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Longitudinal analysis of self-reported health status by mixture latent auto-regressive models

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  • Francesco Bartolucci
  • Silvia Bacci
  • Fulvia Pennoni

Abstract

type="main" xml:id="rssc12030-abs-0001"> Motivated by an application to a longitudinal data set coming from the Health and Retirement Study about self-reported health status, we propose a model for longitudinal data which is based on a latent process to account for the unobserved heterogeneity between sample units in a dynamic fashion. The latent process is modelled by a mixture of auto-regressive AR(1) processes with different means and correlation coefficients, but with equal variances. We show how to perform maximum likelihood estimation of the proposed model by the joint use of an expectation–maximization algorithm and a Newton–Raphson algorithm, implemented by means of recursions developed in the hidden Markov model literature. We also introduce a simple method to obtain standard errors for the parameter estimates and suggest a strategy to choose the number of mixture components. In the application the response variable is ordinal; however, the approach may also be applied in other settings. Moreover, the application to the self-reported health status data set allows us to show that the model proposed is more flexible than other models for longitudinal data based on a continuous latent process. The model also achieves a goodness of fit that is similar to that of models based on a discrete latent process following a Markov chain, while retaining a reduced number of parameters. The effect of different formulations of the latent structure of the model is evaluated in terms of estimates of the regression parameters for the covariates.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssc:v:63:y:2014:i:2:p:267-288
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    File URL: http://hdl.handle.net/10.1111/rssc.2014.63.issue-2
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    References listed on IDEAS

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    7. Mansyur, Carol & Amick, Benjamin C. & Harrist, Ronald B. & Franzini, Luisa, 2008. "Social capital, income inequality, and self-rated health in 45 countries," Social Science & Medicine, Elsevier, vol. 66(1), pages 43-56, January.
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    9. Francesco Bartolucci, 2005. "Clustering Univariate Observations via Mixtures of Unimodal Normal Mixtures," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 203-219, September.
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    11. Bartolucci, Francesco & Farcomeni, Alessio, 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, American Statistical Association, vol. 104(486), pages 816-831.
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    Cited by:

    1. repec:eee:ecosta:v:3:y:2017:i:c:p:112-131 is not listed on IDEAS
    2. Silvia Cagnone & Francesco Bartolucci, 2017. "Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 599-622, April.
    3. 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.
    4. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    5. Francesca Bassi, 2016. "Dynamic segmentation with growth mixture models," 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. 10(2), pages 263-279, June.
    6. Silvia Bianconcini, 2014. "Comments 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 466-468, September.
    7. Xia, Ye-Mao & Tang, Nian-Sheng & Gou, Jian-Wei, 2016. "Generalized linear latent models for multivariate longitudinal measurements mixed with hidden Markov models," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 259-275.
    8. Cagnone, Silvia & Bartolucci, Francesco, 2013. "Adaptive quadrature for likelihood inference on dynamic latent variable models for time-series and panel data," MPRA Paper 51037, University Library of Munich, Germany.

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