Modeling and Testing Differential Item Functioning in Unidimensional Binary Item Response Models with a Single...

Area of Science:

• Psychometrics
• Educational Measurement
• Statistics

Background:

• Differential item functioning (DIF) is a critical item-level diagnostic in psychometric analysis.
• Existing methods for DIF with continuous covariates are often limited by restrictive parametric assumptions.
• Complex interactions between latent variables and covariates are not adequately captured by current models.

Purpose of the Study:

• To develop a flexible semiparametric approach for detecting DIF with continuous covariates.
• To model item response probabilities as a bivariate function of latent traits and covariates.
• To evaluate the accuracy and precision of the proposed DIF detection procedure.

Main Methods:

• Formulating item endorsement probability as a bivariate function of a latent trait and a covariate, approximated by a two-dimensional smoothing spline.
• Developing an extended model using regression splines for simultaneous estimation of item characteristic functions (ICFs) and latent variable density conditional on covariates (when anchor items are available).
• Implementing a permutation DIF test and comparing its performance against conventional parametric methods via Monte Carlo simulations.

Main Results:

• The proposed semiparametric procedure demonstrates accuracy and precision in DIF detection through simulations.
• The extended model effectively estimates ICFs and latent variable densities under covariate influence.
• The permutation DIF test shows comparable or superior performance to traditional parametric approaches.

Conclusions:

• The developed semiparametric DIF testing procedure offers a flexible and powerful alternative to existing parametric methods.
• This approach enhances the ability to model complex interactions in item response theory (IRT) analyses.
• The methodology provides a valuable tool for robust item analysis in the presence of continuous covariates.