Score-based tests of measurement invariance: use in practice.

Ting Wang,Edgar C Merkle,Achim Zeileis

doi:10.3389/fpsyg.2014.00438

Ting Wang, Edgar C Merkle + Show 1 more

Open Access

https://doi.org/10.3389/fpsyg.2014.00438

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Abstract

In this paper, we consider a family of recently-proposed measurement invariance tests that are based on the scores of a fitted model. This family can be used to test for measurement invariance w.r.t. a continuous auxiliary variable, without pre-specification of subgroups. Moreover, the family can be used when one wishes to test for measurement invariance w.r.t. an ordinal auxiliary variable, yielding test statistics that are sensitive to violations that are monotonically related to the ordinal variable (and less sensitive to non-monotonic violations). The paper is specifically aimed at potential users of the tests who may wish to know (1) how the tests can be employed for their data, and (2) whether the tests can accurately identify specific models parameters that violate measurement invariance (possibly in the presence of model misspecification). After providing an overview of the tests, we illustrate their general use via the R packages lavaan and strucchange. We then describe two novel simulations that provide evidence of the tests' practical abilities. As a whole, the paper provides researchers with the tools and knowledge needed to apply these tests to general measurement invariance scenarios.

Highlights

Some of the papers in this special issue focus on the topic of approximate measurement invariance: we know that strict hypotheses of measurement invariance do not hold exactly across different groups, and this should be reflected in corresponding tests of measurement invariance
GENERAL DISCUSSION In this paper, we first described a novel family of test statistics for measurement invariance and illustrated their use via the R packages lavaan and strucchange
We found that the proposed statistics could generally isolate the model parameter violating measurement invariance, so long as the violating parameter is included in the model

Summary

Introduction

Some of the papers in this special issue focus on the topic of approximate measurement invariance: we know that strict hypotheses of measurement invariance do not hold exactly across different groups, and this should be reflected in corresponding tests of measurement invariance. The study of measurement invariance w.r.t. continuous variables is newer and less known: along with the family described here, other methods include moderated factor models (Purcell, 2002; Bauer and Hussong, 2009; Molenaar et al, 2010) and factor mixture models (Dolan and van der Maas, 1998; Lubke and Muthén, 2005) These methods require estimation of a model of greater complexity, while the tests described in this paper work solely on the output of a traditional factor model (see Merkle and Zeileis, 2013, for further comparison of these methods). This procedure is similar in spirit to the calculation of modification indices (Bentler, 1990) and to Lagrange multiplier tests (Satorra, 1989), and, those statistics can be viewed as special cases of the family described here

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