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Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach

Published online by Cambridge University Press:  01 January 2025

Lifang Deng  and
Ke-Hai Yuan
Lifang Deng
Affiliation:
Beihang University
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
*
Correspondence should be made to Ke-Hai Yuan, Department of Psychology, University of Notre Dame, Notre Dame, IN 46556, USA. Email: kyuan@nd.edu
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Abstract

The conventional setup for multi-group structural equation modeling requires a stringent condition of cross-group equality of intercepts before mean comparison with latent variables can be conducted. This article proposes a new setup that allows mean comparison without the need to estimate any mean structural model. By projecting the observed sample means onto the space of the common scores and the space orthogonal to that of the common scores, the new setup allows identifying and estimating the means of the common and specific factors, although, without replicate measures, variances of specific factors cannot be distinguished from those of measurement errors. Under the new setup, testing cross-group mean differences of the common scores is done independently from that of the specific factors. Such independent testing eliminates the requirement for cross-group equality of intercepts by the conventional setup in order to test cross-group equality of means of latent variables using chi-square-difference statistics. The most appealing piece of the new setup is a validity index for mean differences, defined as the percentage of the sum of the squared observed mean differences that is due to that of the mean differences of the common scores. By analyzing real data with two groups, the new setup is shown to offer more information than what is obtained under the conventional setup.

Keywords

measurement invariancecommon scorespecific factorbootstrapchi-square-difference statisticwald statistic
Type
Original Paper
Information
Psychometrika , Volume 81 , Issue 3 , September 2016 , pp. 802 - 829
Copyright
Copyright © 2015 The Psychometric Society

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