Repeated measures regression mixture models

  • Minjung KimEmail author
  • M. Lee Van HornEmail author
  • Thomas Jaki
  • Jeroen Vermunt
  • Daniel Feaster
  • Kenneth L. Lichstein
  • Daniel J. Taylor
  • Brant W. Riedel
  • Andrew J. Bush


Regression mixture models are one increasingly utilized approach for developing theories about and exploring the heterogeneity of effects. In this study we aimed to extend the current use of regression mixtures to a repeated regression mixture method when repeated measures, such as diary-type and experience-sampling method, data are available. We hypothesized that additional information borrowed from the repeated measures would improve the model performance, in terms of class enumeration and accuracy of the parameter estimates. We specifically compared three types of model specifications in regression mixtures: (a) traditional single-outcome model; (b) repeated measures models with three, five, and seven measures; and (c) a single-outcome model with the average of seven repeated measures. The results showed that the repeated measures regression mixture models substantially outperformed the traditional and average single-outcome models in class enumeration, with less bias in the parameter estimates. For sample size, whereas prior recommendations have suggested that regression mixtures require samples of well over 1,000 participants, even for classes at a large distance from each other (classes with regression weights of .20 vs. .70), the present repeated measures regression mixture models allow for samples as low as 200 participants with an increased number (i.e., seven) of repeated measures. We also demonstrate an application of the proposed repeated measures approach using data from the Sleep Research Project. Implications and limitations of the study are discussed.


Regression mixture models Sample size Repeated measures Heterogeneous effects 



  1. Adam, E. K., Snell, E. K., & Pendry, P. (2007). Sleep timing and quantity in ecological and family context: A nationally representative time-diary study. Journal of Family Psychology, 21, 4–19. CrossRefGoogle Scholar
  2. Altevogt, B. M., & Colten, H. R. (2006). Sleep disorders and sleep deprivation: An unmet public health problem. Washington, DC: National Academies Press.Google Scholar
  3. Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338–363. CrossRefGoogle Scholar
  4. Duncan, T. E., Duncan, S. C., & Strycker, L. A. (2013). An introduction to latent variable growth curve modeling: Concepts, issues, and application, Basingstoke: Routledge.CrossRefGoogle Scholar
  5. Dyer, W. J., Pleck, J., & McBride, B. (2012). Using mixture regression to identify varying effects: A demonstration with parental incarceration. Journal of Marriage and Family, 74, 1129–1148.CrossRefGoogle Scholar
  6. Grimm, K. J., Ram, N., & Estabrook, R. (2017). Growth modeling: Structural equation and multilevel modeling approaches. New York: Guilford Press.Google Scholar
  7. Jaki, T., Kim, M., Lamont, A. E., George, M., Chang, C., Feaster, D. J., & Van Horn, M. L. (2019). The effects of sample size on the estimation of regression mixture models. Educational and Psychological Measurement, 79, 358–384. CrossRefGoogle Scholar
  8. Jung, T., & Wickrama, K. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2, 302–317.CrossRefGoogle Scholar
  9. Kliegel, M., & Zimprich, D. (2005). Predictors of cognitive complaints in older adults: A mixture regression approach. European Journal of Ageing, 2, 13–23.CrossRefGoogle Scholar
  10. Kohli, N., Harring, J. R., & Zopluoglu, C. (2016). A finite mixture of nonlinear random coefficient models for continuous repeated measures data. Psychometrika, 81, 851–880.CrossRefGoogle Scholar
  11. Lamont, A. E., Vermunt, J. K., & Van Horn, M. L. (2016). Regression mixture models: Does modeling the covariance between independent variables and latent classes improve the results? Multivariate Behavioral Research, 51, 35–52.CrossRefGoogle Scholar
  12. Lanza, S. T., Cooper, B. R., & Bray, B. C. (2014). Population heterogeneity in the salience of multiple risk factors for adolescent delinquency. Journal of Adolescent Health, 54, 319–325. CrossRefGoogle Scholar
  13. Lanza, S. T., Kugler, K. C., & Mathur, C. (2011). Differential effects for sexual risk behavior: An application of finite mixture regression. Open Family Studies Journal, 4, 81–88.CrossRefGoogle Scholar
  14. Lee, E. J. (2013). Differential susceptibility to the effects of child temperament on maternal warmth and responsiveness. Journal of Genetic Psychology: Research and Theory on Human Development, 174, 429–449.CrossRefGoogle Scholar
  15. Lichstein, K. L., Durrence, H. H., Riedel, B. W., Taylor, D. J., & Bush, A. J. (2004). Epidemiology of sleep: Age, gender, and ethnicity. Mahwah: Erlbaum.Google Scholar
  16. Lubke, G. H., & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21–39. CrossRefGoogle Scholar
  17. McDonald, S. E., Shin, S., Corona, R., Maternick, A., Graham-Bermann, S. A., Ascione, F. R., & Williams, J. H. (2016). Children exposed to intimate partner violence: Identifying differential effects of family environment on children’s trauma and psychopathology symptoms through regression mixture models. Child Abuse & Neglect, 58, 1–11.CrossRefGoogle Scholar
  18. McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: Wiley.CrossRefGoogle Scholar
  19. Moul, D. E., Nofzinger, E. A., Pilkonis, P. A., Houck, P. R., Miewald, J. M., & Buysse, D. J. (2002). Symptom reports in severe chronic insomnia. Sleep, 25, 548–558.CrossRefGoogle Scholar
  20. Muthén, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 345–368). Thousand Oaks: Sage.Google Scholar
  21. Muthén, B., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882–891.CrossRefGoogle Scholar
  22. Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus user’s guide (7th). Los Angeles: Muthén & Muthén.Google Scholar
  23. Ng, S. K., McLachlan, G. J., Wang, K., Ben-Tovim Jones, L., & Ng, S. W. (2006). A mixture model with random-effects components for clustering correlated gene-expression profiles. Bioinformatics, 22, 1745–1752. CrossRefGoogle Scholar
  24. Nilsson, P. M., Rööst, M., Engström, G., Hedblad, B., & Berglund, G. (2004). Incidence of diabetes in middle-aged men is related to sleep disturbances. Diabetes Care, 27, 2464–2469.CrossRefGoogle Scholar
  25. Nylund, K. L., Asparouhov, T., & 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.CrossRefGoogle Scholar
  26. R Core Team. (2017). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from
  27. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd). Thousand Oaks: Sage.Google Scholar
  28. Schmiege, S. J., & Bryan, A. D. (2016). Heterogeneity in the relationship of substance use to risky sexual behavior among justice-involved youth: A regression mixture modeling approach. Aids and Behavior, 20, 821–832.CrossRefGoogle Scholar
  29. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.CrossRefGoogle Scholar
  30. Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333–343.CrossRefGoogle Scholar
  31. Silinskas, G., Kiuru, N., Tolvanen, A., Niemi, P., Lerkkanen, M.-K., & Nurmi, J.-E. (2013). Maternal teaching of reading and children’s reading skills in Grade 1: Patterns and predictors of positive and negative associations. Learning and Individual Differences, 27, 54–66. CrossRefGoogle Scholar
  32. Silinskas, G., Pakarinen, E., Niemi, P., Lerkkanen, M.-K., Poikkeus, A.-M., & Nurmi, J.-E. (2016). The effectiveness of increased support in reading and its relationship to teachers’ affect and children’s motivation. Learning and Individual Differences, 45, 53–64.CrossRefGoogle Scholar
  33. Sperrin, M., Jaki, T., & Wit, E. (2010). Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models. Statistics in Computing, 20, 357–366. CrossRefGoogle Scholar
  34. Taylor, D. J., Mallory, L. J., Lichstein, K. L., Durrence, H. H., Riedel, B. W., & Bush, A. J. (2007). Comorbidity of chronic insomnia with medical problems. Sleep, 30, 213–218.CrossRefGoogle Scholar
  35. Ustinov, Y., Lichstein, K. L., Vander Wal, G. S., Taylor, D. J., Riedel, B. W., & Bush, A. J. (2010). Association between report of insomnia and daytime functioning. Sleep Medicine, 11, 65–68.CrossRefGoogle Scholar
  36. Van Horn, M. L., Jaki, T., Masyn, K., Howe, G., Feaster, D. J., Lamont, A. E., … Kim, M. (2015). Evaluating differential effects using regression interactions and regression mixture models. Educational and Psychological Measurement, 75, 677–714.CrossRefGoogle Scholar
  37. Van Horn, M. L., Smith, J., Fagan, A. A., Jaki, T., Feaster, D. J., Masyn, K., . . . Howe, G. (2012). Not quite normal: Consequences of violating the assumption of normality in regression mixture models. Structural Equation Modeling, 19, 227–249. CrossRefGoogle Scholar
  38. Vitale, J. A., Roveda, E., Montaruli, A., Galasso, L., Weydahl, A., Caumo, A., & Carandente, F. (2014). Chronotype influences activity circadian rhythm and sleep: Differences in sleep quality between weekdays and weekend. Chronobiology International, 32, 405–415. CrossRefGoogle Scholar
  39. Wong, Y. J., Owen, J., & Shea, M. (2012). A latent class regression analysis of men’s conformity to masculine norms and psychological distress. Journal of Counseling Psychology, 59, 176–183. CrossRefGoogle Scholar
  40. Xu, W., & Hedeker, D. (2001). A random-effects mixture model for classifying treatment response in longitudinal clinical trials. Journal of Biopharmaceutical Statistics, 11, 253–273.CrossRefGoogle Scholar
  41. Yau, K. K., Lee, A. H., & Ng, A. S. (2003). Finite mixture regression model with random effects: Application to neonatal hospital length of stay. Computational Statistics and Data Analysis, 41, 359–366.CrossRefGoogle Scholar

Copyright information

© The Psychonomic Society, Inc. 2019

Authors and Affiliations

  • Minjung Kim
    • 1
    Email author
  • M. Lee Van Horn
    • 2
    Email author
  • Thomas Jaki
    • 3
  • Jeroen Vermunt
    • 4
  • Daniel Feaster
    • 5
  • Kenneth L. Lichstein
    • 6
  • Daniel J. Taylor
    • 7
  • Brant W. Riedel
    • 8
  • Andrew J. Bush
    • 9
  1. 1.Department of Educational StudiesOhio State UniversityColumbusUSA
  2. 2.Department of Individual, Family, and Community EducationUniversity of New MexicoAlbuquerqueUSA
  3. 3.Department of Mathematics and StatisticsLancaster UniversityLancasterUK
  4. 4.Department of Methodology and StatisticsTilburg UniversityTilburgThe Netherlands
  5. 5.Department of Public Health Sciences, Division of BiostatisticsUniversity of MiamiMiamiUSA
  6. 6.Department of PsychologyUniversity of AlabamaTuscaloosaUSA
  7. 7.Department of PsychologyUniversity of North TexasDentonUSA
  8. 8.Shelby County SchoolsMemphisUSA
  9. 9.Department of Preventive MedicineUniversity of TennesseeKnoxvilleUSA

Personalised recommendations