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.
Similar content being viewed by others
References
Cook, R.D. (1986). Assessment of local influence. Journal of the Royal Statistical Society, Series B, 48, 133–169.
Labra, F.V., Aoki, R., & Bolfarine, H. (2005). Local influence in null intercept measurement error regression under a Student_t model. Journal of Applied Statistics, 32, 723–739.
Lee, S.Y., & Song, X.Y. (2004). Maximum likelihood analysis of a general latent variable model with hierarchically mixed data. Biometrics, 60, 624–636.
Lee, S.Y., & Tang, N.S. (2004). Local influence analysis of nonlinear structural equation models. Psychometrika, 69, 573–592.
Lee, S.Y., & Wang, S.J. (1996). Sensitivity analysis of structural equation models. Psychometrika, 61, 93–108.
Lee, S.Y., & Xu, L. (2004). Influence analysis of nonlinear mixed-effects models. Computational Statistics and Data Analysis, 45, 321–342.
Lee, S.Y., & Zhu, H.T. (2002). Maximum likelihood estimation of nonlinear structural equation models. Psychometrika, 67, 189–210.
Lesaffre, E., & Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 54, 570–582.
McCulloch, C.E. (1997). Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association, 92, 162–170.
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.
Schumacker, R.E., & Marcoulides, G.A. (Eds.) (1998). Interaction and nonlinear effects in structural equation models. Hillsdale: Lawrence Erlbaum.
Song, X.Y., & Lee, S.Y. (2004). Local influence analysis of two-level latent variable models with continuous and polytomous data. Statistica Sinica, 14, 317–332.
Zhu, H.T., & Lee, S.Y. (2001). Local influence for incomplete data models. Journal of the Royal Statistical Society, Series B, 63, 111–126.
Zhu, H.T., & Lee, S.Y. (2003). Local influence for generalized linear mixed models. Canadian Journal of Statistics, 31, 293–309.
Zhu, H.T., Ibrahim, J.G., Lee, S.Y., & Zhang, H.P. (2007). Perturbation selection and influence measures in local influence analysis. The Annals of Statistics, 35, 2565–2588.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, F., Zhu, HT. & Lee, SY. Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model. Psychometrika 74, 493–516 (2009). https://doi.org/10.1007/s11336-009-9114-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11336-009-9114-3