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Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model

Published online by Cambridge University Press:  01 January 2025

Fei Chen ,
Hong-Tu Zhu  and
Sik-Yum Lee
Fei Chen
Affiliation:
Department of Statistics, The Chinese University of Hong Kong and Department of Statistics, Yunnan University
Hong-Tu Zhu
Affiliation:
Department of Biostatistics, University of North Carolina at Chapel Hill
Sik-Yum Lee*
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
*
Requests for reprints should be sent to Sik-Yum Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong. E-mail: sylee@sta.cuhk.edu.hk
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Abstract

Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure to address this issue in the context of latent variable models. An application to nonlinear structural equation models is considered. Six perturbation schemes are investigated, including three schemes under which simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the influential ones. The proposed procedure is illustrated by artificial examples and a simulation study as well as a real example.

Keywords

appropriate perturbationEM algorithmlocal influencenonlinear structural equation modelinformation matrix for the perturbation
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 3 , September 2009 , pp. 493 - 516
Copyright
Copyright © 2009 The Psychometric Society

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