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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Using the linear mixed model to analyze nonnormal data distributions in longitudinal designs.

Jaume Arnau1, Roser Bono, María J Blanca

  • 1Department of Methodology of the Behavioral Sciences, Faculty of Psychology, University of Barcelona, Passeig de la Vall d'Hebron, 171, 08035, Barcelona, Spain.

Behavior Research Methods
|March 9, 2012
PubMed
Summary

Linear mixed models (LMMs) effectively analyze mixed repeated measures designs. However, the Kenward-Roger (KR) correction

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Area of Science:

  • Statistics
  • Biostatistics
  • Quantitative Psychology

Background:

  • Linear mixed models (LMMs) are powerful tools for analyzing complex data structures.
  • Mixed repeated measures designs require careful consideration of covariance structures and assumptions.

Purpose of the Study:

  • To evaluate the performance of LMMs in mixed repeated measures designs.
  • To assess the impact of data distribution and covariance structure on model fit.
  • To test the robustness of the Kenward-Roger (KR) correction under various conditions.

Main Methods:

  • Monte Carlo simulation was employed to generate data.
  • LMMs were used to select optimal covariance structures for normal, exponential, and log-normal distributions.
  • The Kenward-Roger (KR) correction was applied to assess Type I error rates.

Main Results:

  • The best-fitting covariance structure depended on group covariance homogeneity and pairings.
  • The KR correction maintained Type I error control for normal data but showed reduced robustness with increased skewness.
  • Robustness of KR improved with increased kurtosis, especially when sphericity was violated.

Conclusions:

  • Covariance structure selection in LMMs is sensitive to data characteristics and group properties.
  • The KR correction's robustness is limited under non-normal, skewed data, particularly with violated sphericity.
  • Further research may be needed to refine LMM application and correction methods for non-ideal data conditions.