Testing for Measurement Invariance with Respect to an Ordinal Variable

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Jinyan FanAuburn University Achim ZeileisUniversität Innsbruck AbstractResearchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group, income class, or school grade. In a factoranalytic context, these tests are traditionally carried out via a likelihood ratio test statistic comparing a model where parameters differ across groups to a model where parameters are equal across groups. This test neglects the fact that the auxiliary variable is ordinal, and it is also known to be overly sensitive at large sample sizes. In this paper, we propose test statistics that explicitly account for the ordinality of the auxiliary variable, resulting in higher power against "monotonic" violations of measurement invariance and lower power against "non-monotonic" ones. The statistics are derived from a family of tests based on stochastic processes that have recently received attention in the psychometric literature. The statistics are illustrated via an application involving real data, and their performance is studied via simulation.

Heteroscedastic Latent Trait Models for Dichotomous Data

“…Bauer & Hussong, 2009). Note, however, that other approaches do not require the specification of the exact form of the function between the variance parameters and the moderator (see Merkle, Fan, & Zeileis, 2013).…”

Using recursive partitioning to account for parameter heterogeneity in multinomial processing tree models

“…Merkle and Zeileis (2013) discuss the tests in the context of measurement invariance with respect to structural equation models. Merkle et al (2014) extend the results to ordered categorical covariates.…”

“…The focus of this simulation is restricted to one specific MPT model that is observed under realistic magnitudes of parameter instability and moderate sample sizes. More general simulation results have been reported elsewhere and include power and type I error of score tests for measurement invariance in the context of structural equation modeling (Merkle and Zeileis 2013;Merkle et al 2014), performance of recursive partitioning and comparison to mixture models for linear regression (Frick, Strobl, and Zeileis 2014), performance of Rasch, partial credit, and rating scale trees for detecting di erential item functioning Strobl et al 2015).…”

How Credible Are Shrinking Wage Elasticities of Married Women Labour Supply?

“…It underlies the concept of super-exogeneity in time-series econometrics, and is deemed a strong condition for causal linear stochastic dependence in psychometrics, e.g., see [33]. The within-sample invariance of the IV estimates is examined by means of two types of parameter stability tests-the commonly used Hansen test and the M-fluctuation test for individual parameter stability developed by Merkle et al [38]. The latter is used because the Hansen test is not directly applicable to IV estimators.…”