Statistical methods aimed to explain variation in correlated data by few latent variables

Background: In applications, often many original variables are available which are different characteristics of the same phenomenon and, therefore, are highly correlated. Practitioners want to reduce the high dimension of original data to a small number of transformed or latent variables. This reduction should not entail an excessive loss of variation in data and should ensure that no important direction of variation get lost. Objective: The objective of this study was to evaluate and compare different statistical methods that aim to explain maximal variation in selected variables. The comparison referred to theoretical assumptions, methodological aspects and applications to real data. Methods and data: We applied principal component analysis (PCA), reduced rank regression (RRR) and partial least squares (PLS) to dietary intake data of 39 food groups obtained by a food frequency questionnaire in the European Prospective Investigation into Cancer and Nutrition (EPIC) Potsdam Study. The response set was composed of several nutrients assumed to be important for the development of chronic diseases. Results: The proportion of variation in the original variables explained by the first PCA factors was markedly greater than the corresponding proportion explained by the first RR