Using MCMC for Estimating Precision of Estimates of Complicated Functions of Parameters When Modeling Categorical Data
*Karl Heiner, State University of New York at New Paltz
Keywords: MCMC, Logistic Regression, Log Linear Models, Interactions
The purpose of this presentation is to demonstrate how Marco Chain Monte Carlo methods may be applied to obtain the precision of estimates of complicated functions of parameters when modeling categorical data. For example, when fitting a logistic regression model to a 2^k contingency table, one may be interested in estimating the difference between cell probabilities or differences between these differences. When fitting log linear models, differences between differences of differences play an analogous role. Relative excess risk due to interaction (RERI), attributable proportion due to interaction (AP), and a synergy index (S) in logistic regression models are complicated functions whose estimates require reliable estimates of precision. Using examples from the field of health care quality, we will interpret these and similar measures and demonstrate how MCMC may be used to provide precision estimates.