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Local influence analysis of multivariate probit latent variable models

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  • Lu, Bin
  • Song, Xin-Yuan

Abstract

The multivariate probit model is very useful for analyzing correlated multivariate dichotomous data. Recently, this model has been generalized with a confirmatory factor analysis structure for accommodating more general covariance structure, and it is called the MPCFA model. The main purpose of this paper is to consider local influence analysis, which is a well-recognized important step of data analysis beyond the maximum likelihood estimation, of the MPCFA model. As the observed-data likelihood associated with the MPCFA model is intractable, the famous Cook's approach cannot be applied to achieve local influence measures. Hence, the local influence measures are developed via Zhu and Lee's [Local influence for incomplete data model, J. Roy. Statist. Soc. Ser. B 63 (2001) 111-126.] approach that is closely related to the EM algorithm. The diagnostic measures are derived from the conformal normal curvature of an appropriate function. The building blocks are computed via a sufficiently large random sample of the latent response strengths and latent variables that are generated by the Gibbs sampler. Some useful perturbation schemes are discussed. Results that are obtained from analyses of an artificial example and a real example are presented to illustrate the newly developed methodology.

Suggested Citation

  • Lu, Bin & Song, Xin-Yuan, 2006. "Local influence analysis of multivariate probit latent variable models," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1783-1798, September.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1783-1798
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    References listed on IDEAS

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    1. Sik-Yum Lee & S. Wang, 1996. "Sensitivity analysis of structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 93-108, March.
    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    3. Hong-Tu Zhu & Sik-Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    4. Sik-Yum Lee & Nian-Sheng Tang, 2004. "Local influence analysis of nonlinear structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 573-592, December.
    5. Sik-Yum Lee & Liang Xu, 2003. "On local influence analysis of full information item factor models," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 339-360, September.
    6. Yutaka Tanaka & Yoshimasa Odaka, 1989. "Influential observations in principal factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 475-485, September.
    7. W.-Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    8. Wai-Yin Poon & Shu-Jia Wang & Sik-Yum Lee, 1999. "Influence analysis of structural equation models with polytomous variables," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 461-473, December.
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    Cited by:

    1. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.
    2. Vasconcellos, Klaus L.P. & Zea Fernandez, L.M., 2009. "Influence analysis with homogeneous linear restrictions," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3787-3794, September.
    3. V. Lachos & T. Angolini & C. Abanto-Valle, 2011. "On estimation and local influence analysis for measurement errors models under heavy-tailed distributions," Statistical Papers, Springer, vol. 52(3), pages 567-590, August.

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