Measurement bias and error correction in a two-stage estimation for multilevel IRT models

Area of Science:

• Educational Measurement
• Psychometrics
• Statistical Modeling

Background:

• Multilevel Item Response Theory (IRT) models are widely used in educational and psychological research.
• The two-stage divide-and-conquer strategy offers practical advantages for estimating these models.
• Ignoring measurement error in the second stage of this framework can lead to biased statistical inferences.

Purpose of the Study:

• To propose and evaluate a novel method for correcting measurement bias and error in latent trait estimates within a two-stage multilevel IRT framework.
• To enhance the accuracy of statistical inferences in the structural model estimation.
• To address the limitations of current state-of-the-art estimation methods.

Main Methods:

• Utilized a higher-order IRT (HO-IRT) model as the measurement model.
• Employed a linear mixed effects model for the structural model on higher-order abilities.
• Developed and applied a correction method for measurement bias and error in stage I latent trait estimates during stage II estimation.
• Conducted a simulation study and analyzed real data from the National Educational Longitudinal Survey (NELS 88).

Main Results:

• The proposed correction method effectively addresses measurement bias and error in latent trait estimates.
• Simulation results and real data analysis demonstrate improved recovery of structural parameters compared to uncorrected methods.
• The method enhances the validity of statistical inferences in two-stage multilevel IRT analyses.

Conclusions:

• The novel correction method significantly improves the accuracy of parameter estimation in two-stage multilevel IRT models.
• This approach provides a more reliable framework for secondary data analysis, model calibration, and fit evaluation.
• Researchers should consider this correction method to avoid incorrect statistical inferences when measurement error is present.