Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models

Area of Science:

• * Statistical Modeling
• * Psychometrics
• * Educational Measurement

Background:

• * Latent variables as outcomes in regression analysis often suffer from ignored measurement error.
• * Multilevel item response modeling (IRT) is a common approach to address this issue.
• * While computationally advanced, one-stage IRT models may not always be optimal.

Purpose of the Study:

• * To evaluate the advantages of a two-stage, divide-and-conquer strategy for handling measurement error.
• * To introduce and compare three Stage II methods within the two-stage framework: closed-form marginal MLE, expectation maximization, and moment estimation.
• * To assess the performance of these methods against naive two-stage and one-stage MCMC estimation.

Main Methods:

• * Simulation study comparing five estimation methods: naive two-stage, one-stage MCMC, closed-form marginal MLE, expectation maximization, and moment estimation.
• * Evaluation criteria include model parameter recovery and standard error estimation.
• * Application to real-world data from the National Educational Longitudinal Survey (NELS 88).

Main Results:

• * The simulation study provides empirical evidence on the performance of each method.
• * Parameter recovery and standard error estimation accuracy are key metrics for comparison.
• * Pros and cons of each method are discussed to guide practical application.

Conclusions:

• * The two-stage framework, particularly with specific Stage II methods, offers distinct advantages for handling measurement error.
• * Guidelines are provided for practitioners to select appropriate methods based on study objectives and data characteristics.
• * Real data analysis demonstrates the practical utility of the evaluated methods.