Diagnostics for identifying influential cases in manova

Abstract

Measures of influence of multivariate cases on bilinear combinations of the estimated parameter matrix in MANOVA are extended to the generalized MANOVA (GMANOVA) model. The development is based on the confidence region resulting from the likelihood ratio criterion, and is patterned after the development of Cook's univariate D_I measure. Influence measures corresponding to the other 3 common multivariate test criteria are presented. The measures are shown to be invariant with respect to the conditioning matrices associated with the tests of goodness-of-fit (GOF) and general linear hypotheses. The measures provide a method of assessment of whether the outcome of the GOF test results from the general functional form or the impact of some highly influential cases. The methodology is illustrated in 2 numerical examples.

Keywords:

• influence measures
• multivariate linear model
• Cook's D_I
• confidence regions
• Wilk's likelihood ratio
• Hotelling-Lawley trace
• Pillai's Trace
• Roy's largest root
• goodness-of-fit-test
• invariance