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A Problem with Discretizing Vale–Maurelli in Simulation Studies

Published online by Cambridge University Press:  01 January 2025

Steffen Grønneberg  and
Njål Foldnes Open the ORCID record for Njål Foldnes [Opens in a new window]
Steffen Grønneberg
Affiliation:
BI Norwegian Business School
Njål Foldnes*
Affiliation:
BI Norwegian Business School
*
Correspondence should be made to Njål Foldnes, Department of Economics, BI Norwegian Business School, 0484 Oslo, Norway. Email: njal.foldnes@bi.no
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Abstract

Previous influential simulation studies investigate the effect of underlying non-normality in ordinal data using the Vale–Maurelli (VM) simulation method. We show that discretized data stemming from the VM method with a prescribed target covariance matrix are usually numerically equal to data stemming from discretizing a multivariate normal vector. This normal vector has, however, a different covariance matrix than the target. It follows that these simulation studies have in fact studied data stemming from normal data with a possibly misspecified covariance structure. This observation affects the interpretation of previous simulation studies.

Keywords

polychoric correlationVale–Maurellinon-normal datastructural equation modelingordinal data
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 2 , June 2019 , pp. 554 - 561
Copyright
Copyright © 2019 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-019-09663-8) contains supplementary material, which is available to authorized users.

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