Hal. Kiers et Jmf. Tenberge, HIERARCHICAL RELATIONS BETWEEN METHODS FOR SIMULTANEOUS COMPONENT ANALYSIS AND A TECHNIQUE FOR ROTATION TO A SIMPLE SIMULTANEOUS STRUCTURE, British journal of mathematical & statistical psychology, 47, 1994, pp. 109-126
Citations number
22
Categorie Soggetti
Psychology, Experimental","Psychologym Experimental","Mathematical, Methods, Social Sciences
The present paper discusses several methods for (simultaneous) compone
nt analysis of scores of two or more groups of individuals on the same
variables. Some existing methods are discussed, and a new method (SCA
-S) is developed for simultaneous component analysis in such a way tha
t for each set essentially the same component structure is found (SCA-
S). This method is compared to alternative methods for analysing such
data which employ the same component weights matrix (SCA-W) or the sam
e pattern matrix (SCA-P) across data sets. Among these methods, SCA-W
always explains the highest amount of variance, SCA-S the lowest, and
SCA-P takes the position in between. These explained variances can be
compared to the amount of variance explained by separate PCAs. Implica
tions of such fit differences are discussed. In addition, it is shown
how, for cases where SCA-S does not fit well, one can use SCA-W (and S
CA-P) to find out if and how correlational structures differ. Finally,
some attention is paid to facilitating the interpretation of an SCA-S
solution. Like the other SCA methods, SCA-S has rotational freedom. T
his rotational freedom is exploited in a specially designed simple str
ucture rotation technique for SCA-S. This technique is illustrated on
an empirical data set.