Unifying Differential Item Functioning in Factor Analysis for Categorical Data Under a Discretization of a Normal...

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Multiple-group categorical factor analysis (MC-FA) and graded response models (GRM) are key for detecting differential item functioning (DIF) in polytomous items.
• These models are crucial for identifying measurement bias in educational testing.

Purpose of the Study:

• To unify MC-FA and multiple-group normal-ogive GRM under a common discretization framework.
• To investigate the impact of identifiability constraints on the performance of these models in DIF assessment.
• To compare the effectiveness of categorical FA and GRM approaches for DIF detection.

Main Methods:

• Unification of MC-FA and GRM within a common framework of discretization of a normal variant.
• Justification of identified parameters and determination of identifiability constraints for model estimability.
• Simulation studies comparing categorical FA and GRM performance on DIF assessment using MC-FA models with specific identifiability constraints.

Main Results:

• The distinction between categorical FA and GRM lies primarily in their identifiability constraints.
• Models employing GRM-type identifiability constraints demonstrated superior performance in DIF detection.
• Higher statistical power for DIF detection was observed with GRM-type constraints across various DIF scenarios.

Conclusions:

• GRM-type identifiability constraints generally enhance the power of DIF detection in educational assessments.
• The choice of identifiability constraints significantly impacts the performance of models used for bias detection.
• Guidelines for selecting just-identified parameterizations are provided for practical application in psychometric analysis.