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Influence Diagnostics in Common Principal Components Analysis

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  • Gu, Hong
  • Fung, Wing K.

Abstract

In principal components analysis, the influence function and local influence approaches have been well established as important diagnostic tools. In this article, we first review the generalized local influence approach in the restricted likelihood framework. We then apply the restricted likelihood local influence diagnostic in the common principal components analysis. One special part of this local influence result is an elliptical norm of the empirical influence function, which is comparable to the deletion diagnostic scaled by the same matrix which requires iterative solutions for parameter estimates with every case deleted. Local influence diagnostics are constructed by some basic building blocks that are obtained directly from the maximum likelihood estimates of the parameters, and which are based on the original data and thus require less computation. A numerical example illustrates the technique and some joint influence effects are identified by the proposed method.

Suggested Citation

  • Gu, Hong & Fung, Wing K., 2001. "Influence Diagnostics in Common Principal Components Analysis," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 275-294, November.
    • Handle: RePEc:eee:jmvana:v:79:y:2001:i:2:p:275-294
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    References listed on IDEAS

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    1. Wing K. Fung & C. W. Kwan, 1997. "A Note on Local Influence Based on Normal Curvature," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 839-843.
    2. Pan, Jian-Xin & Fang, Kai-Tai & Liski, Erkki P., 1996. "Bayesian Local Influence for the Growth Curve Model with Rao's Simple Covariance Structure," Journal of Multivariate Analysis, Elsevier, vol. 58(1), pages 55-81, July.
    3. C. Kwan & W. Fung, 1998. "Assessing local influence for specific restricted likelihood: Application to factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 63(1), pages 35-46, March.
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    Cited by:

    1. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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