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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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A Comparison of ML, WLSMV, and Bayesian Methods for Multilevel Structural Equation Models in Small Samples: A

Jana Holtmann1, Tobias Koch2,3, Katharina Lochner4

  • 1a Department of Psychology , Freie Universität Berlin.

Multivariate Behavioral Research
|September 6, 2016
PubMed
Summary

Bayesian estimation for multilevel structural equation models (SEM) shows promise for categorical data with accurate priors. However, inaccurate priors can severely bias estimates, especially in small samples, highlighting the need for careful prior specification in psychological research.

Keywords:
Bayesian statisticsMonte Carlo simulationMultilevel structural equation modelingmultilevel item response theorysample size

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Area of Science:

  • Psychological research methodology
  • Statistical modeling
  • Quantitative psychology

Background:

  • Multilevel structural equation models (SEM) are increasingly used in psychology.
  • Complex SEMs and small sample sizes challenge traditional estimation methods.
  • Bayesian estimation offers a potential alternative to classical techniques.

Purpose of the Study:

  • To compare classical and Bayesian estimation for two-level SEMs.
  • To investigate the impact of prior specifications on estimation accuracy.
  • To examine the effects of sample size (between- and within-level) on estimation.

Main Methods:

  • A Monte Carlo simulation study was conducted.
  • Compared Maximum Likelihood (ML) and Weighted Least Squares Mean and Variance (WLSMV) with Bayesian estimation.
  • Utilized Mplus and Stan software for analysis with continuous and ordinal indicators.

Main Results:

  • For continuous indicators, Bayesian estimation offered no advantage over ML.
  • For categorical indicators, Bayesian estimation outperformed WLSMV only with accurate, strongly informative priors.
  • Inaccurate priors, particularly strong ones, led to biased estimates; diffuse priors in Stan performed better than Mplus.

Conclusions:

  • Bayesian estimation can be advantageous for multilevel SEM with categorical data, but prior choice is critical.
  • Careful prior specification is essential to avoid biased parameter estimates, especially with small sample sizes.
  • The choice of software and prior can influence estimation accuracy in complex multilevel SEM.