Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-12T02:12:37.487Z Has data issue: false hasContentIssue false

8 - Latent Variable Mixture Modeling Approaches to Investigating Longitudinal Recovery Processes

from Part I - Micro Level

Published online by Cambridge University Press:  23 December 2021

Jalie A. Tucker
Affiliation:
University of Florida
Katie Witkiewitz
Affiliation:
University of New Mexico
Get access

Summary

Alcohol researchers are often interested in identifying heterogeneous subgroups of drinkers, such as those with stable patterns of moderation drinking or patterns of heavy episodic drinking. Subgroups may also be identified based on qualitatively different developmental courses in the onset of alcohol use disorder (AUD) or pathways to recovery from AUD. This chapter provides an overview of latent variable mixture modeling, which can be useful for investigating such heterogeneity. First, mixture models applied to cross-sectional data are described, specifically latent class analysis and latent profile analysis. Then conventional latent growth modeling is discussed as a special case of growth mixture models, where subgroups of individuals are identified based on the shape of their growth trajectories. Mixture models applied to mediation analysis are also discussed. The chapter concludes with some practical issues to consider when using mixture modeling.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52(3), 317332. https://doi.org/10.1007/BF02294359CrossRefGoogle Scholar
Anton, R. F., O’Malley, S. S., Ciraulo, D. A., Cisler, R. A., Couper, D., Donovan, D. M., Gastfriend, D. R., Hosking, J., Johnson, B., LoCastro, J., Longabaugh, R., Mason, B., Mattson, M., Miller, W. R., Pettinati, H; Randall, C., Swift, R., Weiss, R., Williams, L., & Zweben, A. (2006). Combined pharmacotherapies and behavioral interventions for alcohol dependence the COMBINE study: A randomized controlled trial. JAMA, 295(17), 20032017. https://doi.org/10.1001/jama.295.17.2003CrossRefGoogle ScholarPubMed
Asparouhov, T., & Muthén, B. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling, 21(3), 329341. https://doi.org/10.1080/10705511.2014.915181CrossRefGoogle Scholar
Bakk, Z., Oberski, D. L., & Vermunt, J. K. (2016). Relating latent class membership to continuous distal outcomes: Improving the LTB approach and a modified three-step implementation. Structural Equation Modeling, 23(2), 278289. https://doi.org/10.1080/10705511.2015.1049698Google Scholar
Bakk, Z., Tekle, F. B., & Vermunt, J. K. (2013). Estimating the association between latent class membership and external variables using bias adjusted three-step approaches. Sociological Methodology, 43(1), 272311. https://doi.org/10.1177/0081175012470644CrossRefGoogle Scholar
Bandeen-roche, K., Miglioretti, D. L., Zeger, S. L., & Rathouz, P. J. (1997). Latent variable regression for multiple discrete outcomes. Journal of the American Statistical Association, 92(440), 13751386. https://doi.org/10.1080/01621459.1997.10473658Google Scholar
Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for over extraction of latent trajectory classes. Psychological Methods, 8(3), 338363. https://doi.org/10.1037/1082-989X.8.3.338Google Scholar
Berlin, K. S., Parra, G. R., & Williams, N. A. (2014). An introduction to latent variable mixture modeling (part 2): Longitudinal latent class growth analysis and growth mixture models. Journal of Pediatric Psychology, 39(2), 188203. https://doi.org/10.1093/jpepsy/jst085Google Scholar
Berlin, K. S., Williams, N. A., & Parra, G. R. (2014). An introduction to latent variable mixture modeling (part 1): Overview of cross-sectional latent class and latent profile analyses. Journal of Pediatric Psychology, 39(2), 174187. https://doi.org/10.1093/jpepsy/jst084Google Scholar
Beseler, C. L., Taylor, L. A., Kraemer, D. T., & Leeman, R. F. (2012). A latent class analysis of DSM-IV alcohol use disorder criteria and binge drinking in undergraduates. AlcoholismClinical & Experimental Research, 36(1), 153161. https://doi.org/10.1111/j.1530-0277.2011.01595.xGoogle Scholar
Bolck, A., Croon, M. A., & Hagenaars, J. A. (2004). Estimating latent structure models with categorical variables: One-step versus three-step estimators. Political Analysis, 12(1), 327. https://doi.org/10.1093/pan/mph001Google Scholar
Bollen, K. A., & Curran, P. J. (2005). Latent curve models: A structural equation perspective. John Wiley & Sons.Google Scholar
Cahalan, D. (1970). Problem drinkers: A national survey. Jossey-Bass.Google Scholar
Cheong, J. (2011). Accuracy of estimates and statistical power for testing mediation in latent growth modeling. Structural Equation Modeling, 18(2), 195211. https://doi.org/10.1080/10705511.2011.557334Google Scholar
Cheong, J., Khoo, S. T., & MacKinnon, D. P. (2009). Growth mixture modeling in mediation: An application of mixture modeling to evaluation of mediating mechanisms in a randomized prevention trial. Paper presented at the Annual Convention of the Society for Prevention Research, Washington, DC.Google Scholar
Cheong, J., Mackinnon, D. P., & Khoo, S. T. (2003). Investigation of mediational processes using parallel process latent growth curve modeling. Structural Equation Modeling, 10(2), 238262. https://doi.org/10.1207/S15328007SEM1002_5CrossRefGoogle ScholarPubMed
Clogg, C. C. (1995). Latent class models. In Arminger, G., Clogg, C. C., & Sobel, M. E. (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 311359). Springer.Google Scholar
Collins, L. M. (2006). Analysis of longitudinal data: The integration of theoretical model, temporal design, and statistical model. Annual Review of Psychology, 57, 505528. https://doi.org/10.1146/annurev.psych.57.102904.190146Google Scholar
Collins, L. M., & Lanza, S. T. (2009). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. Wiley.Google Scholar
Grimm, K. J., Ram, N., & Hamagami, F. (2011). Nonlinear growth curves in developmental research. Child Development, 82(5), 13571371. https://doi.org/10.1111/j.1467-8624.2011.01630.xGoogle Scholar
Hsiao, Y. Y., Kruger, E. S., Van Horn, M. L., Tofighi, D., MacKinnon, D. P., & Witkiewitz, K. (2020). Latent class mediation: A comparison of six approaches. Multivariate Behavioral Research. Advance online publication. https://doi.org/10.1080/00273171.2020.1771674Google Scholar
Kim, M., Van Horn, M. L., Jaki, T., Vermunt, J., Feaster, D., Lichstein, K. L., Taylor, D., Riedel, B., & Bush, A. (2020). Repeated measures regression mixture models. Behavior Research Methods, 52(2), 591606. https://doi.org/10.3758/s13428–019-01257-7Google Scholar
Lanza, S. T., & Cooper, B. R. (2016). Latent class analysis for developmental research. Child Development Perspective, 10(1), 5964. https://doi.org/10.1111/cdep.12163Google Scholar
Lanza, S. T., Tan, X., & Bray, B. C. (2013). Latent class analysis with distal outcomes: A flexible model-based approach. Structural Equation Modeling, 20(1), 126. https://doi.org/10.1080/10705511.2013.742377Google Scholar
Lau-Barraco, C., Braitman, A. L., Stamates, A. L., & Linden-Carmichael, A. N. (2017). A latent profile analysis of drinking patterns among nonstudent emerging adults. Addictive Behaviors, 62(10), 1419. https://doi.org/10.1016/j.addbeh.2016.06.001Google Scholar
Laursen, B., & Hoff, E. (2006). Person-centered and variable-centered approaches to longitudinal data. Merrill-Palmer Quarterly, 52(3), 377389. https://doi.org/10.1353/mpq.2006.0029Google Scholar
Lo, Y., Mendell, N., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767778. https://doi.org/10.1093/biomet/88.3.767Google Scholar
Lubke, G., & Neale, M. (2006). Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood. Multivariate Behavioral Research, 41(4), 499532. https://doi.org/10.1207/s15327906mbr4104_4CrossRefGoogle ScholarPubMed
MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83104. https://doi.org/10.1037/1082-989x.7.1.83Google Scholar
Magnusson, D. (2003). The person approach: Concepts, measurement models, and research strategy. In Peck, S. C. & Roeser, R. W. (Eds.), New directions for child and adolescent development: Person-centered approaches to studying development in context (pp. 323). Jossey-Bass.Google Scholar
Masyn, K. E. (2013). Latent class analysis and finite mixture modeling. In Little, T. (Ed.), Oxford handbook of quantitative methods (pp. 551611). Oxford University Press.Google Scholar
McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58(1), 110133. https://doi.org/10.2307/1130295Google Scholar
McLachlan, G., & Peel, D. (2000). Finite mixture models. Wiley.Google Scholar
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55(1), 107122. https://doi.org/10.1007/BF02294746Google Scholar
Muthén, B. (2001). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class-latent growth modeling. In Collins, L. M. & Sayer, A. G. (Eds.), New methods for the analysis of change (pp. 289322). American Psychological Association.Google Scholar
Muthén, B., & Muthén, L. (1998–2017). Mplus user’s guide: Statistical analysis with latent variables. 8th ed. Muthén & Muthén.Google Scholar
Muthén, B., & Muthén, L. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical & Experimental Research, 24(6), 882891. https://doi.org/10.1111/j.1530-0277.2000.tb02070.xCrossRefGoogle ScholarPubMed
Nagin, D. S. (2005). Group-based modeling of development. Harvard University Press.Google Scholar
No, U., & Hong, S. (2018). A comparison of mixture modeling approaches in latent class models with external variables under small samples. Educational and Psychological Measurement, 78(6), 925951. https://doi.org/10.1177/0013164417726828Google Scholar
Nylund, K., Asparouhov, T., & Muthén, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535569. https://doi.org/10.1080/10705510701575396Google Scholar
Pentz, M. A., Trebow, E. A., Hansen, W. B., MacKinnon, D. P., Dwyer, J. H., Johnson, C. A., Flay, B. R., Daniels, S., & Cormack, C. (1990). Effects of program implementation on adolescent drug use behavior: The Midwestern Prevention Project (MPP). Evaluation Review, 14(3), 264289. https://doi.org/10.1177/0193841X9001400303CrossRefGoogle Scholar
Reboussin, B. A., Ip, E. H., & Wolfson, M. (2008). Locally dependent latent class models with covariates: An application to under-age drinking in the USA. Journal of Royal Statistical Society: Series A, 171(4), 877897. https://doi.org/10.1111/j.1467-985X.2008.00544.xGoogle Scholar
Rinker, D. V., & Neighbors, C. (2015). Latent class analysis of DSM-5 alcohol use disorder criteria among heavy-drinking college students. Journal of Substance Abuse Treatment, 57, 8188. https://doi.org/10.1016/j.jsat.2015.05.006Google Scholar
Rogosa, D. (1988). Myths about longitudinal research. In Schaie, K. W., Campbell, R. T., , W.Meredith, , & Rawlings, S. C. (Eds.), Methodological issues in aging research (pp. 171209). Springer.Google Scholar
Schwartz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461464. https://doi.org/10.1214/aos/1176344136Google Scholar
Sclove, L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52(3), 333343. https://doi.org/10.1007/BF02294360Google Scholar
Singer, J. D., & Willet, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford University Press.CrossRefGoogle Scholar
Skinner, H. A., & Horn, J. L. (1984). Alcohol Dependence Scale (ADS) user’s guide. Addiction Research Foundation.Google Scholar
Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In Leinhardt, S. (Ed.), Sociological methodology (pp. 290312). American Sociological Association.Google Scholar
Tein, J., Coxe, S., & Cham, H. (2013). Statistical power to detect the correct number of classes in latent profile analysis. Structural Equation Modeling, 20(4), 640657. https://doi.org/10.1080/10705511.2013.824781CrossRefGoogle ScholarPubMed
Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. Wiley.Google Scholar
Torrance-Rynard, V. L., & Walter, S. D. (1997). Effects of dependent errors in the assessment of diagnostic test performance. Statistics in Medicine, 16(19), 21572175. https://doi.org/10.1002/(sici)1097-0258(19971015)16:19<2157::aid-sim653>3.0.co;2-xGoogle Scholar
Tucker, J. A., Cheong, J., James, T. G., Jung, S., & Chandler, S. D. (2020). Preresolution drinking problem severity profiles associated with stable moderation outcomes of natural recovery attempts. Alcoholism: Clinical & Experimental Research, 44(3), 738745. https://doi.org/10.1111/acer.14287Google Scholar
Tucker, J. A., Vuchinich, R. E., Black, B. C., & Rippens, P. D. (2006). Significance of a behavioral economic index of reward value in predicting drinking problem resolutions. Journal of Consulting and Clinical Psychology, 74(2), 317326. https://doi.org/10.1037/0022-006X.74.2.317Google Scholar
Vacek, P. M. (1985). The effect of conditional dependence on the evaluation of diagnostic tests. Biometrics, 41(4), 959968. https://doi.org/10.2307/2530967Google Scholar
Vermunt, J. K. (2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18(4), 450469. https://doi.org/10.1093/pan/mpq025Google Scholar
Willet, J. B. (1989). Some results on reliability for the longitudinal measurement of change: Implications for the design of studies of individual growth. Educational and Psychological Measurement, 49(3), 587602. https://doi.org/10.1177/001316448904900309Google Scholar
Witkiewitz, K., Roos, C. R., Tofighi, D., & Van Horn, M. L. (2018). Broad coping repertoire mediates the effect of the Combined Behavioral Intervention on alcohol outcomes in the COMBINE Study: An application of latent class mediation. Journal of Studies on Alcohol and Drugs, 79(2), 199207. https://doi.org/10.15288/jsad.2018.79.199CrossRefGoogle ScholarPubMed
Witkiewitz, K., Wilson, A. D., Pearson, M. R., Montes, K. S., Kirouac, M., Roos, C., Hallgren, K. A., & Maisto, S. A. (2019). Profiles of recovery from alcohol use disorder at three years following treatment: Can the definition of recovery be extended to include high functioning heavy drinkers? Addiction, 114(1), 6980. https://doi.org/10.1111/add.14403Google Scholar
Witkiewitz, K., Wilson, A. D., Roos, C. R., Swan, J. E., Votaw, V. R., Stein, E. R., Pearson, M., Edwards, K., Tonigan, J. S., Hallgren, K., Montes, K., Maisto, S., & Tucker, J. A. (2020). Can individuals with alcohol use disorder sustain non-abstinent recovery? Non-abstinent outcomes 10 years after alcohol use disorder treatment. Journal of Addiction Medicine. Advance online publication. https://doi.org/10.1097/adm.0000000000000760CrossRefGoogle Scholar
Yeater, E. A., Witkiewitz, K., López, G., Ross, R. S., Vitek, K., & Bryan, A. (2018). Latent profile analysis of alcohol consumption and sexual attitudes among college women: Associations with sexual victimization risk. Violence against Women, 24(11), 12791298. https://doi.org/10.1177/1077801218787926Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×