Logistic regression models for short sequences of correlated binary variables possessing first-order Markov dependence.
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Marcovitz, Michelle S.
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In this dissertation we consider a first-order Markov dependence model for a short sequence of correlated Bernoulli random variables. Specifically, we offer logistic regression models with first-order Markov dependency, using preceding responses as covariates. We develop maximum likelihood and Bayesian methods for inference using these models, and compare them in simulation studies. We develop methods for obtaining informative priors for the Bayesian models, including a modified conditional means prior approach, which we refer to as the Markov dependent priors approach. Due to the implicit dependence of transition probabilities on the value of the marginal probability, elicitation of priors for transition probabilities from experts is problematic. With our approach, however, we can induce priors on regression coefficients from prior distributions on the marginal probability and the transition probabilities. We also give details for constructing informative priors when historical data is available, using power priors. Finally, we considered sample size determination for first-order Markov dependence probabilities using the Bayesian two-priors method.