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Examining the Performance of the Metropolis-Hastings Robbins-Monro Algorithm in the Estimation of Multilevel
Bozhidar M Bashkov1, Christine E DeMars2
1American Board of Internal Medicine, Philadelphia, PA, USA.
The Metropolis-Hastings Robbins-Monro (MH-RM) algorithm effectively estimates multilevel multidimensional item response theory (ML-MIRT) models, accurately recovering item, person, and group parameters in simulations.
Area of Science:
- Psychometrics
- Educational Measurement
- Statistical Modeling
Background:
- Multilevel multidimensional item response theory (ML-MIRT) models are crucial for analyzing nested data structures in educational and psychological assessments.
- Efficient estimation methods are needed to accurately recover model parameters in complex ML-MIRT applications.
Purpose of the Study:
- To evaluate the performance of the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for estimating ML-MIRT models.
- To assess the accuracy and efficiency of MH-RM in recovering item parameters, latent variances, covariances, and ability estimates at individual and group levels.
Main Methods:
- A simulation study was conducted across 24 conditions, manipulating dimensions, intraclass correlation, number of clusters, and cluster size.
- The Metropolis-Hastings Robbins-Monro (MH-RM) algorithm was employed to estimate ML-MIRT models.
- Empirical standard errors were compared to analytical standard errors from flexMIRT for parameter recovery assessment.
Main Results:
- The MH-RM algorithm demonstrated good performance in recovering item, person, and group-level parameters.
- Analytical standard errors in flexMIRT were found to be slightly overestimated for cluster-level ability estimates and person-level ability estimates.
- Accuracy of analytical standard errors was confirmed for other model parameters.
Conclusions:
- The MH-RM algorithm is a viable and effective method for estimating ML-MIRT models.
- Caution is advised regarding the interpretation of standard errors for ability estimates in flexMIRT.
- Findings have implications for educational measurement practices and suggest future research directions for robust estimation techniques.
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