We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects 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 expectation–maximization 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 in which the work path of a graduate is considered as the manifestation of his or her human capital-level across time.

Bartolucci, F., Pennoni, F., & Vittadini, G. (2016). Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies. JOURNAL OF EDUCATIONAL AND BEHAVIORAL STATISTICS, 41(2), 146-179 [10.3102/1076998615622234].

Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies

PENNONI, FULVIA;VITTADINI, GIORGIO
2016

Abstract

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects 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 expectation–maximization 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 in which the work path of a graduate is considered as the manifestation of his or her human capital-level across time.
Articolo in rivista - Articolo scientifico
Scientifica
causal inference; expectation–maximization algorithm; hidden Markov models; multiple treatments; policy evaluation; propensity score;
causal inference; expectation–maximization algorithm; hidden Markov models; multiple treatments; policy evaluation; propensity score
English
https://mpra.ub.uni-muenchen.de/66492/
Bartolucci, F., Pennoni, F., & Vittadini, G. (2016). Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies. JOURNAL OF EDUCATIONAL AND BEHAVIORAL STATISTICS, 41(2), 146-179 [10.3102/1076998615622234].
Bartolucci, F; Pennoni, F; Vittadini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/108503
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