Item response parameter estimation performance using Gaussian quadrature and Laplace

TL;DR

This study compares Gaussian quadrature and Laplace methods for item response parameter estimation, finding that Gaussian quadrature offers a viable, accurate, and efficient alternative to Laplace in pharmacometric IRT models, especially with larger samples.

Contribution

It provides a systematic comparison of Gaussian quadrature and Laplace estimation algorithms in pharmacometric IRT, highlighting the advantages of Gaussian quadrature as an alternative.

Findings

Both methods yield similar parameter estimates with good precision for larger samples.

Gaussian quadrature is faster and easier to implement in certain software.

Differences between methods diminish when translating to total score scale.

Abstract

Item parameter estimation in pharmacometric item response theory (IRT) models is predominantly performed using the Laplace estimation algorithm as implemented in NONMEM. In psychometrics a wide range of different software tools, including several packages for the open-source software R for implementation of IRT are also available. Each have their own set of benefits and limitations and to date a systematic comparison of the primary estimation algorithms has not been evaluated. A simulation study evaluating varying number of hypothetical sample sizes and item scenarios at baseline was performed using both Laplace and Gauss-hermite quadrature (GHQ-EM). In scenarios with at least 20 items and more than 100 subjects, item parameters were estimated with good precision and were similar between estimation algorithms as demonstrated by several measures of bias and precision. The minimal differences observed for certain parameters or sample size scenarios were reduced when translating to the total score scale. The ease of use, speed of estimation and relative accuracy of the GHQ-EM method employed in mirt make it an appropriate alternative or supportive analytical approach to NONMEM for potential pharmacometrics IRT applications.