Two strategies for fitting real data to Rasch polytomous models.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Latent Trait Theory (LTT) models are crucial for understanding measurement properties.
• Assessing data fit to LTT models is essential for valid interpretations.
• Existing strategies for data fitting may yield different results based on their procedural order.

Purpose of the Study:

• To comparatively analyze two distinct strategies for fitting data to Latent Trait Theory Models.
• To investigate the impact of procedural order (person-fit first vs. item-fit first) on model evaluation.
• To propose a method for controlling the sensitivity of fit statistics to sample size.

Main Methods:

• A comparative study was conducted using two fitting strategies: Total-Persons-Items (TPI) and Total-Items-Persons (TIP).
• Data from 821 persons on a 30-item religious attitude scale were analyzed.
• The Partial Credit Model and the Rating Scale Model were employed.

Main Results:

• The TPI strategy maximized the number of persons demonstrating good fit to the models.
• The TIP strategy maximized the number of items demonstrating good fit to the models.
• A procedure to control for sample size's influence on fit assessment was developed.

Conclusions:

• The choice between TPI and TIP strategies significantly influences whether person or item fit is prioritized.
• Researchers must consider the implications of each strategy for their specific research questions.
• The proposed method aids in robustly evaluating model fit across different sample sizes.