroendocrinology , 34 : 50 – 61 .
   PubMed Web of Science ®Google Scholar
• Verbeke , G. and Lessafre , E. 1996 . A linear mixed-effects model with heterogeneity in the random-effects population . Journal of the American Statistical Association , 91 : 217 – 221 .
   Web of Science ®Google Scholar
• Verbeke , G. and Lessafre , E. 1997 . The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data . Computational Statistics & Data Analysis , 23 : 541 – 556 .
   Web of Science ®Google Scholar
• Vermunt , J. K. and Van Dijk , L. 2001 . A nonparametric random-coefficients approach: The latent class regression model . Multilevel Modelling Newsletter , 13 : 6 – 13 .
   Google Scholar
• Walton , K. E. , Ormel , J. and Krueger , R. 2011 . The dimensional nature of externalizing behaviors in adolescence: Evidence from a direct comparison of categorical, dimensional, and hybrid models . Journal of Abnormal Child Psychology , 39 : 553 – 561 .
   PubMed Web of Science ®Google Scholar
• Wiesner , M. and Kim , H. 2006 . Co-occurring delinquency and depressive symptoms of adolescent boys and girls: A dual trajectory modeling approach . Developmental Psychology , 42 : 1220 – 1235 .
   PubMed Web of Science ®Google Scholar
• Xie , H. , McHugo , G. , He , X. and Drake , R. 2010 . Using the group-based dual trajectory model to analyze two related longitudinal outcomes . Journal of Drug Issues , 1 : 45 – 62 .
   Google Scholar
• Zhang , D. and Davidian , M. 2001 . Linear mixed models with flexible distributions of random effects for longitudinal data . Biometrics , 57 : 795 – 802 .
   PubMed Web of Science ®Google Scholar