Random Effects Coefficient of Determination for Mixed and Meta-Analysis Models

• Activity Number: 245
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Eugene Demidenko*+
• Companies: Dartmouth College
• Keywords: clustered data ; random effects ; growth curve ; dummy variable

Abstract

The key feature of a mixed model is the presence of random effects. We have developed a coefficient, called the random effects coefficient of determination that estimates the proportion of the conditional variance of the dependent variable explained by random effects. This coefficient takes values from 0 to 1 and indicates how strong the random effects are. If this coefficient is close to 0, there is weak support for random effects in the model because the reduction of the variance of the dependent variable due to random effects is small; consequently, random effects may be ignored and the model simplifies to standard linear regression. The value of this coefficient apart from 0 indicates the evidence of the variance reduction in support of the mixed model. If random effects coefficient of determination is close to 1 the variance of random effects is very large and random effects turn into free fixed effects---the model can be estimated using the dummy variable approach. Coefficient of determination is illustrated by three examples of mixed and meta-analysis models.