Regime-Switching Bivariate Dual Change Score Model

Multivariate Behavioral Research

Volumn 48, Issue 4, 2013, Pages 463-502

  Chow, Sy Miin ^a   Grimm, Kevin J ^b   Filteau, Guillaume ^c   Dolan, Conor V ^d   McArdle, John J ^e  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF NORTH CAROLINA   (United States)

^d UNIVERSITY OF AMSTERDAM   (Netherlands)

^e UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84880939610     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1080/00273171.2013.787870     Document Type: Article

References (90)

1. Aiken, L. R. Jr. 1971. Verbal factors and mathematics learning: A review of research. Journal for Research in Mathematics Education, 2: 304 - 313.
2. Aptech Systems Inc. 2009. GAUSS (Version 10) [Computer software manual] Black Diamond, WA: Aptech Systems Inc.
3. Arminger, G. and Muthén, B. 1998. A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, 63: 271 - 300.
4. Asparouhov, T. and Muthén, B. O. 2011. C on C and X (Mplus technical appendix) Los Angeles, CA: Muthén & Muthén.
5. Bartholomew, D. J. and Knott, M. 1999. Latent variable models and factor analysis, 2nd ed. London, UK: Griffin.
6. Boker, S. M., Neale, H., Maes, H., Wilde, M., Spiegel, M., Brick, T. and Fox, J. 2011. OpenMx: An open source extended structural equation modeling framework. Psychometrika, 76: 306 - 317.
7. Carey, S. 2004. Bootstrapping and the origin of concepts. Daedulus, 133: 59 - 68.
8. Cattell, Raymond B. 1963. The interaction of hereditary and environmental influences. The British Journal of Statistical Psychology, 16: 191 - 210.
9. Cattell, R. B. 1971. Abilities: Their structure, growth, and action Boston, MA: Houghton Mifflin.
10. Cho, S., Cohen, A. S., Kim, S. and Bottge, B. 2010. Latent transition analysis with a mixture item response theory measurement model. Applied Psychological Measurement, 34: 483 - 504.
11. Chow, S.-M., Ho, M.-H. R., Hamaker, E. J. and Dolan, C. V. 2010. Equivalences and differences between structural equation and state-space modeling frameworks. Structural Equation Modeling, 17: 303 - 332.
12. Chow, S.-M., Zu, J., Shifren, K. and Zhang, G. 2011. Dynamic factor analysis models with time-varying parameters. Multivariate Behavioral Research, 46: 303 - 339.
13. Collins, L. M. and Wugalter, S. E. 1992. Latent class models for stage-sequential dynamic latent variables. Multivariate Behavioral Research, 28: 131 - 157.
14. Cummins, D. D., Kintsch, W., Reusser, K. and Weimer, R. 1988. The role of understanding in solving word problems. Cognitive Psychology, 20: 405 - 438.
15. Dacco, R. and Satchell, S. 1999. Why do regime-switching models forecast so badly?. Journal of Forecasting, 18: 1 - 16.
16. Dempster, A. P., Laird, N. M. and Rubin, D. B. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39: 1 - 38.
17. Dolan, C. V. 2009. " Structural equation mixture modeling. ". In The SAGE handbook of quantitative methods in psychology Edited by: Millsap, R. E. and Maydeu-Olivares, A. 568 - 592. Thousand Oaks, CA: Sage.
18. Dolan, C. V., Jansen, B. R. and van der Maas, H. L. J. 2004. Constrained and unconstrained multivariate normal finite mixture modeling of piagetian data. Multivariate Behaviorial Research, 39: 69 - 98.
19. Dolan, C. V., Schmittmann, V. D., Lubke, G. H. and Neale, M. C. 2005. Regime switching in the latent growth curve mixture model. Structural Equation Modeling, 12: 94 - 119.
20. Dolan, C. V. and van der Maas, H. L. J. 1998. Fitting multivariate normal finite mixtures subject to structural equation modeling. Psychometrika, 63: 227 - 253.
21. Doornik, J. A. 1998. Object-oriented matrix programming using Ox 2.0 London, UK: Timberlake Consultants Press.
22. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P. and Japel, C. 2007. School readiness and later achievement. Developmental Psychology, 43: 1428 - 1446.
23. Early, D. M., Iruka, I. U., Ritchie, S., Barbarin, O. A., Winn, D. C., Crawford, G. M. and Pianta, R. C. 2010. How do pre-kindergarteners spend their time? Gender, ethnicity, and income as predictors of experiences in pre-kindergarten classrooms. Early Childhood Research Quarterly, 25: 177 - 193.
24. Elliott, R. J., Aggoun, L. and Moore, J. B. 1995. Hidden markov models: Estimation and control New York, NY: Springer.
25. Everitt, B. S. and Hand, D. J. 1981. Finite mixture distributions London, UK: Chapman & Hall.
26. Ferrer, E. and McArdle, J. J. 2004. An experimental analysis of dynamic hypotheses about cognitive abilities and achievement from childhood to early adulthood. Developmental Psychology, 40: 935 - 952.
27. Ferrer, E. and Widaman, K. F. 2008. " Dynamic factor analysis of dyadic affective processes with intergroup differences. ". In Modeling dyadic and interdependent data in the developmental and behavioral sciences Edited by: Card, N. A., Selig, J. and Little, T. 107 - 138. New York, NY: Routledge.
28. Fukuda, K. and Ishihara, K. 1997. Development of human sleep and wakefulness rhythm during the first six months of life: Discontinuous changes at the 7th and 12th week after birth. Biological Rhythm Research, 28: 94 - 103.
29. Gelman, R. and Butterworth, B. 2005. Number and language: How are they related?. Trends in Cognitive Sciences, 9: 6 - 10.
30. Gibson, W. A. 1959. Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 24: 229 - 252.
31. Goldberger, A. S. and Duncan, O. D., eds. 1973. Structural equation models in the social sciences. New York, NY: Academic Press.
32. Grimm, K. J. 2006. A longitudinal dynamic analysis of the impacts of reading on mathematical ability in children and adolescents Charlottesville, VA: University of Virginia. (Unpublished doctoral dissertation)
33. Grimm, K. J. and Ram, N. 2011. " Growth curve modeling from an SEM perspective. ". In Handbook of developmental research methods Edited by: Little, T., Laursen, B. and Card, N. 411 - 431. New York, NY: Guilford Press.
34. Grimm, K. J., Ram, N. and Estabrook, R. 2010. Nonlinear structured growth mixture models in Mplus and OpenMx. Multivariate Behavioral Research, 45: 887 - 909.
35. Hamaker, E. L., Dolan, C. V. and Molenaar, P. C. M. 2003. ARMA-based SEM when the number of time points T exceeds the number of cases N: Raw data maximum likelihood. Structural Equation Modeling, 10: 352 - 379.
36. Hamilton, J. D. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57: 357 - 384.
37. Hamilton, J. D. 1994. Time series analysis Princeton, NJ: Princeton University Press.
38. Henson, J. M., Reise, S. P. and Kim, K. H. 2007. Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling: A Multidisciplinary Journal, 14: 202 - 226. Retrieved from http://www.tandfonline.com/doi/abs/10.1080/10705510709336744. doi: 10.1080/10705510709336744
39. Horn, J. L. and Cattell, R. B. 1966. Refinement and test of the theory of fluid and crystallized general intelligences. Journal of Educational Psychology, 57: 253 - 270.
40. Hosenfeld, B. 1997. Indicators of discontinuous change in the development of analogical reasoning. Journal of Experimental Child Psychology, 64: 367 - 395.
41. Hosmer, D. W. 1974. Maximum likelihood estimates of parameters of a mixture of two regression lines. Communications in Statistics: Theory and Methods, 3: 995 - 1006.
42. Jackson, C. H. 2011. Multi-state models for panel data: The msm package for R. Journal of Statistical Software, 38: 1 - 29. Retrieved from http://www.jstatsoft.org/v38/i08/
43. Jedidi, K., Jagpal, H. S. and DeSarbo, W. S. 1997a. Stemm: A general finite mixture structural equation model. Journal of Classification, 14: 23 - 50. Retrieved from http://dx.doi.org/10.1007/s003579900002. doi: 10.1007/s003579900002
44. Jedidi, K., Jagpal, H. S. and DeSarbo, W. S. 1997b. Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16: 39 - 59.
45. Kaplan, D. 2008. An overview of Markov chain methods for the study of stage-sequential developmental processes. Developmental Psychology, 44: 457 - 467.
46. Kim, C.-J. and Nelson, C. R. 1999. State-space models with regime switching: Classical and Gibbs-sampling approaches with applications. Cambridge, MA: MIT Press.
47. Kohlberg, L. and Kramer, R. 1969. Continuities and discontinuities in childhood and adult moral development. Human Development, 12: 3 - 120.
48. Lanza, S. T. and Collins, L. M. 2008. A new SAS procedure for latent transition analysis: Transitions in dating and sexual risk behavior. Developmental Psychology, 44: 446 - 456.
49. Lanza, S. T., Patrick, M. E. and Maggs, J. L. 2010. Latent transition analysis: Benefits of a latent variable approach to modeling transitions in substance use. Journal of Drug Issues, 40: 93 - 120.
50. Lazarsfeld, P. F. and Henry, N. W. 1968. Latent structure analysis Boston, MA: Houghton Mifflin.
51. Lubke, G. H. 2005. Investigating population heterogeneity with factor mixture models. Psychological Methods, 10: 21 - 39.
52. Lubke, G. H. and Muthén, B. O. 2007. Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling, 14: 26 - 47.
53. Marsh, H. W. 1989. Sex differences in the development of verbal and mathematics constructs: The high school and beyond study. American Educational Research Journal, 26: 191 - 225.
54. McArdle, J. J. and Grimm, K. J. 2010. " Five steps in latent curve and latent change score modeling with longitudinal data. ". In Longitudinal research with latent variables Edited by: van Montfort, K., Oud, J. and Satorra, A. 245 - 274. Heidelberg, Germany: Springer-Verlag.
55. McArdle, J. J. and Hamagami, F. 2001. " Latent difference score structural models for linear dynamic analysis with incomplete longitudinal data. ". In New methods for the analysis of change Edited by: Collins, L. and Sayer, A. 139 - 175. Washington, DC: American Psychological Association.
56. McLachlan, G. and Peel, D. 1995. Finite mixture models New York, NY: Wiley.
57. Mercer, J. 1998. Infant development: A multidisciplinary introduction Pacific Grove, CA: Brooks/Cole.
58. Mix, K. S., Huttenlocher, J. and Levine, S. C. 2002. Quantitative development in infancy and early childhood New York, NY: Oxford University Press.
59. Monroe, W. S. and Englehart, M. D. 1931. A critical summary of research relating to the teaching of arithmetic Vol. 58, Urbana, IL: University of Illinois.
60. Muscio, R. D. 1962. Factors related to quantitative understanding in the sixth grade. Arithmetic Teacher, 9: 258 - 262.
61. Muthén, B. O. 2001. " Latent variable mixture modeling. ". In New developments and techniques in structural equation modeling Edited by: Marcoulides, G. A. and Schumaker, R. E. 1 - 33. Mahwah, NJ: Erlbaum.
62. Muthén and Bengt, O. Beyond SEM: General latent variable modeling. Behaviormetrika, 29 81 - 117.
63. Muthén, B. O. and Asparouhov, T. July 2011. LTA in Mplus: Transition probabilities influenced by covariates July, Los Angeles, CA: Muthén & Muthén. (Mplus Web Notes: No. 13)
64. Muthén, B. O. and Shedden, K. 1992. Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55: 463 - 469.
65. Muthén, L. K. and Muthén, B. O. 2001. Mplus: The comprehensive modeling program for applied researchers. User's guide. Los Angeles, CA: Author.
66. 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.
67. National Institute of Child Health and Human Development Early Child Care Research Network. 2005. A day in third grade: A large-scale study of classroom quality and teacher and student behavior. The Elementary School Journal, 105: 305 - 323.
68. 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. Retrieved from http://www.scopus.com/record/display.urlquest;view=extended&origin=resultslist&eid=2-s2.0-36849091981
69. Nylund-Gibson, K., Muthén, B., Nishina, A., Bellmore, A. and Graham, S. Stability and instability of peer victimization during middle school: Using latent transition analysis with covariates, distal outcomes, and modeling extensions (under review)
70. Piaget, J. and Inhelder, B. 1969. The psychology of the child New York, NY: Basic Books.
71. Pianta, R. C., Belsky, J., Houts, R. and Morrison, F. 2007. Opportunities to learn in America's elementary classrooms. Science, 315: 1795 - 1796.
72. R Development Core Team. 2009. R: A language and environment for statistical computing [Computer software manual] Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org(ISBN 3-900051-07-0)
73. SAS Institute Inc. 2008. SAS 9.2 Help and Documentation [Computer software manual] Cary, NC: Author.
74. Schmittmann, V. D., Dolan, C. V., van der Maas, H. and Neale, M. C. 2005. Discrete latent Markov models for normally distributed response data. Multivariate Behavioral Research, 40: 207 - 233.
75. Skaalvik, E. M. and Rankin, R. J. 1990. Math, verbal, and general academic self-concept: The internal/external frame of reference model and gender differences in self-concept structure. Journal of Educational Psychology, 82: 546 - 554.
76. Snow, C. E., Burns, S. M. and Griffin, P., eds. 1998. Preventing reading difficulties in young children Washington, DC: National Academy Press.
77. Tiao, G. C. and Tsay, R. S. 1994. Some advances in non-linear and adaptive modelling in time-series. Journal of Forecasting, 13: 109 - 131.
78. Titterington, D. M., Smith, A. F. M. and Makov, U. E. 1985. Statistical analysis of finite mixture distributions Chichester, UK: Wiley.
79. Tong, H. and Lim, K. S. 1980. Threshold autoregression, limit cycles and cyclical data. Journal of the Royal Statistical Society, Series B, 42: 245 - 292.
80. Tueller, S. and Lubke, G. 2010. Evaluation of structural equation mixture models: Parameter estimates and correct class assignment. Structural Equation Modeling, 17: 165 - 192. doi: 10.1080/10705511003659318
81. U.S. Department of Education, Office of the Deputy Secretary. 2004. No child left behind: A toolkit for teachers Washington, DC
82. U.S. Department of Education, National Center for Education Statistics. 2010. Early childhood longitudinal study, kindergarten class of 1998-99 (ECLS-K) kindergarten through fifth grade approaches to learning and self-description questionnaire (SDQ) items and public-use data files (nces 2010-070). Washington, DC: Author.
83. Van der Maas, H. L. J., Dolan, C. V., Grasman, R., Wicherts, J. M., Huizenga, H. M. and Raijmakers, M. 2006. A dynamical model of general intelligence: The positive manifold of intelligence by mutualism. Psychological Review, 113: 842 - 861.
84. Van der Maas, H. L. J. and Molenaar, P. C. M. 1992. Stagewise cognitive development: An application of catastrophe theory. Psychological Review, 99: 395 - 417.
85. Van Dijk, M. and Van Geert, P. 2007. Wobbles, humps and sudden jumps: A case study of continuity, discontinuity and variability in early language development. Infant and Child Development, 16: 7 - 33.
86. Vermunt, J. K. and Magidson, J. 2005. " Structural equation models: Mixtrue models. ". In Encyclopedia of statistics in behavioral science Edited by: Everitt, B. and Howell, D. 1922 - 1927. Chichester, UK: Wiley.
87. Visser, I. 2007. Depmix: An R-package for fitting mixture models on mixed multivariate data with Markov dependencies (Tech. Rep.) University of Amsterdam. Retrieved from http://cran.r-project.org
88. Wrigley, C., Saunders, D. and Neuhaus, J. O. 1958. Applications of the quartimax method of rotation to Thurstone's priamry mental abilities study. Pyschometricka, 23: 151 - 168.
89. Yang, M. and Chow, S.-M. 2010. Using state-space model with regime switching to represent the dynamics of facial electromyography (emg) data. Psychometrika, 74: 744 - 771.
90. Yung, Y. F. 1997. Finite mixtures in confirmatory factor-analysis models. Psychometrika, 62: 297 - 330.