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A Comparison of Estimation Methods for a Multi-unidimensional Graded Response IRT Model
1Department of Counseling, Quantitative Methods, and Special Education, Southern Illinois University Carbondale Carbondale, IL, USA.
Frontiers in Psychology
|July 5, 2016
Summary
This study compared parameter estimation methods for multi-unidimensional graded response models. Hastings-within-Gibbs showed superior parameter recovery for item discrimination and intertrait correlation when dimensions were moderately or highly correlated.
Area of Science:
- Psychometrics
- Statistical Modeling
- Educational Measurement
Background:
- Multi-unidimensional graded response models are crucial for analyzing complex data structures in educational and psychological assessments.
- Accurate parameter estimation is vital for model validity and reliable interpretation of results.
- Various statistical software packages offer different estimation algorithms, necessitating comparative studies.
Purpose of the Study:
- To compare the performance of several parameter estimation methods for multi-unidimensional graded response models.
- To evaluate the accuracy of parameter recovery across different estimation algorithms under varying conditions of intertrait correlation.
- To assess the influence of sample size and test length on the performance of these methods.
Main Methods:
- Comparison of two marginal maximum likelihood (MML) approaches: Bock-Aitkin expectation-maximum algorithm and adaptive quadrature.
- Evaluation of four fully Bayesian algorithms: Gibbs sampling, Metropolis-Hastings, Hastings-within-Gibbs, and blocked Metropolis.
- Assessment of the Metropolis-Hastings Robbins-Monro (MHRM) algorithm using IRTPRO, BMIRT, and MATLAB software.
Main Results:
- All tested estimation methods yielded similar results when the intertrait correlation was low.
- The Hastings-within-Gibbs algorithm demonstrated superior parameter recovery for item discrimination and intertrait correlation when dimensions were moderately or highly correlated.
- Performance variations were observed based on sample size and test length, warranting further investigation.
Conclusions:
- The choice of parameter estimation method significantly impacts results, particularly in models with correlated dimensions.
- Hastings-within-Gibbs is recommended for multi-unidimensional graded response models with moderate to high intertrait correlations.
- Further research should explore the nuances of sample size and test length effects on these estimation techniques.
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