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On Local Influence Analysis of Full Information Item Factor Models

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee  and
Liang Xu
Sik-Yum Lee*
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
Liang Xu
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, N.T., HONG KONG. E-mail: [email protected]
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Abstract

The full information item factor (FIIF) model is very useful for analyzing relations of dichotomous variables. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the FIIF model. The development is based on a Q-displacement function which is closely related with the Monte Carlo EM algorithm in the ML estimation. In the E-step of this algorithm, the conditional expectations are approximated by sample means of observations simulated by the Gibbs sampler from the appropriate conditional distributions. It turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures. The diagnoses are based on the conformal normal curvature that can be computed easily. A number of interesting perturbation schemes are considered. The methodology is illustrated with two real examples.

Keywords

dichotomous variablesMonte Carlo EM algorithmQ-displacement functionGibbs samplerconformal normal curvature
Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 339 - 360
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

The research is fully supported by a grant (CUHK 4356/00H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the Editor, Associate Editor, anonymous reviewers, and W.Y. Poon for valuable comments for improving the paper, and to ICPSR and the relevant founding agency for allowing us to use of their data. The assistance of Michael Leung and Esther Tam is gratefully acknowledged.

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