Estimation of IRT graded response models: limited versus full information methods

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• F. Samejima's graded response model is widely used in psychometric analysis.
• Accurate parameter estimation and standard errors are crucial for model-based inferences.
• Comparing different estimation methods is essential for practical application.

Purpose of the Study:

• To compare the performance of Full Information Maximum Likelihood (FIML) and a 3-stage Categorical Item Factor Analysis (CIFA) estimator.
• To evaluate parameter estimates and standard errors for Samejima's graded response model under various conditions.
• To identify optimal estimation strategies based on sample size and model characteristics.

Main Methods:

• Simulation study across 324 conditions.
• Comparison of FIML with a 3-stage CIFA using unweighted least squares in the final stage.
• Analysis focused on parameter estimates and standard errors.

Main Results:

• CIFA demonstrated faster computation, especially for multidimensional models with correlated dimensions.
• CIFA provided slightly more accurate parameter estimates; FIML provided slightly more accurate standard errors.
• Differences between methods were negligible across most conditions.
• FIML was optimal for small sample sizes (N=200); CIFA was preferred for larger samples due to computational efficiency.
• Both methods showed failures under specific conditions (small N, few indicators, skewed items, low loadings).

Conclusions:

• FIML and CIFA are viable estimation methods for Samejima's graded response model, with performance varying by sample size and computational needs.
• Researchers should avoid conditions leading to estimation failures, particularly in small samples or with problematic item characteristics.
• The choice between FIML and CIFA depends on the balance between accuracy, computational speed, and sample size.