Smoothed ANOVA with Spatial Effects as a Competitor to MCAR

• Activity Number: 476
• Type: Contributed
• Date/Time: Wednesday, August 1, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yufen Zhang*+ and Hodges S. James
• Companies: The University of Minnesota and The University of Minnesota
• Keywords: Analysis of variance ; Conditional autoregressive model ; Hierarchical model ; Degree of freedom

Abstract

Smoothed ANOVA (SANOVA; Hodges et al 2007 Technometrics) is a way to smooth ANOVA that shrinks interactions by embedding SANOVA in a hierarchical model to do shrinkage. Instead of simply shrinking effects without any structure, SANOVA can use spatial structure to smooth effects. In this talk, we will extend SANOVA to model cases in which one factor is a spatial lattice, which is smoothed using a conditional autoregressive model (CAR), and a second factor is, for example, type of cancer. As such, SANOVA may be a competitor to the multivariate CAR (MCAR) model. Simulations are done to compare SANOVA under different design matrix settings versus MCAR under different prior settings, with advantages of each approach discussed. A cancer-surveillance dataset, describing incidence of 3 cancers in Minnesota's 87 counties, is analyzed using different methods and their results are discussed.