Bartolucci, Francesco and Lupparelli, Monia (2012): Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data.
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In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we propose an approach based on nested hidden (latent) Markov chains, which are associated to every sample unit and to every cluster. The approach allows us to account for the mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation which may arise between the responses provided by the units belonging to the same cluster. Given the complexity in computing the manifest distribution of these response variables, we make inference on the proposed model through a composite likelihood function based on all the possible pairs of subjects within every cluster. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed.
|Item Type:||MPRA Paper|
|Original Title:||Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data|
|Keywords:||composite likelihood, EM algorithm, latent Markov model, pairwise likelihood|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C33 - Models with Panel Data; Longitudinal Data; Spatial Time Series
|Depositing User:||Francesco Bartolucci|
|Date Deposited:||09. Aug 2012 12:45|
|Last Modified:||15. Feb 2013 21:23|
Bartolucci, F. (2006). Likelihood inference for a class of latent markov models under linear hypotheses on the transition probabilities. Journal of the Royal Statistical Society, series B, 68:155–178.
Bartolucci, F., Bacci, S., and Pennoni, F. (2010a). Mixture latent autoregressive models for longitudinal data. Technical Report 1108.1498v1, arXiv.
Bartolucci, F. and Farcomeni, A. (2009). A multivariate extension of the dynamic logit model for longitudinal data based on a latent markov heterogeneity structure. Journal of the American Statistical Association, 104:816–831.
Bartolucci, F., Farcomeni, A., and Pennoni, F. (2010b). An overview of latent markov models for longitudinal categorical data. Statistical Science, submitted.
Bartolucci, F., Lupparelli, M., and Montanari, G. E. (2009). Latent markov model for bi- nary longitudinal data: an application to the performance evaluation of nursing homes. Annals of Applied Statistics, 3:611–636.
Bartolucci, F. and Nigro, V. (2007). Maximum likelihood estimation of an extended latent markov model for clustered binary panel data. Computational Statistics and Data Analysis, 51:3470–3483.
Bartolucci, F., Pennoni, F., and Vittadini, G. (2011). Assessment of school performance through a multilevel latent Markov Rasch model. Journal of Educational and Be- havioural Statistics, 36:491–522.
Baum, L., Petrie, T., Soules, G., and Weiss, N. (1970). A maximization technique occur- ring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics, 41:164–171.
Cox, D. R. and Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika, 91:729–737. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977).
Maximum likelihood from incomplete data via the em algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39:1–38.
Diggle, P. J., Heagerty, P., Liang, K.-Y., and Zeger, S. L. (2002). Analysis of Longitudinal Data. Oxford University Press, New York.
Fitzmaurice, G., Davidian, M., Verbeke, G., and Molenberghs, G. (2009). Longitudinal data analysis. Chapman and Hall, CRC, London.
Frees, E. W. (2004). Longitudinal and Panel Data: Analysis and Applications in the Social Sciences. Cambridge University Press, Cambridge.
Heiss, F. (2008). Sequential numerical integration in nonlinear state space models for microeconometric panel data. Journal of Applied Econometrics, 23:373–389.
Hjort, N. L. and Varin, C. (2008). Ml, pl, ql in markov chain models. Scandinavian Journal of Statistics, 35:64–82.
Hsiao, C. (2003). Analysis of Panel Data. Cambridge University Press, New York.
Levinson, S. E., Rabiner, L. R., and Sondhi, M. M. (1983). An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition. Bell System Technical Journal, 62:1035–1074.
Lindsay, B. (1988). Composite likelihood methods. In Prabhu, N., editor, Statistical Inference from Stochastic Process, pages 221–239, Providence. American Mathematical Society.
MacDonald, I. L. and Zucchini, W. (1997). Hidden Markov and other Models for Discrete- Valued Time Series. Chapman and Hall, London.
Maruotti, A. (2011). Mixed hidden markov models for longitudinal data: An overview. International Statistical Review, 79:427–454.
Renard, D., Molenberghs, G., and Geys, H. (2004). A pairwise likelihood approach to estimation in multilevel probit models. Computational Statistics and Data Analysis, 44:649–667.
van de Pol, F. and Langeheine, R. (1990). Mixed markov latent class models. Sociological Methodology, 20:213–247.
Varin, C. and Czado, C. (2010). A mixed autoregressive probit model for ordinal longi- tudinal data. Biostatistics, 11:127–138.
Varin, C. and Vidoni, P. (2005). A note on the composite likelihood inference and model selection. Biometrika, 92:519–528.