Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?

References

• Bai, X., Yao, W., & Boyer, J. E. (2012). Robust fitting of mixture regression models. Computational Statistics & Data Analysis, 56(7), 2347–2359. doi:10.1016/j.csda.2012.01.016
   Web of Science ®Google Scholar
• Bartolucci, F., & Scaccia, L. (2005). The use of mixtures for dealing with non-normal regression errors. Computational Statistics & Data Analysis, 48(4), 821–834. doi:10.1016/j.csda.2004.04.005
   Web of Science ®Google Scholar
• Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8(3), 338–363.
   PubMed Web of Science ®Google Scholar
• Cicchetti, D., & Rogosch, F. A. (1996). Equifinality and multifinality in developmental psychopathology. Development and Psychopathology, 8(4), 597--600. doi: 10.1017/s0954579400007318
   Google Scholar
• Cleaver, G., & Wedel, M. (2001). Identifying random-scoring respondents in sensory research using finite mixture regression models. Food quality and preference, 12(5/7), 373–384. doi:10.1016/S0950-3293(01)00028-3
   Web of Science ®Google Scholar
• Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829–836.
   Web of Science ®Google Scholar
• Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
   Google Scholar
• Dayton, M., & Macready, G. B. (1988). Concomitant-variable latent-class models. Journal of the American Statistical Association, 83, 173–178. doi:10.2307/2288938
   Web of Science ®Google Scholar
• Desarbo, W. S., Jedidi, K., & Sinha, I. (2001). Customer value analysis in a heterogeneous market. Strategic Management Journal, 22(9), 846. doi:10.1002/smj.191
   Web of Science ®Google Scholar
• Ding, C. (2006). Using regression mixture analysis in educational research. Practical Assessment Research & Evaluation, 11(11), Available online: http://pareonline.net/getvn.asp?v = 11&n = 11.
   Google Scholar
• Dunn, L. M., & Dunn, L. M. (1981). Peabody picture vocabulary test-revised. Circle Pines, MN: American Guidance Service.
   Google Scholar
• Dunst, C. J., & Leet, H. E. (1994). Measuring the adequacy of resources in households with young children. In: C. J. Dunst (ed.) Supporting & strengthening families. Cambridge, MA: Brookline Books Inc. pp. 105--114.
   Google Scholar
• Dunst, C. J., Leet, H. E., & Trivette. C. M. (1988). Family resources, personal well-being, and early intervention. Journal of Special Education, 22, 108--116.
   Google Scholar
• Dyer, W. J., Pleck, J., & McBride, B. (2012). Using mixture regression to identify varying effects: A demonstration with paternal incarceration. Journal of Marriage and Family, 74(5), 1129–1148. doi:10.1111/j.1741-3737.2012.01012.x
   Web of Science ®Google Scholar
• Fagan, A. A., Van Horn, M. L., Hawkins, J., & Jaki, T. (2012). Differential effects of parental controls on adolescent substance use: For whom is the family most important? Journal of Quantitative Criminology, 29(347–368). doi:10.1007/s10940-012-9183-9
   Web of Science ®Google Scholar
• George, M. R. W., Yang, N., Jaki, T., Lamont, A. E., Wilson, D. K., & Van Horn, M. L. (2013). Finite mixtures for simultaneously modeling differential effects and nonnormal distributions. Multivariate Behavioral Research, 48(6), 816–844. doi:10.1080/00273171.2013.830065
   PubMed Web of Science ®Google Scholar
• George, M. R. W., Yang, N., Van Horn, M. L., Smith, J., Jaki, T., Feaster, D. J.,… Howe, G. (2013). Using regression mixture models with non-normal data: Examining an ordered polytomous approach. Journal of Statistical Computation and Simulation, 83(4), 759–772. doi:10.1080/00949655.2011.636363
   Web of Science ®Google Scholar
• Grewal, R., Chandrashekaran, M., Johnson, J., & Mallapragada, G. (2013). Environments, unobserved heterogeneity, and the effect of market orientation on outcomes for high-tech firms. Journal of the Academy of Marketing Science, 41(2), 206–233. doi:10.1007/s11747-011-0295-9
   Web of Science ®Google Scholar
• Ingrassia, S., Minotti, S. C., & Vittadini, G. (2012). Local statistical modeling via a cluster-weighted approach with elliptical distributions. Journal of Classification, 29, 363–401. doi:10.1007/s00357-012-9114-3
   Web of Science ®Google Scholar
• Jaki, T., Kim, M., Lamont, A. E., & Van Horn, M. L. (under review). The effects of sample size on the estimation of regression mixture models.
   Google Scholar
• Jedidi, K., Ramaswamy, V., DeSarbo, W. S., & Wedel, M. (1996). On estimating finite mixtures of multivariate regression and simutaneous equation models. Structural Equation Modeling, 3(3), 266–289. doi:10.1080/10705519609540044
   Web of Science ®Google Scholar
• Liu, M., & Lin, T.-I. (2014). A skew-normal mixture regression model. Educational and Psychological Measurement, 74(1), 139–162. doi:10.1177/0013164413498603
   Web of Science ®Google Scholar
• Manchia, M., Zai, C. C., Squassina, A., Vincent, J. B., De Luca, V., & Kennedy, J. L. (2010). Mixture regression analysis on age at onset in bipolar disorder patients: Investigation of the role of serotonergic genes. European Neuropsychopharmacology, 20(9), 663–670. doi:10.1016/j.euroneuro.2010.04.001
   PubMed Web of Science ®Google Scholar
• McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: John Wiley & Sons, Inc.
   Google Scholar
• Montgomery, K. L., Vaughn, M. G., Thompson, S. J., & Howard, M. O. (2013). Heterogeneity in drug abuse among juvenile offenders: Is mixture regression more informative than standard regression?. International Journal of Offender Therapy and Comparative Criminology, 57(11), 1326–1346. doi:10.1177/0306624×12459185
   PubMed Web of Science ®Google Scholar
• Muthén, B. O. (2006). The potential of growth mixture modelling. Infant and Child Development, 15(6), 623–625. doi:10.1002/icd.482
   Web of Science ®Google Scholar
• Muthén, B. O., & Asparouhov, T. (2009). Multilevel regression mixture analysis. Journal of the Royal Statistical Society, Series A, 172, 639–657. doi:10.1111/j.1467-985X.2009.00589.x
   Web of Science ®Google Scholar
• Muthén, B. O., Brown, C. H., Masyn, K., Jo, B., Khoo, S., Yang, C.,… Liao, J. (2002). General growth mixture modeling for randomized prevention trials. Biostatistics, 3, 459–475. doi:10.1093/biostatistics/3.4.459
   PubMed Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus (Version 7). Los Angeles: Muthén & Muthén.
   Google Scholar
• Nagin, D. S. (2005). Group based modeling of development. Cambridge, MA: Harvard University Press.
   Google Scholar
• Nagin, D. S., Farrington, D. P., & Moffitt, T. E. (1995). Life-course trajectories of different types of offenders. Criminology, 33(1), 111–139. doi:10.1111/j.1745-9125.1995.tb01173.x
   Web of Science ®Google Scholar
• Nowrouzi, B., Souza, R. P., Zai, C., Shinkai, T., Monda, M., Lieberman, J.,… De Luca, V. (2013). Finite mixture regression model analysis on antipsychotics induced weight gain: Investigation of the role of the serotonergic genes. European Neuropsychopharmacology, 23(3), 224–228. doi:10.1016/j.euroneuro.2012.05.008
   PubMed Web of Science ®Google Scholar
• Quandt, R. E. (1972). A new approach to estimating switching regressions. Journal of the American Statistical Association, 67(338), 306. doi:10.2307/2284373
   Google Scholar
• Quandt, R. E., & Ramsey, J. B. (1978). Estimating mixtures of normal distributions and switching regressions. Journal of the American Statistical Association, 73(364), 730. doi:10.2307/2286266
   Web of Science ®Google Scholar
• R Core Team. (2015). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from URL http://www.R-project.org/
   Google Scholar
• Ramey, C. T., Ramey, S. L., & Phillips, M. M. (1996). Head Start children's entry into public school: An interim report on the National Head Start - Public School Early Childhood Transition Demonstration Study. Washington, DC: US Department of Health and Human Services.
   Google Scholar
• Ramey, S. L., Ramey, C. T., Phillips, M. M., Lanzi, R. G., Brezausek, C., Katholi, C. R., & Snyder, S. (2001). Head Start children's entry in public school: A report on the National Head Start/Public School Early Childhood Transition Demonstration Study. Washington, DC: US Department of Health and Human Services.
   Google Scholar
• Sarstedt, M. (2008). Market segmentation with mixture regression models: Understanding measures that guide model selection. Journal of Targeting, Measurement & Analysis for Marketing, 16(3), 228–246. doi:10.1057/jt.2008.9
   Google Scholar
• Schmiege, S., Levin, M., & Bryan, A. (2009). Regression mixture models of alcohol use and risky sexual behavior among criminally-involved adolescents. Prevention Science, 10(4), 335–344. doi:10.1007/s11121-009-0135-z
   PubMed Web of Science ®Google Scholar
• Schwarz, Gideon E. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461--464, doi:10.1214/aos/1176344136
   Google Scholar
• 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. doi:10.1007/s11222-009-9129-8
   Web of Science ®Google Scholar
• Van Horn, M. L., Bellis, J. M., & Snyder, S. W. (2001). Family Resource Scale-Revised: Psychometrics and validation of a measure of family resources in a sample of low-income families. Journal of Psychoeducational Assessment, 19(1), 54–68. doi:10.1177/073428290101900104
   Web of Science ®Google Scholar
• Van Horn, M. L., Jaki, T., Masyn, K., Ramey, S. L., Smith, J. A., & Antaramian, S. (2009). Assessing differential effects: Applying regression mixture models to identify variations in the influence of family resources on academic achievement. Developmental Psychology, 45(5), 1298–1313. doi:10.1037/a0016427
   PubMed Web of Science ®Google Scholar
• 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(2), 227–249. doi:10.1080/10705511.2012.659622
   PubMed Web of Science ®Google Scholar
• Vermunt, J. K., & Magidson, J. (2005). Latent GOLD. Belmont, Massachusetts: Statistical Innovations Inc.
   Google Scholar
• Wedel, M. (2002). Concomitant variables in finite mixture models. Statistica Neerlandica, 56, 362–375. doi:10.1111/1467-9574.t01-1-00072
   Web of Science ®Google Scholar
• Wedel, M., & DeSarbo, W. S. (1994). A review of recent developments in latent class regression models. In R. P. Bagozzi (Ed.), Advanced methods of marketing research (pp. 352–388). Cambridge: Blackwell Publishers.
   Google Scholar
• Wedel, M., & DeSarbo, W. S. (1995). A mixture likelihood approach for generalized linear models. Journal of Classification, 12(1), 21–55. doi:10.1007/bf01202266
   Web of Science ®Google Scholar
• Woodcock, R., & Johnson, M. (1990). Woodcock-Johnson Psycho-Educational Battery-Revised. Allen, TX: DLM Teaching Resources.
   Google Scholar
• Yau, K. K. W., Lee, A. H., & Ng, A. S. K. (2003). Finite mixture regression model with random effects: Application to neonatal hospital length of stay. Computational Statistics & Data Analysis, 41(3–4), 359–366. doi:10.1016/S0167-9473(02)00180-9
   Web of Science ®Google Scholar
• Zhu, H.-T., & Heping, Z. (2004). Hypothesis testing in mixture regression models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(1), 3–16. doi:10.1046/j.1369-7412.2003.05379.x
   Web of Science ®Google Scholar
• Zou, Y., Zhang, Y., & Lord, D. (2013). Application of finite mixture of negative binomial regression models with varying weight parameters for vehicle crash data analysis. Accident Analysis and Prevention, 50, 1042–1051. doi:10.1016/j.aap.2012.08.004
   PubMed Web of Science ®Google Scholar