Based on the local influence approach with an appropriate perturbation scheme, measures are developed to assess the influence of an individual cell in contingency tables. The authors demonstrate that the developed measures are particularly suitable for sensitivity analysis in tables with sampling zeros. The independence model and the log-linear model, together with numerical examples, are presented for illustration.
Agresti, Alan. 1990. Categorical Data Analysis. New York: John Wiley.
2.
Agresti, Alan, and Ming-Chung Yang. 1987. “An Empirical Investigation of Some Effects of Sparseness in Contingency Tables.” Computational Statistics and Data Analysis5: 9-21.
3.
Andersen, Erling B.1992. “Diagnostics in Categorical Data Analysis.” Journal of the Royal Statistical Society B54: 781-91.
4.
Belsley, David A., Edwin Kuh, and Roy E. Welsch. 1980. Regression Diagnostics. New York: John Wiley.
5.
Bishop, Yvonne V.V., Stephen E. Fienberg, and Paul W. Holland. 1975. Discrete Multivariate Analysis. Cambridge, MA: MIT Press.
6.
Cook, R. Dennis. 1986. “Assessment of Local Influence (With Discussion).” Journal of the Royal Statistical Society, B, 48: 133-69.
7.
Everitt, B.S.1992. The Analysis of Contingency Tables. New York: Chapman & Hall.
8.
IMSL Math/Library. 1994. FORTRAN Subroutines for Mathematical Applications. Houston, TX: Visual Numerics, Inc.
9.
Poon, Wai-Yin, Shing-Fong Lew, and Yat S. Poon. 2000. “A Local Influence Approach to Identifying Multiple Multivariate Outliers.” British Journal of Mathematical and Statistical Psychology53: 255-73.
10.
Poon, Wai-Yin and Sau-Chun Ng. 2002. “Identification of Influential Cells in the Analysis of Ordinal Square Tables.” British Journal of Mathematical and Statistical Psychology55: 231-46.
11.
Poon, Wai-Yin, and Yat S. Poon. 1999. “Conformal Normal Curvature and Assessment of Local Influence.” Journal of the Royal Statistical Society B61: 51-61.
12.
—. 2001. “Conditional Local Influence in Case-Weights Linear Regression.” British Journal of Mathematical and Statistical Psychology54: 177-91.
13.
—. 2002. “Influential Observations in the Estimation of Mean Vector and Covariance Matrix.” British Journal of Mathematical and Statistical Psychology55: 177-92.
14.
Pregibon, Darye. 1981. “Logistic Regression Diagnostics.” The Annals of Statistics9: 705-24.
15.
Radelet, Michael. 1981. “Racial Characteristics and the Imposition of the Death Penalty.” American Sociological Review46: 918-27.
16.
Thomas, William and R.D. Cook. 1990. “Assessing Influence on Predictions in Generalized Linear Models.” Technometrics32: 39-65.
17.
Yuan, Ke-Hai and Peter M. Bentler. 2001. “Effect of Outliers on Estimators and Tests in Covariance Structure Analysis.” British Journal of Mathematical and Statistical Psychology54: 161-75.
18.
Yuan, Ke-Hai, Wai Chan, and Peter M. Bentler. 2000. “Robust Transformation With Applications to Structural Equation Modelling.” British Journal of Mathematical and Statistical Psychology53: 31-50.