Hostname: page-component-5db58dd55d-bthnr Total loading time: 0 Render date: 2026-05-25T07:30:23.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Local Influence Analysis of Nonlinear Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee  and
Nian-Sheng Tang
Sik-Yum Lee*
Affiliation:
The Chinese University of Hong Kong
Nian-Sheng Tang
Affiliation:
Yunnan University
*
Requests for reprints should be sent to: Prof. S.Y. Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. E-mail: sylee@sparc2.sta.cuhk.edu.hk.
Get access Rights & Permissions [Opens in a new window]

Abstract

By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis are computed via observations of the latent variables generated by the Metropolis-Hastings algorithm, while the diagnostic measures are obtained via the conformal normal curvature. Seven perturbation schemes, including some perturbation schemes on latent vectors, are investigated. The proposed procedure is illustrated by a simulation study and a real example.

Keywords

Benchmarkconformal normal curvaturelocal influenceMetropolis-Hastings algorithmQ-displacement function

Information

Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 4 , December 2004 , pp. 573 - 592
Copyright
Copyright © 2004 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Acknowledgment: This research is fully supported by a grant (CUHK 4243/02H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are indebted to ICPSR and the relevant funding agency for allowing use of their data, and to the Editor and reviewers for their valuable comments for improving the paper.

References

Beckman, R.J., Cook, R.D. (1983). Outliers. Technometrices, 25, 119–149Google Scholar
Cook, R.D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society, 48, 133–169CrossRefGoogle 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, 39, 1–38CrossRefGoogle Scholar
Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their application. Biometrika, 57, 97–10910.1093/biomet/57.1.97CrossRefGoogle Scholar
Jöreskog, K.G., Sörbom, D. (2004). LISREL 8:Structural equation modeling with the SIMPLIS command language, Hove and London: Scientific Software InternationalGoogle Scholar
Kenney, D.A., Judd, C.M. (1984). Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin, 96, 201–21010.1037/0033-2909.96.1.201CrossRefGoogle Scholar
Kwan, C.W., Fung, W.K. (1998). Assessing local influence for specific restricted likelihood: Application to factor analysis. Psychometrika, 63, 35–46CrossRefGoogle Scholar
Lee, S.Y., Song, X.Y. (2003). Estimation and model comparison for a nonlinear latent variable model with fixed covariates. Psychometrika, 68, 27–4710.1007/BF02296651CrossRefGoogle Scholar
Lee, S.Y., Wang, S.J. (2004). Sensitivity analysis of structural equation models. Psychometrika, 61, 93–10810.1007/BF02296960CrossRefGoogle Scholar
Lee, S.Y., Xu, L. (2003). Local influence analysis of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology, 56, 249–270CrossRefGoogle Scholar
Lee, S.Y., Xu, L. (2003). On local influence analysis of full information item model. Psychometrika, 68, 339–36010.1007/BF02294731CrossRefGoogle Scholar
Lee, S.Y., Xu, L. (2004). Influence analysis of nonlinear mixed-effects models. Computational Statistics and Data Analysis, 45, 321–34110.1016/S0167-9473(02)00303-1CrossRefGoogle Scholar
Lee, S.Y., Zhu, H.T. (2000). Statistical analysis of nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology, 53, 209–232CrossRefGoogle Scholar
Lee, S.Y., Zhu, H.T. (2002). Maximum likelihood estimation of nonlinear structural equation models. Psychometrika, 67, 189–210CrossRefGoogle Scholar
Lee, S.Y., Song, X.Y., Lee, J.C.K. (2003). Maximum likelihood estimation of nonlinear structural equation models with ignorable missing data. Journal of Educational and Behavioral Statistics, 28, 111–134CrossRefGoogle Scholar
Lee, S.Y., Song, X.Y., Poon, W.Y. (2004). Comparison of approaches in estimating interaction and quadratic effect of latent variables. Multivariate Behavioral Research, 39, 37–6710.1207/s15327906mbr3901_2CrossRefGoogle ScholarPubMed
Lesaffre, E., Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 54, 570–582CrossRefGoogle ScholarPubMed
Meng, X.L., Rubin, D.B. (2003). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267–27810.1093/biomet/80.2.267CrossRefGoogle Scholar
Meng, X.L., Wong, W.H. (2004). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica, 6, 831–860Google Scholar
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E. (1953). Equations of state calculations by fast computing machine. Journal of Chemical Physics, 21, 1087–1091CrossRefGoogle Scholar
Pan, J.X., Fang, K.T., Liski, E.P. (2004). Bayesian local influence for the growth curve model with Rao's simple covariance structure. Journal of Multivariate Analysis, 58, 55–8110.1006/jmva.1996.0039CrossRefGoogle Scholar
Poon, W.Y., Chan, W. (2002). Influence analysis of ranking data. Psychometrika, 67, 421–43610.1007/BF02294994CrossRefGoogle Scholar
Poon, W.Y., Poon, Y. S. (1999). Conformal normal curvature and assessment of local influence. Journal of the Royal Statistical Society, 61, 51–6110.1111/1467-9868.00162CrossRefGoogle Scholar
Poon, W.Y., Wang, S.J., Lee, S.Y. (1999). Influence analysis of structural equation models with polytomous variables. Psychometrika, 64, 461–473CrossRefGoogle Scholar
Schumacker, R.E., Marcoulides, G.A. (1998). Interaction and nonlinear effects in structural equation models, Mahwah, NJ: Lawrence ErlbaumGoogle Scholar
Shi, L. (1997). Local influence in principal components analysis. Biometrika, 84, 175–186CrossRefGoogle Scholar
Song, X.Y., Lee, S.Y. (2004). Local inference analysis for mixture of structural equation models. Journal of Classification, 21, 111–13710.1007/s00357-004-0008-xCrossRefGoogle Scholar
Song, X.Y., Lee, S.Y (2004). Local inference of two-level latent variable models with continuous and polytomous data. Statistica Sinica, 14, 317–332Google Scholar
Tanaka, Y., Odaka, Y. (1989). Influential observations in principal factor analysis. Psychometrika, 54, 475–48510.1007/BF02294630CrossRefGoogle Scholar
Wei, G.C.G., Tanner, M.A. (1990). A Monte Carlo implementation of the EM algorithm and the Poor man's data augmentation algorithm. Journal of the American Statistical Association, 85, 699–70410.1080/01621459.1990.10474930CrossRefGoogle Scholar
Zhu, H.T., Lee, S.Y. (2001). Local influence for incomplete data models. Journal of the Royal Statistical Society, 63, 111–12610.1111/1467-9868.00279CrossRefGoogle Scholar