A Finite Mixture Item Response Theory Model for Continuous Measurement Outcomes

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Traditional continuous response models may not capture nuanced respondent behaviors.
• Identifying distinct respondent groups is crucial for accurate data interpretation.

Purpose of the Study:

• To introduce a mixture extension of Samejima's continuous response model for continuous outcomes.
• To evaluate an estimation approach using limited-information factor analysis.
• To demonstrate the model's ability to detect distinct respondent groups.

Main Methods:

• Developed a mixture extension of Samejima's continuous response model.
• Employed a heuristic estimation approach based on limited-information factor analysis.
• Validated the approach using an empirical dataset and a Monte Carlo simulation study.

Main Results:

• The model successfully identified two distinct respondent groups with differing response behaviors.
• The heuristic estimation approach yielded reliable parameter estimates.
• Model convergence rates exceeded 80% with sample sizes of 250 and 90% with 500-1,000 participants.

Conclusions:

• The mixture extension of Samejima's model is effective for identifying heterogeneous respondent groups.
• The heuristic estimation method is reliable and performs well under various conditions.
• The findings support the use of this model for analyzing continuous measurement outcomes.