Abstract
A Comparison of Two Matrices for Testing Covariance Matrix in Unbalanced Linear Mixed Models
Highlights
An important practical problem is how to discriminate between a linear regression model and a linear mixed model
In order to address the issue of which model is more suitable, one might use standard model selection measures based on information criteria
When we extend the analysis to multiple variance components, the complexity and difficulties increase
Summary
Despite the widespread use of mixed-effects regression model, available methods for testing the covariance matrix of random effects are quite limited. In these cases, because of complexity and difficulties coming from an analysis of multiple variance components, inference based on testing the equality of two positive semi definite matrices seems most appropriate. We propose a test statistic based on a comparison between an estimate of a covariance matrix defined when data come from a linear regression model (covariance matrix zero) and an appropriate sample variance covariance matrix. The defined parameter bypasses boundary value problem that typically precludes use of tests based on chi-square statistics, c.
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