I want to check if I really understood [classic, linear] factor analysis (FA), especially assumptions that are made before (and possibly after) FA.
Some of the data should be initially correlated and there is a possible linear relation between them. After doing factor analysis, the data are normally distributed (bivariate distribution for each pairs) and there is no correlation between factors (common and specifics), and no correlation between variables from one factor and variables from other factors.
Is it correct?
Best Answer
Input data assumptions of linear FA (I'm not speaking here about internal assumptions/properties of the FA model or about checking the fitting quality of results).
p
correlated vectors must span p-dim space to accomodate their p mutually perpendicular unique components. So, no singularity for theoretical reasons$^1$ (and hence automaticallyn observations > p variables
, without saying; and bettern>>p
). Not that complete multicollinearity is allowed though; yet it may cause computational problems in most of FA algorithms (see also).$^1$ ULS/minres methods of FA can work with singular and even non p.s.d. correlation matrix, but strictly theoretically such an analysis is dubious, for me.