In factor analysis (FA), Anderson-Rubin method of computation of
factor scores is meant for orthogonal factors only.

If you do FA on some correlations of some data and obliquely rotate
the extracted factors, so that they correlatte, the subsequently
computed AR factor scores come out nevertheless uncorrelated.

It is well known that McDonald's factor scores, also known as
McDonald-Anderson-Rubin factor scores, are

**the extension of**
Anderson-Rubin method applicable for oblique factors as well. The
computed factor scores display correlations exactly equal to
correlations between the factors - be the factors orthogonal or
correlated. Some FA packages even just compute
McDonald-Anderson-Rubin factor scores while calling them
"Anderson-Rubin".

In SPSS Statistics, FACTOR does not (strangely!) compute
McDonald-Anderson-Rubin factor scores. At least up to version 22 (I
can't say of the later ones at this time).

What that might be - simply negligence? or some reason?

References:

James W. Grice. Computing and Evaluating Factor Scores //
Psychological Methods 2001, Vol. 6, No. 4, 430-450

Christine DiStefano et al. Understanding and Using Factor Scores //
Practical Assessment, Research & Evaluation, Vol 14, No 20

Jos M.F. ten Berge et al. Some new results on correlation-preserving
factor scores prediction methods // Linear Algebra and its
Applications 289 (1999) 311-318.

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