5,532
Views
21
CrossRef citations to date
0
Altmetric
Articles

On the Use of Mixed Markov Models for Intensive Longitudinal Data

, ORCID Icon, , , &

References

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. doi: s10.1109/TAC.1974.1100705
  • Albert, J. H., & Chib, S. (1993). Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts. Journal of Business & Economic Statistics, 11(1), 1–15. doi: 10.1080/07350015.1993.10509929
  • Altman, R. M. K. (2007). Mixed hidden Markov models. Journal of the American Statistical Association, 102(477), 201–210. doi: 10.1198/016214506000001086
  • Bacci, S., Pandolfi, S., & Pennoni, F. (2014). A comparison of some criteria for states selection in the latent Markov model for longitudinal data. Advances in Data Analysis and Classification, 8(2), 125–145. doi: 10.1007/s11634-013-0154-2
  • Bartolucci, F., Farcomeni, A., & Pennoni, F. (2013). Latent Markov models for longitudinal data. Boca Raton, FL: Chapman & Hall/CRC.
  • 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. doi: 10.1037/1082-989X.8.3.338
  • Bergeman, C. S., & Deboeck, P. R. (2014). Trait stress resistance and dynamic stress dissipation on health and well-being: The reservoir model. Research in Human Development, 11(2), 108–125. doi: 10.1080/15427609.2014.906736
  • Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M. A., Guo, J., Li, P., & Riddell, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1), 1–32. doi: 10.18637/jss.v076.i01
  • Celeux, G. (1998). Bayesian inference for mixture: The label switching problem. In R. Payne & P. Green (Eds.), Compstat: Proceedings in Computational Statistics 13th Symposium held in Bristol, Great Britain, 1998, (pp. 227–232), Heidelberg: Physica-Verlag HD
  • Celeux, G., Forbes, F., Robert, C. P., & Titterington, D. M. (2006). Deviance information criteria for missing data models. Bayesian Analysis, 1(4), 651–673. doi: 10.1214/06-BA122
  • Celeux, G., Hurn, M., & Robert, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association, 95(451), 957–970. doi: 10.1080/01621459.2000.10474285
  • Crayen, C., Eid, M., Lischetzke, T., Courvoisier, D. S., & Vermunt, J. K. (2012). Exploring dynamics in mood regulation – Mixture Latent Markov modeling of ambulatory assessment data. Psychosomatic Medicine, 74(4), 366–376. doi: 10.1097/PSY.0b013e31825474cb
  • de Haan-Rietdijk, S., Gottman, J. M., Bergeman, C. S., & Hamaker, E. L. (2016). Get over it! A multilevel threshold autoregressive model for state-dependent affect regulation. Psychometrika, 81, 217–241. doi: 10.1007/s11336-014-9417-x
  • Deboeck, P. R., & Preacher, K. J. (2016). No need to be discrete: A method for continuous time mediation analysis. Structural Equation Modeling: A Multidisciplinary Journal, 23(1), 61–75. doi: 10.1080/10705511.2014.973960
  • DeSantis, S. M., & Bandyopadhyay, D. (2011). Hidden Markov models for zero-inflated Poisson counts with an application to substance use. Statistics in Medicine, 30(14), 1678–1694. doi: 10.1002/sim.4207
  • Dormann, C., & Griffin, M. A. (2015). Optimal time lags in panel studies. Psychological Methods, 20(4), 489–505. doi: 10.1037/met0000041
  • Fiorentini, G., Planas, C., & Rossi, A. (2016). Skewness and kurtosis of multivariate Markov-switching processes. Computational Statistics & Data Analysis, 100, 153–159. doi: 10.1016/j.csda.2015.06.009
  • Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. New York, NY: Springer Science and Business Media.
  • Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515–534. doi: 10.1214/06-BA117A
  • Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y. S. (2008). A weakly informative default prior distribution for logistic and other regression models. The Annals of Applied Statistics, 2(4), 1360–1383. doi: 10.2307/30245139
  • Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711–732. doi: 10.2307/2337340
  • Hamaker, E. L., Ceulemans, E., Grasman, R. P. P. P., & Tuerlinckx, F. (2015). Modeling affect dynamics: State of the art and future challenges. Emotion Review, 7(4), 316–322. doi: 10.1177/1754073915590619
  • Hamaker, E. L., Grasman, R. P. P. P., & Kamphuis, J. H. (2016). Modeling BAS dysregulation in bipolar disorder: Illustrating the potential of time series analysis. Assessment, 23(4), 436–446. doi: 10.1177/1073191116632339
  • Harris, G. R. (1997). Regime switching vector autoregressions: A Bayesian Markov chain Monte Carlo approach. Proceedings of the 7th International AFIR Colloquium, Cairns, Australia, vol. 1, pp. 421–451.
  • Haslam, N., Holland, E., & Kuppens, P. (2012). Categories versus dimensions in personality and psychopathology: A quantitative review of taxometric research. Psychological Medicine, 42(5), 903–920. doi: 10.1017/S0033291711001966
  • Hops, H., Biglan, A., Tolman, A., Arthur, J., & Longoria, N. (1995). Living in family environments (Life) coding system: Manual for coders (revised). Eugene, OR: Oregon Research Institute.
  • Hox, J. J. (2010). Multilevel analysis. Techniques and applications (2nd ed.). Oxford: Routledge.
  • Humphreys, K. (1998). The latent Markov chain with multivariate random effects. Sociological Methods & Research, 26(3), 269–299. doi: 10.1177/0049124198026003001
  • Jackson, C. H. (2014). Multi-state modelling with R: The msm package. Version 1.3.2. [Computer software manual]. Retrieved from https://cran.r-project.org/package=msm
  • Jackson, J. C., Albert, P. S., & Zhang, Z. (2015). A two-state mixed hidden Markov model for risky teenage driving behavior. The Annals of Applied Statistics, 9(2), 849–865. doi: 10.1214/14-AOAS765
  • Jasra, A., Holmes, C. C., & Stephens, D. A. (2005). Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistical Science, 20(1), 50–67. doi: 10.2307/20061160
  • Kaplan, D. (2008). An overview of Markov chain methods for the study of stage-sequential developmental processes. Developmental Psychology, 44(2), 457–467. doi: 10.1037/0012-1649.44.2.457
  • Karlin, S., & Taylor, H. M. (1975). A first course in stochastic processes. New York, USA: Academic Press.
  • Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795. doi: 10.1080/01621459.1995.10476572
  • Kim, C.-J., & Nelson, C. R. (1999). State-space models with regime switching: Classical and Gibbs-sampling approaches with applications (2nd ed.). Cambridge, MA: MIT Press.
  • Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Cambridge, MA: Academic Press.
  • Kuppens, P., Allen, N. B., & Sheeber, L. B. (2010). Emotional inertia and psychological maladjustment. Psychological Science, 21(7), 984–991. doi: 10.1177/0956797610372634
  • Langeheine, R., & Van de Pol, F. (2002). Latent Markov chains. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 304–341). Cambridge: Cambridge University Press.
  • Larson, R., & Csikszentmihalyi, M. (1983). The experience sampling method. In H. T. Reis (Ed.), Naturalistic approaches to studying social interaction. New directions for methodology of social and behavioral science, Vol. 15. San Francisco: Jossey-Bass, 41–56.
  • Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGS project: Evolution, critique and future directions. Statistics in Medicine, 28(25), 3049–3067. doi: 10.1002/sim.3680
  • Lynch, S. M. (2007). Introduction to applied Bayesian statistics and estimation for social scientists. New York, NY: Springer Verlag.
  • MacDonald, I. L., & Zucchini, W. (2009). Hidden Markov models for time series: An introduction using R. Boca Raton, FL: Chapman & Hall/CRC.
  • Maruotti, A. (2011). Mixed hidden Markov models for longitudinal data: An overview. International Statistical Review, 79(3), 427–454. doi: 10.1111/j.1751-5823.2011.00160.x
  • Maruotti, A., & Rocci, R. (2012). A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption. Statistics in Medicine, 31(9), 871–886. doi: 10.1002/sim.4478
  • Maruotti, A., & Rydén, T. (2009). A semiparametric approach to hidden Markov models under longitudinal observations. Statistics and Computing, 19(4), 381–393. doi: 10.1007/s11222-008-9099-2
  • Muthén, L. K., & Muthén, B. O. (1998–2015). Mplus user’s guide (7th ed.), [Computer software manual]. Los Angeles, CA. Retrieved from https://www.statmodel.com/download/usersguide/Mplus%20user%20guide%20Ver_7_r6_web.pdf.
  • 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(4), 535–569. doi: 10.1080/10705510701575396
  • Plummer, M. (2013a). JAGS Version 3.4.0 user manual [Computer software manual]. Retrieved from http://mcmc-jags.sourceforge.net/.
  • Plummer, M. (2013b). Package ‘rjags’. The Comprehensive R Archive Network [Computer software manual]. Retrieved from http://cran.r-project.org/.
  • Prisciandaro, J. J., DeSantis, S. M., Chiuzan, C., Brown, D. G., Brady, K. T., & Tolliver, B. K. (2012). Impact of depressive symptoms on future alcohol use in patients with co-occurring bipolar disorder and alcohol dependence: A prospective analysis in an 8-week randomized controlled trial of acamprosate. Alcoholism: Clinical and Experimental Research, 36(3), 490–496. doi: 10.1111/j.1530-0277.2011.01645.x
  • R Development Core Team (2012). R: A Language and Environment for Statistical Computing [Computer software manual]. Vienna, Austria. Retrieved from http://www.R-project.org/.
  • Reichardt, C. S. (2011). Commentary: Are three waves of data sufficient for assessing mediation? Multivariate Behavioral Research, 46(5), 842–851. doi: 10.1080/00273171.2011.606740
  • Richardson, S., & Green, P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59(4), 731–792. doi: 10.1111/1467-9868.00095
  • Rijmen, F., Ip, E. H., Rapp, S., & Shaw, E. G. (2008a). Qualitative longitudinal analysis of symptoms in patients with primary and metastatic brain tumours. Journal of the Royal Statistical Society: Series A (Statistics in Society), 171(3), 739–753. doi: 10.1111/j.1467-985X.2008.00529.x
  • Rijmen, F., Vansteelandt, K., & De Boeck, P. (2008b). Latent class models for diary method data: Parameter estimation by local computations. Psychometrika, 73(2), 167–182. doi: 10.1007/s11336-007-9001-8
  • Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177. doi: 10.1037/1082-989X.7.2.147
  • Schuurman, N. K., Grasman, R. P. P. P., & Hamaker, E. L. (2016). A comparison of Inverse-Wishart prior specifications for covariance matrices in multilevel autoregressive models. Multivariate Behavioral Research, 51(2–3), 185–206. doi: 10.1080/00273171.2015.1065398
  • Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. doi: 10.1214/aos/1176344136
  • Seltman, H. J. (2002). Hidden Markov models for analysis of biological rhythm data. In C. Gatsonis, R. E. Kass, B. Carlin, A. Carriquiry, A. Gelman, I. Verdinelli, & M. West (Eds.), Case studies in Bayesian statistics (Vol. V, pp. 397–405). New York, NY: Springer.
  • Sheeber, L. B., Allen, N. B., Leve, C., Davis, B., Shortt, J. W., & Katz, L. F. (2009). Dynamics of affective experience and behavior in depressed adolescents. Journal of Child Psychology and Psychiatry, 50(11), 1419–1427. doi: 10.1111/j.1469-7610.2009.02148.x
  • Shirley, K. E., Small, D. S., Lynch, K. G., Maisto, S. A., & Oslin, D. W. (2010). Hidden Markov models for alcoholism treatment trial data. The Annals of Applied Statistics, 4(1), 366–395. doi: 10.2307/27801591
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 64(4), 583–639. doi: 10.1111/1467-9868.00353
  • Stephens, M. (2000). Dealing with label switching in mixture models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(4), 795–809. doi: 10.1111/1467-9868.00265
  • Van der Maas, H. L., & Molenaar, P. C. (1992). Stagewise cognitive development: An application of catastrophe theory. Psychological Review, 99(3), 395–417. doi: 10.1037/0033-295X.99.3.395
  • Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413–1432. doi: 10.1007/s11222-016-9696-4
  • Vermunt, J. K., Langeheine, R., & Bockenholt, U. (1999). Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. Journal of Educational and Behavioral Statistics, 24(2), 179–207. doi: 10.3102/10769986024002179
  • Visser, I. (2011). Seven things to remember about hidden Markov models: A tutorial on Markovian models for time series. Journal of Mathematical Psychology, 55(6), 403–415. doi: 10.1016/j.jmp.2011.08.002
  • Wagenmakers, E.-J., Farrell, S., & Ratcliff, R. (2004). Estimation and interpretation of 1/fα noise in human cognition. Psychonomic Bulletin & Review, 11(4), 579–615. doi: 10.3758/BF03196615
  • Wall, M. M., & Li, R. (2009). Multiple indicator hidden Markov model with an application to medical utilization data. Statistics in Medicine, 28(2), 293–310. doi: 10.1002/sim.3463
  • Walls, T. A., & Schafer, J. L. (2006). Models for intensive longitudinal data. USA: Oxford University Press.
  • Warren, K., Hawkins, R. C., & Sprott, J. C. (2003). Substance abuse as a dynamical disease: Evidence and clinical implications of nonlinearity in a time series of daily alcohol consumption. Addictive Behaviors, 28(2), 369–374. doi: 10.1016/S0306-4603(01)00234-9
  • Watson, D., Clark, L. A., & Tellegen, A. (1988). Development and validation of brief measures of positive and negative affect: The PANAS scales. Journal of Personality and Social Psychology, 54(6), 1063–1070. doi: 10.1037/0022-3514.54.6.1063
  • Whitehead, B. R., & Bergeman, C. S. (2014). Ups and downs of daily life: Age effects on the impact of daily appraisal variability on depressive symptoms. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 69(3), 387–396. doi: 10.1093/geronb/gbt019
  • Zhang, Q., Snow Jones, A., Rijmen, F., & Ip, E. H. (2010). Multivariate discrete hidden Markov models for domain-based measurements and assessment of risk factors in child development. Journal of Computational and Graphical Statistics, 19(3), 746–765. doi: 10.1198/jcgs.2010.09015