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Quantifying Adventitious Error in a Covariance Structure as a Random Effect

Published online by Cambridge University Press:  01 January 2025

Hao Wu  and
Michael W. Browne
Hao Wu*
Affiliation:
Boston College
Michael W. Browne
Affiliation:
The Ohio State University
*
Correspondence should be made to HaoWu, Department of Psychology, Boston College, Chestnut Hill, MA02467, USA. Email: hao.wu.5@bc.edu
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Abstract

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the root mean square error of approximation. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations.

Keywords

covariance structureadventitious errormisspecificationPitman driftRMSEArandom effect

Information

Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 3 , September 2015 , pp. 571 - 600
Copyright
Copyright © 2014 The Psychometric Society

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