Acyclic Directed Graph Markov Models For Seemingly Unrelated Regression With Missing Data

• Activity Number: 333
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Mathias Drton*+ and Steen Andersson and Michael D. Perlman
• Companies: University of Washington and Indiana University and University of Washington
• Keywords: graphical model ; missing data ; incomplete data ; MANOVA ; maximum likelihood estimator ; seemingly unrelated regressions

Abstract

In multivariate analysis of variance (MANOVA), multiple normally distributed variables are each regressed on the same mean space. Seemingly unrelated regression (SUR) allows different mean spaces for different variables. As opposed to MANOVA models, SUR models, in general, are not amenable to explicit likelihood inference and can have a multimodal likelihood. Similar inference problems arise in MANOVA with missing data. However, a minimal set of conditional independences can be imposed such that a SUR model or a MANOVA model with missing data factors into a product of (complete-data) MANOVA models. The factorization permits explicit likelihood inference with a unimodal likelihood. We review the construction of the conditional independences using the framework of acyclic directed graph Markov models and demonstrate how the SUR methodology and the missing data methodolgy can be combined and applied to SUR models with missing data. If the conditional independence assumptions can be justified, our results facilitate likelihood inference in a restricted model. Otherwise, our results can yield improved starting values for iterative procedures to fit the original model.