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Covariance Structure Analysis of Ordinal Ipsative Data

Published online by Cambridge University Press:  01 January 2025

Wai Chan  and
Peter M. Bentler
Wai Chan*
Affiliation:
The Chinese University of Hong Kong
Peter M. Bentler
Affiliation:
University of California, Los Angeles
*
Correspondence concerning this article should be addressed to Wai Chan, Department of Psychology, The Chinese University of Hong Kong, Shatin, HONG KONG.
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Abstract

Data are ipsative if they are subject to a constant-sum constraint for each individual. In the present study, ordinal ipsative data (OID) are defined as the ordinal rankings across a vector of variables. It is assumed that OID are the manifestations of their underlying nonipsative vector y, which are difficult to observe directly. A two-stage estimation procedure is suggested for the analysis of structural equation models with OID. In the first stage, the partition maximum likelihood (PML) method and the generalized least squares (GLS) method are proposed for estimating the means and the covariance matrix of Acy, where Ac is a known contrast matrix. Based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, the generalized least squares method is used to estimate the structural parameters in the second stage. A goodness-of-fit statistic is given for testing the hypothesized covariance structure. Simulation results show that the proposed method works properly when a sufficiently large sample is available.

Keywords

covariance structure analysisordinal ipsative datapartition maximum likelihood methodpseudo maximum likelihood methodtwo-stage estimation
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 4 , December 1998 , pp. 369 - 399
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

This research was supported by National Institute on Drug Abuse Grants DA01070 and DA10017. The authors are indebted to Dr. Lee Cooper, Dr. Eric Holman, Dr. Thomas Wickens for their valuable suggestions on this study, and Dr. Fanny Cheung for allowing us to use her CPAI data set in this article. The authors would also like to acknowledge the helpful comments from the editor and the two anonymous reviewers.

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