A semiparametric approach for item response function estimation to detect item misfit.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Item response theory (IRT) relies on accurate model fit for valid data scaling.
• Existing item fit statistics have limitations, including dependence on sample size and item count.
• Assessing the magnitude of misfit as an effect size is crucial but hindered by current methods.

Purpose of the Study:

• To develop and empirically test a new approach for estimating the distance between predicted and true item response functions (IRFs).
• To address the limitations of existing item fit statistics in item response theory.
• To provide a reliable effect size measure for item misfit.

Main Methods:

• Developed an estimator for the distance between predicted and true IRFs using semiparametric adaptation.
• Employed extended basis functions and group lasso for regularization and item selection in IRF adaptation.
• Defined IRFs as a sum of a linear term and a flexible term via basis function expansions.

Main Results:

• The proposed semiparametric adaptation method effectively estimates the distance between predicted and true IRFs.
• The group lasso acts as a selection criterion for items requiring semiparametric adjustment.
• The method demonstrated satisfactory performance in simulation studies with large sample sizes (N ≥ 1,000).

Conclusions:

• The new method offers a robust way to assess item fit and quantify misfit in IRT.
• This approach overcomes the limitations of traditional fit statistics, providing a more reliable effect size.
• The semiparametric adaptation technique is particularly effective for large-scale data analysis in psychometrics.