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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: sylee@sparc2.sta.cuhk.edu.hk
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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.

References

Beckman, R.J., & Cook, R.D. (1983). Outliers. Technometrics, 25, 119–149.Google Scholar
Beckman, R.J., Nachtsheim, C.J., & Cook, R, D. (1987). Diagnostics for mixed model analysis of variance. Technometrics, 29, 413–426.Google Scholar
Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 37, 29–51.Google Scholar
Bock, R.D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261–280.CrossRefGoogle Scholar
Bock, R.D., & Lieberman, M. (1970). Fitting a response model for dichotomously scored items. Psychometrika, 35, 179–197.CrossRefGoogle Scholar
Cook, R.D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society, Series B, 48, 133–169.CrossRefGoogle Scholar
Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1–38.CrossRefGoogle Scholar
Escobar, L.A., & Meeker, W.Q. (1992). Assessing influence in regression analysis with censored data. Biometrics, 48, 507–528.CrossRefGoogle ScholarPubMed
Fung, W.K., & Kwan, C.W. (1995). Sensitivity analysis in factor analysis: Difference between using covariance and correlation matrices. Psychometrika, 60, 607–614.CrossRefGoogle Scholar
Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.CrossRefGoogle ScholarPubMed
Kwan, C.W., & Fung, W.K. (1998). Assessing local influence for specific restricted likelihood: Application to factor analysis. Psychometrika, 63, 35–46.CrossRefGoogle Scholar
Lee, S.Y., Poon, W.Y., & Bentler, P.M. (1995). A two-stage estimation of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology, 48, 339–358.CrossRefGoogle ScholarPubMed
Lee, S.Y., & Wang, S.J. (1996). Sensitivity analysis of structural equation models. Psychometrika, 61, 93–108.CrossRefGoogle Scholar
Lee, S.Y., & Xu, Liang. (in press). Local influence analysis of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology.Google Scholar
Lesaffre, E., & Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 54, 570–582.CrossRefGoogle ScholarPubMed
Meng, X.L., & Schilling, S. (1996). Fitting full-information item factor models and an empirical investigation of bridge sampling. Journal of American Statistical Association, 91, 1254–1267.CrossRefGoogle Scholar
Meng, X.L., & Schilling, S. (2002). Warp bridge sampling. Journal of Computational and Graphical Statistics, 11, 552–586.CrossRefGoogle Scholar
Meng, X.L., & Wong, W.H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica, 6, 831–860.Google Scholar
Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115–132.CrossRefGoogle Scholar
Ouwens, M.J.N.M., Tan, F.E.S., & Berger, M.P.F. (2001). Local influence to detect influential data structures for generalized linear mixed models. Biometrics, 57, 1166–1172.CrossRefGoogle ScholarPubMed
Poon, W.Y., & Poon, Y.S. (1999). Conformal normal curvature and assessment of local influence. Journal of the Royal Statistical Society, Series B, 61, 51–61.CrossRefGoogle Scholar
Poon, W.Y., & Ng, S.C. (2002). Identification of influential cells in the analysis of ordinal square tables. British Journal of Mathematical and Statistical Psychology, 55, 231–246.CrossRefGoogle ScholarPubMed
Poon, W.Y., Wang, S.J., & Lee, S.Y. (1999). Influence analysis of structural equation models with polytomous variables. Psychometrika, 64, 461–473.CrossRefGoogle Scholar
Poon, W.Y., & Poon, Y.S. (2001). Conditional local influences in case-weights linear regression. British Journal of Mathematical and Statistical Psychology, 54, 171–191.CrossRefGoogle ScholarPubMed
Shi, J.Q., & Lee, S.Y. (2000). Latent Variable Models with Mixed continuous and Polytomous Data. Journal of the Royal Statistical Society, Series B, 62, 77–87.CrossRefGoogle Scholar
Shi, L. (1997). Local influence in principal component analysis. Biometrika, 84, 175–186.CrossRefGoogle Scholar
Tanaka, Y., & Odaka, Y. (1989). Influential observations in principal factor analysis. Psychometrika, 54, 475–485.CrossRefGoogle Scholar
Tanaka, Y., & Odaka, Y. (1989). Sensitivity analysis in maximum likelihood factor analysis. Communications in Statistics, Series A, 18, 4067–4084.CrossRefGoogle Scholar
Tanaka, Y., Watadani, S., & Moon, S.H. (1991). Influence in covariance structure analysis: With an application to confirmatory factor analysis. Communications in Statistics, Series A, 20, 3805–3821.CrossRefGoogle Scholar
Thomas, W., & Cook, R.D. (1989). Assessing influence on regression coefficients in generalized linear models. Biometrika, 76, 741–749.CrossRefGoogle Scholar
Thomas, W., & Cook, R.D. (1990). Assessing influence on predictions from generalized linear models. Technometrics, 32, 59–65.CrossRefGoogle Scholar
Wang, S.J., & Lee, S.Y. (1996). Sensitivity analysis of structure equation models with equality functional constrains. Computational Statistics & Data Analysis, 23, 239–256.CrossRefGoogle Scholar
Wei, G.C.G., & Tanner, M.A. (1990). Posterior computations for censored regression data. Journal of American Statistical Association, 85, 829–839.CrossRefGoogle Scholar
Weissfeld, L.A., & Schneider, H. (1990). Influence diagnostics for the Weibull model fit to censored data. Statistics and Probability Letters, 9, 67–73.CrossRefGoogle Scholar
Yuan, Ke-Hai, & Benter, P.M. (2001). Effect of outliers on estimators and test in covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 54, 161–175.CrossRefGoogle ScholarPubMed
Zhu, H.T., & Lee, S.Y. (2001). Local influence for incomplete data models. Journal of the Royal Statistical Society, Series B, 63, 111–126.CrossRefGoogle Scholar
Zhu, H.T., Lee, S.Y., Wei, B.C., & Zhou, J. (2001). Case-deletion measures for models with incomplete data. Biometrika, 88, 727–737.CrossRefGoogle Scholar