When conducting factor analysis (FA), retained factors are standardised. I want to know if it is possible to obtain the factor scores in the same metric as the untandardized observed variables. This is the only answer I could find to my question, and a similar one here. However, in that example, there is only ONE factor. It seems in general that such "un-standardisation" is not normally performed, as there are no references to it at all.
My questions are:
- Is it possible to unstandardize my factor scores when there is more than one factor?
- What is the mathematical explanation for that (whether possible or not)?
- Will it be dependent on the orthogonality of the factors? (i.e., what if I use an oblique rotation and factors are correlated?)
I'm attaching a similar code in R to the referenced question, only with factors = 3 and oblique rotation. Is this calculation valid?
v1 <- c(1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,4,5,6) v2 <- c(1,2,1,1,1,1,2,1,2,1,3,4,3,3,3,4,6,5) v3 <- c(3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,5,4,6) v4 <- c(3,3,4,3,3,1,1,2,1,1,1,1,2,1,1,5,6,4) v5 <- c(1,1,1,1,1,3,3,3,3,3,1,1,1,1,1,6,4,5) v6 <- c(1,1,1,2,1,3,3,3,4,3,1,1,1,2,1,6,5,4) observed_matrix <- cbind(v1,v2,v3,v4,v5,v6) fa = factanal(observed_matrix, factors = 3, scores = "regression", rotation='promax') FactorScores <- fa$scores FactorLoadings <- fa$loadings UnstandardizedFactorScores<-rowMeans(observed_matrix)+apply(observed_matrix,1,sd)*FactorScores