Addressing Alternative Missing-data Mechanisms in Multivariate Probit Models for Incomplete Ordinal Data

• Activity Number: 390
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jun Xing*+ and Alan Rong and Thomas R. Belin
• Companies: University of California, Los Angeles and Amgen, Inc. and University of California, Los Angeles
• Keywords: Latent variable ; Missing-at-random ; Multivariate probit model ; Nonignorable models ; Threshold specification

Abstract

It is challenging to analyze correlated ordinal outcomes due to modeling and estimation of the implied cross-sectional associations, especially when the number of outcomes is large. Instead of directly modeling ordinal responses, the concept of latent continuous variables is introduced to derive the joint distribution of multivariate ordinal outcomes. This approach assumes the observed ordinal outcomes are generated by latent multivariate normal variables through a threshold specification. Therefore, the cross-sectional associations among multiple ordinal outcomes are modeled through the correlation matrix of the underlying multivariate normal variables. Under a missing-at-random assumption, the unknown parameters are assessed by Gibbs sampling using a set of conditional distributions. Further, the proposed model will be extended to accommodate alternative missing-data mechanisms. In particular, we will consider both ignorable models assuming missing-at-random and nonignorable models where there is an assumed selection mechanism that also has a probit-model structure. The method will be compared to simpler imputation techniques in real data analysis and simulation study.