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Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison

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  • Pennoni, Fulvia
  • Romeo, Isabella

Abstract

We propose a short review between two alternative ways of modeling stability and change of longitudinal data when time-fixed and time-varying covariates referred to the observed individuals are available. They both build on the foundation of the finite mixture models and are commonly applied in many fields. They look at the data by a different perspective and in the literature they have not been compared when the ordinal nature of the response variable is of interest. The latent Markov model is based on time-varying latent variables to explain the observable behavior of the individuals. The model is proposed in a semi-parametric formulation as the latent Markov process has a discrete distribution and it is characterized by a Markov structure. The growth mixture model is based on a latent categorical variable that accounts for the unobserved heterogeneity in the observed trajectories and on a mixture of normally distributed random variable to account for the variability of growth rates. To illustrate the main differences among them we refer to a real data example on the self reported health status.

Suggested Citation

  • Pennoni, Fulvia & Romeo, Isabella, 2016. "Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison," MPRA Paper 72939, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72939
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    References listed on IDEAS

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    2. Lu, Tong-Yu & Poon, Wai-Yin & Tsang, Yim-Fan, 2011. "Latent growth curve modeling for longitudinal ordinal responses with applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1488-1497, March.
    3. Francesco Bartolucci & Silvia Bacci & Fulvia Pennoni, 2014. "Longitudinal analysis of self-reported health status by mixture latent auto-regressive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 267-288, February.
    4. R. C. H. Cheng & W. B. Liu, 2001. "The Consistency of Estimators in Finite Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 603-616, December.
    5. Bengt Muthén & Kerby Shedden, 1999. "Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm," Biometrics, The International Biometric Society, vol. 55(2), pages 463-469, June.
    6. Ledyard Tucker, 1958. "Determination of parameters of a functional relation by factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(1), pages 19-23, March.
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    8. William Meredith & John Tisak, 1990. "Latent curve analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 107-122, March.
    9. 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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    Cited by:

    1. Marco Guerra & Francesca Bassi & José G. Dias, 2020. "A Multiple-Indicator Latent Growth Mixture Model to Track Courses with Low-Quality Teaching," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 147(2), pages 361-381, January.
    2. Francesco Dotto & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "A dynamic inhomogeneous latent state model for measuring material deprivation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 495-516, February.
    3. 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.
    4. Giovanni Piumatti, 2020. "Longitudinal Trends in Self-Rated Health During Times of Economic Uncertainty in Italy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 148(2), pages 599-633, April.

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    More about this item

    Keywords

    Dynamic factor model; Expectation-Maximization algorithm; Forward-Backward recursions; Latent trajectories; Maximum likelihood; Monte Carlo methods.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • I11 - Health, Education, and Welfare - - Health - - - Analysis of Health Care Markets
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior

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