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On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models

Published online by Cambridge University Press:  01 January 2025

Njål Foldnes Open the ORCID record for Njål Foldnes [Opens in a new window]  and
Steffen Grønneberg
Njål Foldnes*
Affiliation:
BI Norwegian Business School
Steffen Grønneberg
Affiliation:
BI Norwegian Business School
*
Correspondence should be made to Njål Foldnes, Department of Economics, BI Norwegian Business School,4014 Stavanger, Norway. Email:njal.foldnes@bi.no
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Abstract

A standard approach for handling ordinal data in covariance analysis such as structural equation modeling is to assume that the data were produced by discretizing a multivariate normal vector. Recently, concern has been raised that this approach may be less robust to violation of the normality assumption than previously reported. We propose a new perspective for studying the robustness toward distributional misspecification in ordinal models using a class of non-normal ordinal covariance models. We show how to simulate data from such models, and our simulation results indicate that standard methodology is sensitive to violation of normality. This emphasizes the importance of testing distributional assumptions in empirical studies. We include simulation results on the performance of such tests.

Keywords

simulationordinal datastructural equation modelspolychoric correlationsIRT
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 4 , December 2019 , pp. 1000 - 1017
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/s11336-019-09688-z) contains supplementary material, which is available to authorized users.

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