Title: On Wald Tests for Differential Item Functioning Detection
Authors: Michela Battauz
Affiliation: University of Udine
Abstract:
Lord's chi-square test is a Wald-type test commonly used for Differential
Item Functioning detection using Item Response Theory (IRT) methods.
However, simulation studies reported in the literature showed that empirical
type I error rates are largely greater than the significance level for the
3PL model, while they are smaller for the 2PL model.
Two improvements of the test are proposed.
1. Item parameter estimates and their covariance matrix should be transformed
to a common scale before calculating the test statistics. This transformation
is performed using the equating coefficients, which are estimated by applying
the methods proposed in the literature. However, these coefficients are treated
as known constants in the computation of the covariance matrix. The proposal
is to account for the estimation of the equating coefficients in the
computation of the covariance matrix of the transformed item parameters.
2. The parameterization of the IRT model used to estimate the item parameters
is usually different from the usual IRT parameterization. Item parameters
estimates (and their covariance matrix) are then transformed to the usual IRT
parameterization. The proposal is to apply the Wald test to the untransformed
item parameters.
Simulation studies show that these two proposals lead to empirical type I error
rates closer to the significance level for both the 2PL and the 3PL models.
The procedure applies also to multiple groups.