A Note on Improving Variational Estimation for Multidimensional Item Response Theory

TL;DR

This paper introduces an importance weighted variant of the GVEM algorithm to reduce bias in variational estimation of multidimensional item response theory models, improving accuracy with minimal additional computation.

Contribution

It proposes IW-GVEM, an enhanced variational estimation method that corrects bias in MIRT model parameters, building on existing GVEM techniques.

Findings

IW-GVEM effectively reduces bias in discrimination parameters.

The method incurs only a modest increase in computation time.

Simulations demonstrate improved estimation accuracy over GVEM.

Abstract

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian Variational Expectation Maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.