Scaling in ANOVA-simultaneous component analysis.

In omics research often high-dimensional data is collected according to an experimental design. Typically, the manipulations involved yield differential effects on subsets of variables. An effective approach to identify those effects is ANOVA-simultaneous component analysis (ASCA), which combines analysis of variance with principal component analysis. So far, pre-treatment in ASCA received hardly any attention, whereas its effects can be huge. In this paper, we describe various strategies for scaling, and identify a rational approach. We present the approaches in matrix algebra terms and illustrate them with an insightful simulated example. We show that scaling directly influences which data aspects are stressed in the analysis, and hence become apparent in the solution. Therefore, the cornerstone for proper scaling is to use a scaling factor that is free from the effect of interest. This implies that proper scaling depends on the effect(s) of interest, and that different types of scaling may be proper for the different effect matrices. We illustrate that different scaling approaches can greatly affect the ASCA interpretation with a real-life example from nutritional research. The principle that scaling factors should be free from the effect of interest generalizes to other statistical methods that involve scaling, as classification methods.