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2015 ; 11
(5
): 1265-1276
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Scaling in ANOVA-simultaneous component analysis
#MMPMID26366136
Timmerman ME
; Hoefsloot HC
; Smilde AK
; Ceulemans E
Metabolomics
2015[]; 11
(5
): 1265-1276
PMID26366136
show ga
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.