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Related Experiment Video

Updated: Jun 30, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

An R2 statistic for fixed effects in the linear mixed model.

Lloyd J Edwards¹, Keith E Muller, Russell D Wolfinger

¹Department of Biostatistics, School of Public Health, CB# 7420, The University of North Carolina, Chapel Hill, NC 27599, USA. Lloyd Edwards@unc.edu

Statistics in Medicine

|September 26, 2008

Summary

We introduce a new R(2) statistic for linear mixed models to quantify the association between repeated outcomes and fixed effects. This statistical measure helps assess the scientific importance of predictors in longitudinal data analysis.

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Last Updated: Jun 30, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Statistics
Biostatistics
Longitudinal Data Analysis

Background:

Linear mixed models are standard for Gaussian longitudinal data.
The R(2) statistic is familiar and valuable in univariate models.
Extending R(2) to mixed models is of significant interest.

Purpose of the Study:

Define and compute a model R(2) statistic for linear mixed models.
Measure the multivariate association between repeated outcomes and fixed effects.
Develop a partial R(2) statistic for mixed models.

Main Methods:

The proposed R(2) is a function of an F statistic for testing fixed effects.
It compares a full model to a null model with identical covariance structure.
The method utilizes a single model for computation.

Main Results:

The R(2) statistic quantifies the association between fixed effects and longitudinal outcomes.
A case study on blood pressure (BP) and ethnicity illustrates its utility.
A small R(2) value indicated negligible scientific importance despite a small p-value.

Conclusions:

The new R(2) statistic provides a measure of statistical and scientific importance for fixed effects in mixed models.
It offers a valuable complement to p-values for assessing predictor relevance.
The statistic aids in interpreting the practical significance of findings in longitudinal studies.