# Same rotated component matrix in Factor Analysis despite using different data normalizations

I'm using SPSS for factor analysis with these options:

FACTOR
/VARIABLES VAR00001 VAR00002 VAR00003 VAR00004 VAR00005 VAR00006
/MISSING LISTWISE
/ANALYSIS VAR00001 VAR00002 VAR00003 VAR00004 VAR00005 VAR00006
/PRINT UNIVARIATE INITIAL CORRELATION SIG DET KMO INV REPR AIC EXTRACTION ROTATION
/PLOT EIGEN ROTATION
/CRITERIA MINEIGEN(1) ITERATE(25)
/EXTRACTION PC
/CRITERIA ITERATE(25)
/ROTATION VARIMAX
/METHOD=CORRELATION.


Before inserting data to the software I normalized (and in one case standardize) data:

1. Using values-min/max-min transformation.
2. Using values A as denominator of all features.
3. Using B values (different with A) as denominator of all features.
4. Using C values (different with A and B) as denominator of all features.
5. standardize data using mean and std.
6. Using Raw data as input of factor analysis of SPSS.

Output of SPSS:

Rotated Component Matrix
Component
1       2
VAR00001    .973    -.062
VAR00002    .911    -.134
VAR00003    .833    -.035
VAR00004    .972    -.102
VAR00005    -.236   .823
VAR00006    .062    .878
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
a Rotation converged in 3 iterations.


In all cases I have same Rotated Component Matrix (other reports are same too)! Why? Is this a bug or because of Correlation Method or VARIMAX rotation?

## 1 Answer

It seems (/METHOD=CORRELATION) that you are asking SPSS to perform FA on the correlation matrix (actually by typing /EXTRACTION PC you seem to be performing PCA and not FA, but it does not matter for this question).

Correlation matrix does not change if you scale individual variables, so any amount of normalizing or standardizing would not change it. You can think of it as if all the variables are automatically standardized to have zero mean and unit variance prior to the PCA/FA analysis. No wonder you always get the same result.

Varimax rotation has nothing to do with it.