Title: A comparison of methods to detect invariant reference indicators in structural equation modelling

Authors: Tiffany A. Whittaker; Jam Khojasteh

Addresses: Department of Educational Psychology, The University of Texas at Austin, 1 University Station, D5800, SZB 504, Austin, TX 78712-0383, USA ' School of Educational Studies, Research, Evaluation, Measurement and Statistics, Oklahoma State University at Tulsa, 700 North Greenwood Avenue, Mail Hall 2444A, Tulsa, OK 74106, USA

Abstract: Measurement invariance via multiple-group methods in structural equation modelling is becoming more widely tested by applied researchers. When conducting invariance tests, the selection of an invariant reference indicator is an important concern because it has implications when attempting to detect non-invariance at other levels within a model. Cheung and Rensvold (1999) and Yoon and Millsap (2007) have proposed two methods, respectively, which may be used to select an invariant reference indicator. This study compared these two reference indicator selection methods under varied conditions to assess their accuracy with respect to identifying non-invariant and invariant factor loadings. The two methods performed more optimally in certain conditions. Overall, the method proposed by Yoon and Millsap (2007) performed more accurately when detecting non-invariant indicators whereas the method proposed by Cheung and Rensvold (1999) performed more accurately when detecting invariant indicators. Implications and recommendations are provided.

Keywords: measurement invariance; reference indicator selection; factor-ratio test; invariance testing; modification indices; invariance detection; invariant reference indicators; structural equation modelling; SEM.

DOI: 10.1504/IJQRE.2013.058310

International Journal of Quantitative Research in Education, 2013 Vol.1 No.4, pp.426 - 443

Received: 09 Jan 2013
Accepted: 15 Aug 2013

Published online: 29 Apr 2014 *

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