Likelihood Ratio Tests for Multiple Variance Components

• Activity Number: 544
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Ana-Maria Staicu*+ and Yichi Zhang and Arnab Maity
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: variance components ; tests ; additive models ; nonparametric regression

Abstract

We consider testing for several variance components in linear mixed models with multiple variance components. Our approach is based on the likelihood ratio test statistic. Similar to Crainiceanu and Ruppert (2004) who consider likelihood ratio testing in linear mixed models with one variance component, we show that the null distribution of the proposed likelihood ratio test is non-standard. Although our results are based on somewhat restrictive conditions of the fixed/random design matrices, we show that they have wide applicability. We extend our testing procedure to the case when the response is non-normal (binary or counts etc.). Application to testing for additivity in a multiple nonparametric regression model is discussed. The proposed method is illustrated through simulations and data application.