An R2 statistic for covariance model selection in the linear mixed model

Byron C. Jaeger, Lloyd J Edwards, Matthew J. Gurka

Research output: Contribution to journalArticle

Abstract

The linear mixed model, sometimes referred to as the multi-level model, is one of the most widely used tools for analyses involving clustered data. Various definitions of R2 have been proposed for the linear mixed model, but several limitations prevail. Presently, there is no method to compute R2 for the linear mixed model that accommodates an interpretation based on variance partitioning, a method to quantify uncertainty and produce confidence limits for the R2 statistic, and a capacity to use the R2 statistic to conduct covariance model selection in a manner similar to information criteria. In this article, we introduce such an R2 statistic. The proposed R2 measures the proportion of generalized variance explained by fixed effects in the linear mixed model. Simulated and real longitudinal data are used to illustrate the statistical properties of the proposed R2 and its capacity to be applied to covariance model selection.

LanguageEnglish (US)
Pages164-184
Number of pages21
JournalJournal of Applied Statistics
Volume46
Issue number1
DOIs
StatePublished - Jan 2 2019

Fingerprint

Covariance Selection
Linear Mixed Model
Model Selection
Statistic
Generalized Variance
Multilevel Models
Clustered Data
Confidence Limits
Information Criterion
Fixed Effects
Longitudinal Data
Statistical property
Partitioning
Quantify
Proportion
Uncertainty
Statistics
Mixed model
Model selection

Keywords

  • R
  • explained variance
  • linear mixed model
  • longitudinal data
  • multi-level model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

An R2 statistic for covariance model selection in the linear mixed model. / Jaeger, Byron C.; Edwards, Lloyd J; Gurka, Matthew J.

In: Journal of Applied Statistics, Vol. 46, No. 1, 02.01.2019, p. 164-184.

Research output: Contribution to journalArticle

Jaeger, Byron C. ; Edwards, Lloyd J ; Gurka, Matthew J. / An R2 statistic for covariance model selection in the linear mixed model. In: Journal of Applied Statistics. 2019 ; Vol. 46, No. 1. pp. 164-184.
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