A Bayesian Approach in Estimating Transition Probabilities of a Discrete-time Markov Chain for Ignorable Intermittent Missing Data

Junsheng Ma, Xiaoying Yu, Elaine Symanski, Rachelle Doody, Wenyaw Chan

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

This article focuses on data analyses under the scenario of missing at random within discrete-time Markov chain models. The naive method, nonlinear (NL) method, and Expectation-Maximization (EM) algorithm are discussed. We extend the NL method into a Bayesian framework, using an adjusted rejection algorithm to sample the posterior distribution, and estimating the transition probabilities with a Monte Carlo algorithm. We compare the Bayesian nonlinear (BNL) method with the naive method and the EM algorithm with various missing rates, and comprehensively evaluate estimators in terms of biases, variances, mean square errors, and coverage probabilities (CPs). Our simulation results show that the EM algorithm usually offers smallest variances but with poorest CP, while the BNL method has smaller variances and better/similar CP as compared to the naive method. When the missing rate is low (about 9%, MAR), the three methods are comparable. Whereas when the missing rate is high (about 25%, MAR), overall, the BNL method performs slightly but consistently better than the naive method regarding variances and CP. Data from a longitudinal study of stress level among caregivers of individuals with Alzheimer’s disease is used to illustrate these methods.

Original languageEnglish (US)
Pages (from-to)2598-2616
Number of pages19
JournalCommunications in Statistics: Simulation and Computation
Volume45
Issue number7
DOIs
StatePublished - Aug 8 2016
Externally publishedYes

Keywords

  • Bayesian
  • EM algorithm
  • Markov chain
  • Missing data
  • Rejection algorithm

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation

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