A Note on Cook`s Distance in the Multivariate Linear Model Bae, Whasoo; Hwang, Hyunmi; Kim, Choongrak;
We propose a version of Cook`s distance (called local distance) in the multivariate linear model. The proposed version is a matrix, while the existing version of Cook`s distance (called global distance) is a scalar. The existing Cook`s distance is the trace of the proposed Cook`s distance. In addition, we argue that the proposed Cook`s distance has a more natural extension of the Cook`s distance in the univariate linear model than the existing Cook`s distance. An illustrative example based on a real data set is given.
Global distance;influential observations;local distance;
Altunkaynak, B. and Ekni, M. (2002). Detection of influential observation vectors for multivariate linear regression, Journal of Mathematics and Statistics, 31, 139-151.
Banerjee, M. and Frees, E. W. (1997). Influence diagnostics for linear longitudinal models, Journal of the American Statistical Association, 92, 999-1005.
Caroni, C. (1987). Residuals and influence in the multivariate linear model, The Statistician, 36, 365-370.
Cook, R. D. (1977). Detection of influential observations in linear regression, Technometrics, 19, 15-18.
Cook, R. D. (1986). Assessment of local influence, Journal of the Royal Statistical Society, Series B, 48, 133-169.
Cook, R. D., Pena, D. and Weisberg, S. (1988). The likelihood displacement, Communications in Statistics - Theory and Methods, 17, 623-640.
Diaz-Garcia, J. A., Rohas, M. G. and Leiva-Sanchez, V. (2003). Influence diagnostics for elliptical multivariate linear regression models, Communications in Statistics - Theory and Methods, 32, 625-641.
Fung, W. K. (1999). Outlier diagnostics in several multivariate samples, Journal of the Royal Statistical Society, Series D, 48, 73-84.
Green, P. E. (1978). Analyzing Multivariate Data, Hindsdale, Ill, The Dryden Press.
Lindsey, P. J. and Lindsey, J. K. (2000). Diagnostic tools for random effects in the repeated measures growth curve model, Computational Statistics and Data Analysis, 33, 79-100.
Preisser, J. S. and Qaqish, B. F. (1996). Deletion diagnostics for generalized estimating equations, Biometrika, 83, 551-562.
Tang, M. K. and Fung, W. K. (1997). Case-deletion diagnostics for test statistics in multivariate regression, Australian and New Zealand Journal of Statistics, 39, 345-353.