Likelihood analysis of the multivariate ordinal probit model for repeated and spatial ordered categorical responses.

摘要

This dissertation is about the likelihood analysis of ordered categorical responses in a longitudinal/spatial study, meaning regression-like analysis when the response variable is categorical with ordered categories, and is measured repeatedly over time or space on the experimental or sampling units. Particular attention is given to the multivariate ordinal probit regression model, in which the correlation between ordered categorical responses on the same unit at different times or locations is modeled with a latent variable that has a multivariate normal distribution. An algorithm for maximum likelihood analysis of this model is proposed and the analysis is demonstrated on several examples. Simulations show that the maximum likelihood estimates can be substantially more efficient than generalized estimating equations (GEE) estimates of regression coefficients. We also propose likelihood analysis of a regression model for spatial-temporal ordered categorical data, and with particular attention to an investigation of determinants of Coho salmon densities in Oregon. This approach avoids defining a neighborhood for each site, which is an awkward step that is required for existing approaches.