Bartolucci, Francesco and Pennoni, Fulvia and Vittadini, Giorgio (2015): Causal latent Markov model for the comparison of multiple treatments in observational longitudinal studies.

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Abstract
We extend to the longitudinal setting a latent class approach that has beed recently introduced by \cite{lanza:et:al:2013} to estimate the causal effect of a treatment. The proposed approach permits the evaluation of the effect of multiple treatments on subpopulations of individuals from a dynamic perspective, as it relies on a Latent Markov (LM) model that is estimated taking into account propensity score weights based on individual pretreatment covariates. These weights are involved in the expression of the likelihood function of the LM model and allow us to balance the groups receiving different treatments. This likelihood function is maximized through a modified version of the traditional expectationmaximization algorithm, while standard errors for the parameter estimates are obtained by a nonparametric bootstrap method. We study in detail the asymptotic properties of the causal effect estimator based on the maximization of this likelihood function and we illustrate its finite sample properties through a series of simulations showing that the estimator has the expected behavior. As an illustration, we consider an application aimed at assessing the relative effectiveness of certain degree programs on the basis of three ordinal response variables when the work path of a graduate is considered as the manifestation of his/her human capital level across time.
Item Type:  MPRA Paper 

Original Title:  Causal latent Markov model for the comparison of multiple treatments in observational longitudinal studies 
English Title:  Causal latent Markov model for the comparison of multiple treatments in observational longitudinal studies 
Language:  English 
Keywords:  Causal inference, ExpectationMaximization algorithm, Hidden Markov models, Multiple treatments, Policy evaluation, Propensity score. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C54  Quantitative Policy Modeling I  Health, Education, and Welfare > I2  Education and Research Institutions > I23  Higher Education ; Research Institutions J  Labor and Demographic Economics > J4  Particular Labor Markets > J44  Professional Labor Markets ; Occupational Licensing 
Item ID:  66492 
Depositing User:  Prof. Fulvia Pennoni 
Date Deposited:  08. Sep 2015 14:53 
Last Modified:  08. Sep 2015 15:34 
References:  Aalen, O. O., Roysland, K., Gran, J. M., and Ledergerber, B. (2012). Causality, mediation and time: a dynamic viewpoint. Journal of the Royal Statistical Society: Series A, 175:831–861. Angrist, J. D. (1991). Groupeddata estimation and testing in simple laborsupply models. Journal of Econometrics, 47:243–266. Arjas, E. (2013). Time to consider time, and time to predict? Statistics in Biosciences, 6:1–15. Bacci, S., Pandolfi, S., and Pennoni, F. (2013). A comparison of some criteria for states selection in the latent Markov model for longitudinal data. Advances in Data Analysis and Classification, 8:125–145. 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. 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. (2013). Latent Markov Models for Longitudinal Data. Chapman & Hall/CRC, Boca Raton, FL. Bartolucci, F., Farcomeni, A., and Pennoni, F. (2014). Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates (with discussion). Test, 23:433–486. Bartolucci, F. and Pennoni, F. (2011). Impact evaluation of job training programs by a latent variable model. In New Perspectives in Statistical Modeling and Data Analysis, pages 65–73. SpringerVerlag, Berlin. Bartolucci, F., Pennoni, F., and Vittadini, G. (2011). Assessment of school performance through a multilevel latent Markov Rasch model. Journal of Educational and Behavioural Statistics, 36:491–522. Baum, L., Petrie, T., Soules, G., and Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics, 41:164–171. Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press, Cambridge, MA. 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. Gao, X. and Song, P. X.K. (2010). Composite likelihood Bayesian information criteria for model selection in high dimensional data. Journal of the American Statistical Association, 105:1531–1540. Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61:215–231. 26 Guo, S. and Fraser, M. W. (2010). Propensity Score Analysis: Statistical Methods and Applications. Sage, Thousand Oaks, CA. Hambleton, R. K. and Swaminathan, H. (1985). Item Response Theory: Principles and Applications. Kluwer Nijhoff, Boston. Harpan, I. and Draghici, A. (2014). Debate on the multilevel model of the human capital measurement. Procedia  Social and Behavioral Sciences, 124:170 – 177. Heckman, J. J. (2000). Policies to foster human capital. Research in Economics, 54:3–56. Hernan, M. A., Brumback, B., and Robins, J. M. (2001). Marginal structural models to estimate the joint causal effect of nonrandomized treatments. Journal of the American Statistical Association, 96:440–448. Hirano, K., Imbens, G. W., and Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 71:1161–1189. Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47:663–685. Imbens, G. W. (2000). The role of the propensity score in estimating doseresponse functions. Biometrika, 87:706–710. Ip, E., Zhang, Q., Rejeski, J., Harris, T., and Kritchevsky, S. (2013). Partially ordered mixed hidden Markov model for the disablement process of older adults. Journal of the American Statistical Association, 108:370–384. Keribin, C. (2000). Consistent estimation of the order of mixture models. Sankhya: The Indian Journal of Statistics, Series A, 62:49–66. Lanza, S. T., Coffman, D. L., and Xu, S. (2013). Causal inference in latent class analysis. Structural Equation Modeling: A Multidisciplinary Journal, 20:361–383. Lazarsfeld, P. F. and Henry, N. W. (1968). Latent Structure Analysis. Houghton Mifflin, Boston. McCaffrey, D. F., Griffin, B. A., Almirall, D., Slaughter, M. E., Ramchand, R., and Burgette, L. F. (2013). A tutorial on propensity score estimation for multiple treatments using generalized boosted models. Statistics in Medicine, 32:3388–3414. McCullagh, P. (1980). Regression models for ordinal data (with discussion). Journal of the Royal Statistical Society, Series B, 42:109–142. McLachlan, G. and Peel, D. (2000). Finite Mixture Models. Wiley, New York. Pennoni, F. (2014). Issues on the Estimation of Latent Variables and Latent Class Models. Scholars’ Press, Saarbucken. 27 Robins, J., Hernan, M., and Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11:550–560. Rosenbaum, P. R. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70:41–55. Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66:688–701. Rubin, D. B. (2005). Causal inference using potential outcomes: design, modeling, decisions. Journal of the American Statistical Association, 100:322–331. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6:461–464. Vermunt, J. K., Langeheine, R., and B ̈ockenholt, U. (1999). Discretetime discretestate latent Markov models with timeconstant and timevarying covariates. Journal of Educational and Behavioral Statistics, 24:179–207. Welch, L. R. (2003). Hidden Markov models and the BaumWelch algorithm. IEEE Information Theory Society Newsletter, 53:1–13. Wiggins, L. (1955). Mathematical models for the analysis of multiwave panels. In Ph.D. Dissertation, Ann Arbor. Columbia University. Zucchini, W. and MacDonald, I. L. (2009). Hidden Markov Models for Time Series: An Introduction Using R. SpringerVerlag, New York. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/66492 