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An extension of the Dirichlet prior for the analysis of longitudinal multinomial data

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  • Paul Gustafson
  • Lawrence Walker

Abstract

Studies producing longitudinal multinomial data arise in several subject areas. This article suggests a Bayesian approach to the analysis of such data. Rather than infusing a latent model structure, we develop a prior distribution for the multinomial parameters which reflects the longitudinal nature of the observations. This distribution is constructed by modifying the prior that posits independent Dirichlet distributions for the multinomial parameters across time. Posterior analysis, which is implemented using Monte Carlo methods, can then be used to assess the temporal behaviour of the multinomial parameters underlying the observed data. We test this methodology on simulated data, opinion polling data, and data from a study concerning the development of moral reasoning.

Suggested Citation

  • Paul Gustafson & Lawrence Walker, 2003. "An extension of the Dirichlet prior for the analysis of longitudinal multinomial data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 293-310.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:3:p:293-310
    DOI: 10.1080/0266476022000030075
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    1. Thorsten Meiser, 1996. "Loglinear Rasch models for the analysis of stability and change," Psychometrika, Springer;The Psychometric Society, vol. 61(4), pages 629-645, December.
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    Cited by:

    1. Ivan Jeliazkov & Dale J. Poirier, 2007. "Dynamic and Structural Features of Intifada Violence: A Markov Process Approach," Working Papers 070801, University of California-Irvine, Department of Economics.

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