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Historical Measurement Information Can Be Used to Improve Estimation of Structural Parameters in Structural Equation
James Ohisei Uanhoro1, Olushola O Soyoye2
1University of North Texas, Denton, USA.
Educational and Psychological Measurement
|June 19, 2025
Summary
Incorporating historical measurement data as priors in Bayesian Structural Equation Modeling (BSEM) improves structural parameter estimates, especially for small correlations common in psychological research.
Area of Science:
- Psychometrics
- Statistical Modeling
Background:
- Small sample sizes often hinder accurate parameter estimation in Structural Equation Models (SEM).
- Published factor analysis results offer valuable historical measurement information (e.g., loadings, standard errors).
Purpose of the Study:
- To investigate the utility of incorporating historical measurement information as informative priors in Bayesian SEM (BSEM) for small samples.
- To enhance the estimation of structural parameters, specifically the correlation between two constructs, when measurement error causes bias.
Main Methods:
- Utilized Bayesian SEM (BSEM) to estimate correlations between constructs.
- Generated data simulating bias in Pearson correlations of sum scores due to measurement error.
- Incorporated historical measurement information as informative priors in BSEM.
Main Results:
- Using historical data as priors improved correlation estimates, particularly for small true correlations.
- Priors from meta-analytic estimates demonstrated high accuracy and acceptable coverage.
- Weakly informative priors on all parameters were optimal for large true correlations.
Conclusions:
- Leveraging historical measurement information in BSEM can significantly enhance structural parameter estimation in small samples.
- This approach offers a practical solution for improving model accuracy when dealing with measurement error and limited data.
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