Assessing fit of alternative unidimensional polytomous IRT models using posterior predictive model checking

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Posterior predictive model checking (PPMC) is established for dichotomous item response theory (IRT) models.
• Limited research exists on PPMC for polytomous IRT models, particularly divide-by-total models.
• Assessing model fit is crucial for accurate interpretation of polytomous IRT results.

Purpose of the Study:

• To investigate the application and performance of PPMC for unidimensional polytomous IRT models.
• To evaluate PPMC's ability to detect various sources of model misfit in the partial credit model family.
• To extend PPMC methodology beyond dichotomous IRT applications.

Main Methods:

• A Monte Carlo simulation study was employed.
• The generalized partial credit model and other partial credit model variants were simulated.
• Various discrepancy measures were used in conjunction with PPMC.

Main Results:

• PPMC demonstrated adequate power in detecting different sources of misfit for the partial credit model family.
• Global odds ratio and item total correlation showed distinct patterns for slope parameter absence.
• Yen's Q1 was effective in identifying misfit related to category intersection parameter constraints.

Conclusions:

• PPMC is a viable and powerful tool for assessing model fit in unidimensional polytomous IRT models.
• Specific discrepancy measures are sensitive to particular types of model misspecification.
• This research expands the utility of PPMC in psychometric analysis for polytomous data.