Fitting Rasch model using appropriateness measure statistics.

Area of Science:

• Psychometrics
• Educational Measurement
• Item Response Theory

Background:

• Item fit statistics are crucial for evaluating the quality of items within measurement models.
• Traditional statistics like Outfit and Infit mean square (T-outfit, T-infit) and Lz have limitations in standardization and power.
• The Rasch model is a widely used item response theory model requiring rigorous item fit assessment.

Purpose of the Study:

• To compare the distributional properties and power rates of Lz, Eci2z, and Eci4z item fit statistics.
• To evaluate these statistics against the t-transformation of Outfit and Infit mean square.
• To determine the effectiveness of Eci2z and Eci4z in detecting items that do not fit the Rasch model.

Main Methods:

• Simulations were conducted with varying sample sizes (100-1000), ability distributions (uniform/normal), and item difficulty ranges (+/-1, +/-2 logits).
• Test lengths of 15 and 30 items were used, with a fixed pseudo-guessing parameter of 0.25.
• Distributional properties and power rates of Lz, Eci2z, Eci4z, T-infit, and T-outfit were analyzed.

Main Results:

• T-outfit, T-infit, and Lz statistics exhibited poor standardization across conditions.
• Eci2z and Eci4z statistics demonstrated satisfactory standardization under all simulated conditions.
• Eci2z and Eci4z showed 5% to 10% higher power rates in detecting Rasch model misfit compared to Lz, T-outfit, and T-infit.

Conclusions:

• Eci2z and Eci4z are recommended as superior item fit statistics for Rasch model analysis due to their robust standardization and enhanced detection power.
• These findings suggest that Eci2z and Eci4z offer improved accuracy in identifying problematic items in educational and psychological assessments.
• The study highlights the importance of selecting appropriate item fit statistics for valid measurement.