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

Author

Listed:
  • Francesco Bartolucci

    (University of Perugia)

  • Fulvia Pennoni

    (University of Milano–Bicocca)

  • Giorgio Vittadini

    (University of Milano–Bicocca)

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.

Suggested Citation

  • Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2016. "Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 146-179, April.
  • Handle: RePEc:sae:jedbes:v:41:y:2016:i:2:p:146-179
    DOI: 10.3102/1076998615622234
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    References listed on IDEAS

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    10. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Rejoinder on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 484-486, September.
    11. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
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    13. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
    14. Gao, Xin & Song, Peter X.-K., 2010. "Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1531-1540.
    15. Hernan M. A & Brumback B. & Robins J. M, 2001. "Marginal Structural Models to Estimate the Joint Causal Effect of Nonrandomized Treatments," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 440-448, June.
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    Cited by:

    1. Fulvia Pennoni & Ewa Genge, 2020. "Analysing the course of public trust via hidden Markov models: a focus on the Polish society," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 399-425, June.
    2. Pantelis Samartsidis & Shaun R. Seaman & Silvia Montagna & André Charlett & Matthew Hickman & Daniela De Angelis, 2020. "A Bayesian multivariate factor analysis model for evaluating an intervention by using observational time series data on multiple outcomes," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1437-1459, October.
    3. Antonello Maruotti & Jan Bulla & Tanya Mark, 2019. "Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 19-42, April.
    4. Tullio, Federico & Bartolucci, Francesco, 2019. "Evaluating time-varying treatment effects in latent Markov models: An application to the effect of remittances on poverty dynamics," MPRA Paper 91459, University Library of Munich, Germany.
    5. F. J. Clouth & S. Pauws & F. Mols & J. K. Vermunt, 2022. "A new three-step method for using inverse propensity weighting with latent class analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 351-371, June.
    6. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2023. "A Causal Latent Transition Model With Multivariate Outcomes and Unobserved Heterogeneity: Application to Human Capital Development," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 387-419, August.

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    More about this item

    Keywords

    causal inference; expectation–maximization algorithm; hidden Markov models; multiple treatments; policy evaluation; propensity score;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • I23 - Health, Education, and Welfare - - Education - - - Higher Education; Research Institutions
    • J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

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