Data-Based Transformations in Multivariate Analysis. Final Report

摘要

Univariate transformations are considered initially, because of the common practice of transforming separately the marginal distribution of each variable of a multivariate observation. Familiar examples include those based on a priori assumptions about the underlying sampling distribution, as well as several general classes of empirical transformations recommended in a recent text by Mosteller and Tukey. Multi-normal criteria are considered as a basis for obtaining and evaluating multivariate transformations, including the likelihood criterion and various transformations to uniform statistics. The extension of power and shifted-power transformations to multivariate analysis is reviewed in detail, including recently published work involving q-sample problems. Finally, applications of projective transformations are proposed in order to remove the effects of extraneous sources of variation, e.g., specimens of different ages, from different nutritional backgrounds, etc. It is shown that the actual values of these ancillary variables will not be required if the analysis is performed in a subspace which is orthogonal to the gradients attributable to these variables. Models are proposed for principal components analysis, canonical correlation, linear classification functions, and discriminant function analysis in the general MANOVA context. (ERA citation 07:048894)