Blus Residuals in Multivariate Linear Models
The examination of residuals is always an important aspect of fitting data to statistical models in terms of identifying influential observations and detecting violations of assumptions. The latter use is difficult to perform for the ordinary residuals in the univariate linear model because these residuals are not independent. This led researchers to consider alternative sets of residuals, such as the best linear, unbiased, scalar-type variance (BLUS) residuals. In this article the definition of BLUS residuals is extended to multivariate models. The extension is relatively straightforward for the multivariate analysis of variance (MANOVA) model, but not for the generalized multivariate analysis of variance (GMANOVA) model and the mixed MANOVA-GMANOVA model. For each of the GMANOVA and mixed MANOVA-GMANOVA models two sets of BLUS residuals arise naturally, namely, a “between” set and a “within” set.
Key words and phrasesMANOVA GMANOVA residual analysis
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- Mardia, K.V. (1980). ‘Tests of Univariate and Multivariate Normality,’ in Handbook of Statistics, Volume I (P.R. Krishnaiah, editor). North-Holland: New York, 279–320.Google Scholar
- Rao, C.R. (1967). ‘Least Squares Theory Using an Estimated Dispersion Matrix and Its Application to Measurement of Signals,’ in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume I (L.M. LeCam and J. Neyman, editors). University of California Press: Berkeley, California, 355–372.Google Scholar