The Q-Matrix Anchored Mixture Rasch Model.

Area of Science:

• Educational Measurement
• Psychometrics
• Statistical Modeling

Background:

• Mixture item response theory (IRT) models account for latent subpopulations with distinct characteristics.
• Accurate scale construction across these subpopulations requires identifying anchor items.
• Current methods face challenges in establishing a common scale for parameter estimation.

Purpose of the Study:

• To propose a novel method for scale construction in mixture IRT models.
• To introduce the Q-matrix anchored mixture Rasch model (QAMRM).
• To evaluate the performance of QAMRM compared to existing models.

Main Methods:

• Developed the Q-matrix anchored mixture Rasch model (QAMRM), integrating a Q-matrix with the traditional mixture Rasch model.
• Utilized class-invariant items within the Q-matrix to anchor parameter estimates across latent classes.
• Conducted a simulation study to assess parameter recovery and analyzed a real dataset from the Certificate of Proficiency in English.

Main Results:

• The QAMRM successfully placed model parameter estimates from different latent classes onto a common scale.
• Simulation studies indicated fair recovery of estimated parameters using QAMRM.
• QAMRM demonstrated superior model fit indices compared to the Latent Class Dependent Model (LCDM) when applied to real-world data.

Conclusions:

• The QAMRM provides an effective framework for scale construction in mixture IRT models.
• Anchor items identified via a Q-matrix facilitate common scale estimation regardless of ability distribution.
• QAMRM offers improved model fit over LCDM for analyzing complex student response data.