Bayesian Analysis of Transition Model for Longitudinal Ordinal Response Data: Application to Insomnia Data
DOI:
https://doi.org/10.6000/1929-6029.2012.01.02.08Keywords:
Bayesian Analysis, Bayes Factor, Conditional Predictive Ordinate, Logistic Regression, Markov ModelAbstract
In this paper, we present a Bayesian framework for analyzing longitudinal ordinal response data. In analyzing longitudinal data, the possibility of correlations between responses given by the same individual needs to be taken into account. Various models can be used to handle such correlations such as marginal modeling, random effect modeling and transition (Markov) modeling. Here a transition modeling is used and a Bayesian approach is presented for analyzing longitudinal data. A cumulative logistic regression model and the Bayesian method, using MCMC, are implemented for obtaining the parameters estimates. Our approach is applied on a two-period longitudinal Insomnia data where the Bayesian estimate for measure of association, , between the initial and follow-up ordinal responses is obtained in each level of a treatment variable. Then, the sensitivity of posterior summaries to changes of prior hyperparameters is investigated. We also use Bayes factor criterion for testing some important hypotheses
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