Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• Item response theory (IRT) models commonly assume a normal distribution for the latent population.
• Existing methods may lack flexibility when the latent distribution deviates from normality.
• Accurate estimation of latent distributions is crucial for reliable IRT analyses.

Purpose of the Study:

• To introduce a novel method for fitting IRT models using splines to estimate the latent population distribution directly from data.
• To provide a more flexible alternative to traditional IRT procedures that rely on pre-specified distributional forms.
• To evaluate the performance of the spline-based method against existing approaches.

Main Methods:

• Development of a spline-based density estimation system for latent population distributions in IRT.
• Implementation of the new procedure for fitting IRT models.
• Conducting a simulation study to assess feasibility and performance.
• Comparison with the standard normal distribution model and the empirical histogram approach using real data.

Main Results:

• The spline-based method is shown to be feasible in practice.
• Significant improvements in two-parameter logistic (2PL) item parameter estimates and expected a posteriori (EAP) scores were observed when the latent distribution was not normal.
• The new method demonstrated advantages over the normal model when distributional assumptions were violated.

Conclusions:

• Spline-based density estimation offers a flexible and effective approach for modeling latent population distributions in IRT.
• This method can enhance the accuracy of item parameter estimation and score prediction, particularly in non-normal distribution scenarios.
• The findings support the adoption of flexible density estimation techniques in IRT analyses.