Stochastic EM for estimating the parameters of a multilevel IRT model

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Multilevel models are widely used but often overlook measurement error in latent variables.
• Item Response Theory (IRT) provides a framework for modeling item and person characteristics.
• Integrating IRT with multilevel models can enhance the accuracy of dependent variable estimation.

Purpose of the Study:

• To propose and evaluate an integrated item response theory (IRT) and multilevel modeling framework.
• To utilize latent scores from an IRT model as the dependent variable in a multilevel model.
• To demonstrate the advantages of accounting for measurement error in multilevel analyses.

Main Methods:

• Employed a two-parameter normal ogive (2PN) IRT model to represent the latent dependent variable.
• Utilized the stochastic Expectation-Maximization (EM) algorithm for parameter estimation.
• Compared the EM algorithm's performance with a Bayesian Gibbs sampler implementation.
• Applied the methodology to real-world data for validation.

Main Results:

• The stochastic EM algorithm provides parameter estimates comparable to maximum likelihood estimates.
• The integrated model successfully separates the influence of item difficulty and individual ability.
• The approach effectively models response variation and measurement error within a multilevel structure.
• The proposed method is computationally feasible and easily implemented.

Conclusions:

• Integrating IRT with multilevel models offers a superior approach to analyzing latent dependent variables.
• The stochastic EM algorithm is a practical and efficient method for parameter estimation in this integrated framework.
• This methodology enhances the understanding of measurement error and its impact on multilevel analyses.
• The findings have implications for educational assessment and psychological measurement.