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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Bayesian methods for the analysis of small sample multilevel data with a complex variance structure.

Scott A Baldwin1, Gilbert W Fellingham

  • 1Department of Psychology, Brigham Young University, Provo, UT 84602, USA. scott_baldwin@byu.edu

Psychological Methods
|November 15, 2012
PubMed
Summary
This summary is machine-generated.

Bayesian and adjusted likelihood methods offer accurate multilevel model inferences. Bayesian models with specific priors showed improved variance component estimation but sensitivity in small samples.

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Multilevel models are complex, especially in small samples or with intricate data structures.
  • Standard likelihood methods (REML) often require adjustments for accurate fixed-effect inferences.
  • Likelihood adjustments do not fully resolve issues in estimating variance/covariance components.

Purpose of the Study:

  • To contrast the benefits and limitations of likelihood versus Bayesian methods for multilevel model estimation.
  • To evaluate these methods in the context of partially clustered intervention studies.
  • To compare adjusted restricted maximum likelihood (REML) with Bayesian analysis via Monte Carlo simulation.

Main Methods:

  • Monte Carlo simulation comparing adjusted REML and Bayesian analyses.
  • Analysis focused on fixed effects and variance/covariance components estimation.
  • Application to data from a partially clustered intervention trial.

Main Results:

  • Both methods performed equally well for fixed effects regarding bias, efficiency, and interval coverage.
  • Bayesian models with gamma priors for variance components were more efficient but slightly more biased.
  • Inferences for variance components in small, partially clustered samples are sensitive to prior selection.

Conclusions:

  • Bayesian methods provide a viable alternative to adjusted likelihood for multilevel models, particularly in complex designs.
  • Careful prior selection is crucial for Bayesian estimation of variance components in small, clustered studies.
  • Both approaches yield comparable results for fixed effects, but Bayesian methods offer potential advantages for variance components.