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

Ping Chen¹, Chun Wang²

¹Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing Normal University, No. 19, Xin Jie Kou Wai Street, Hai Dian District, Beijing, 100875, China. pchen@bnu.edu.cn.

|February 16, 2021

Summary

This summary is machine-generated.

Rescaling during expectation-maximization (EM) cycles improves convergence speed for finite mixture models in item response theory without impacting accuracy. Standard errors for parameters are reliably estimated with larger sample sizes.

Keywords:

EM algorithm for finite mixtures Error covariance matrix Multidimensional item response theory Rescaling scheme Standard error Supplemented EM

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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.