Using EM Algorithm for Finite Mixtures and Reformed Supplemented EM for MIRT Calibration

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• Parameter estimation in multidimensional item response theory (MIRT) presents challenges.
• The expectation-maximization (EM) algorithm for finite mixtures (EM-FM) is a common approach.
• Computational details, such as rescaling and standard error estimation, require thorough investigation.

Purpose of the Study:

• To investigate optimal rescaling strategies within the EM-FM algorithm for MIRT.
• To adapt the supplemented EM algorithm for accurate standard error estimation in EM-FM.
• To provide empirical evidence through a comprehensive simulation study.

Main Methods:

• Implementing the expectation-maximization (EM) algorithm for finite mixtures (EM-FM).
• Comparing rescaling after each EM cycle versus after the final cycle.
• Adapting the supplemented EM algorithm to estimate standard errors (SEs) for all model parameters.

Main Results:

• Rescaling after each EM cycle accelerates convergence.
• Calibration accuracy is maintained when rescaling after each EM cycle.
• Standard errors for item parameters and mixing proportions are well-recovered with large sample sizes (N=2000).

Conclusions:

• Rescaling at each EM cycle is an efficient strategy for EM-FM in MIRT.
• The supplemented EM algorithm effectively estimates SEs for MIRT parameters.
• Sufficient sample size is crucial for reliable standard error estimation in MIRT models.