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A Bayesian hierarchical model for categorical longitudinal data from a social survey of immigrants

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  • A. N. Pettitt
  • T. T. Tran
  • M. A. Haynes
  • J. L. Hay

Abstract

Summary. The paper investigates a Bayesian hierarchical model for the analysis of categorical longitudinal data from a large social survey of immigrants to Australia. Data for each subject are observed on three separate occasions, or waves, of the survey. One of the features of the data set is that observations for some variables are missing for at least one wave. A model for the employment status of immigrants is developed by introducing, at the first stage of a hierarchical model, a multinomial model for the response and then subsequent terms are introduced to explain wave and subject effects. To estimate the model, we use the Gibbs sampler, which allows missing data for both the response and the explanatory variables to be imputed at each iteration of the algorithm, given some appropriate prior distributions. After accounting for significant covariate effects in the model, results show that the relative probability of remaining unemployed diminished with time following arrival in Australia.

Suggested Citation

  • A. N. Pettitt & T. T. Tran & M. A. Haynes & J. L. Hay, 2006. "A Bayesian hierarchical model for categorical longitudinal data from a social survey of immigrants," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(1), pages 97-114, January.
    • Handle: RePEc:bla:jorssa:v:169:y:2006:i:1:p:97-114
    DOI: 10.1111/j.1467-985X.2005.00389.x
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    References listed on IDEAS

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    1. Gong, Xiaodong & Van Soest, Arthur & Villagomez, Elizabeth, 2004. "Mobility in the Urban Labor Market: A Panel Data Analysis for Mexico," Economic Development and Cultural Change, University of Chicago Press, vol. 53(1), pages 1-36, October.
    2. Patrick J. Heagerty, 2002. "Marginalized Transition Models and Likelihood Inference for Longitudinal Categorical Data," Biometrics, The International Biometric Society, vol. 58(2), pages 342-351, June.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    1. repec:jss:jstsof:19:i07 is not listed on IDEAS
    2. I. Albarrán & P. Alonso-González & J. M. Marin, 2017. "Some criticism to a general model in Solvency II: an explanation from a clustering point of view," Empirical Economics, Springer, vol. 52(4), pages 1289-1308, June.
    3. Carrigan, Gretchen & Barnett, Adrian G. & Dobson, Annette J. & Mishra, Gita, 2007. "Compensating for Missing Data from Longitudinal Studies Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i07).
    4. Gerber Eric A. E. & Craig Bruce A., 2021. "A mixed effects multinomial logistic-normal model for forecasting baseball performance," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(3), pages 221-239, September.
    5. Alonso, Pablo J., 2011. "Why using a general model in Solvency II is not a good idea : an explanation from a Bayesian point of view," DES - Working Papers. Statistics and Econometrics. WS ws113729, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Ramon I. Garcia & Joseph G. Ibrahim & Hongtu Zhu, 2010. "Variable Selection in the Cox Regression Model with Covariates Missing at Random," Biometrics, The International Biometric Society, vol. 66(1), pages 97-104, March.

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