How to interpret the scores generated from factor analysis in R

r
factor_analysis

#1

Hello,

For scoring in factor analysis I have used:

scores <- factanal(na.omit(auto_copy), 3,
                   rotation="varimax",
                   scores = "regression")

The output is:


> head(scores$scores)
     Factor1    Factor2     Factor3
1 -0.4586964 -0.8566645 -0.78793644
2  0.7730385  0.4050716 -0.61917887
4  0.3071091  0.6336516  0.11593273
5 -0.4485194 -0.6062352 -0.28122567
6  0.1819791  0.3317409  0.10670386
7  2.1689047  0.4844853  0.09329937 

So these three factors explain all the variables (14) in the data.How do I interpret these scores??Is it like factor 1 is negatively correlated(-0.45) to the first record or something like that?



#2

The factor scores determines the location of each observation on the factor.

It is analogous to predicted values (yhat) from regression. A good reference to understand the factor scores (interpretation and different methods) is: Understanding and Using Factor Scores:
Considerations for the Applied Researcher

Since you have used method = “regression” this is what it implies:
“independent variables in the regression equation are the standardized observed values of the items in the estimated factors or components. These predictor variables are weighted by regression coefficients, which are obtained by multiplying the inverse of the observed variable correlation matrix by the matrix of factor loadings and, in the case of oblique factors, the factor correlation matrix”