A Comparison of Item Response Theory and Confirmatory Factor Analytic Methodologies for Establishing Measurement Equivalence/Invariance

Abstract

Recently, there has been increased interest in tests of measurement equivalence/ invariance (ME/I). This study uses simulated data with known properties to assess the appropriateness, similarities, and differences between confirmatory factor analysis and item response theory methods of assessing ME/I. Results indicate that although neither approach is without flaw, the item response theory-based approach seems to be better suited for some types of ME/I analyses.

Assessing construct structural validity of epidemiological measurement tools: a seven-step roadmap

“…Unlike MG-CFA, the IRT approach starts from the most restricted model, in which all parameters are constrained to equality across groups. This baseline model is then compared with models in which item parameters are allowed to vary freely across groups, one at a time 52 . An IRT approach may be advantageous is some circumstances such as when items are ordinal since it assesses several b ik parameters per item for each k ≥ 2 threshold, whereas only one threshold can be estimated for each item in a traditional MG-CFA.…”

“…An IRT approach may be advantageous is some circumstances such as when items are ordinal since it assesses several b ik parameters per item for each k ≥ 2 threshold, whereas only one threshold can be estimated for each item in a traditional MG-CFA. However, IRT requires a one-dimensional construct, larger sample sizes and more items per scale for statistical efficiency, and works better when invariance is evaluated in no more than two groups 52 .…”

Towards a Comprehensive Procedure for Developing Measurement Scales for Cross-Cultural Management Research

“…If covariance matrices did not differ across groups, full measurement equivalence was considered to be established (Vandenberg & Lance, 2000). However, some authors have questioned the usefulness of this particular test on the grounds that it can indicate that measurement invariance is supported when more specific tests of measurement invariance find otherwise (Meade & Lautenschlager, 2004a;Raju, Byrne, & Laffitte, 2002). Then, it seems more reasonable to directly inspect each level of invariance.…”

“…"Measurement equivalence" refers here to scales and to the issues related to designing and examining whether instruments work the same way in different cultures, whereas "measurement invariance" is narrower and refers here to the statistical tests designed to verify the measurement equivalence of scales. Issues regarding measurement equivalence are getting more and more popular in organizational research after the publication of several state-of-the art articles on the topic (e.g., Cavusgil & Das, 1997;Hui & Triandis, 1985;A. W. Meade & Lautenschlager, 2004a;Peng, Peterson, & Shyi, 1991;Reise et al, 1993;Schaffer & Riordan, 2003;Singh, 1995;Steenkamp & Baumgartner, 1998;Vandenberg, 2002;Vandenberg & Lance, 2000).…”

IRT model fit from different perspectives

“…First, the sample size was varied. Earlier studies have found the effects of sample size (Glas, 1999;Meade & Lautenschlager, 2004). Sample sizes of 400 (small) and 1000 (large) were chosen as they frequently occurred in the educational and psychological measurement.…”