Investigating latent constructs with item response models: a MATLAB IRTm toolbox

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Item response theory (IRT) models are fundamental in modern psychometrics and measurement.
• Standard IRT models like Rasch and two-parameter logistic models have limitations in flexibility.
• Advanced modeling is needed to accommodate complex data structures and assumptions.

Purpose of the Study:

• To introduce a freely available MATLAB toolbox for flexible item response theory modeling (IRTm).
• To provide users with control and flexibility in building custom IRT models.
• To incorporate advanced features such as copula IRT models for local item dependencies.

Main Methods:

• Development of a MATLAB toolbox (IRTm) utilizing a design matrix approach.
• Implementation of a wide range of unidimensional IRT models for binary responses.
• Inclusion of copula IRT models to address local item dependencies.

Main Results:

• The IRTm toolbox allows for the construction of diverse IRT models beyond standard ones.
• It facilitates the incorporation of additional person and item information.
• The toolbox supports deviations from common IRT model assumptions and handles local dependencies.

Conclusions:

• The IRTm toolbox offers a powerful and flexible environment for advanced psychometric modeling.
• It empowers researchers to build sophisticated IRT models tailored to specific research needs.
• The toolbox, particularly its copula IRT feature, advances the analysis of dependent item responses.