** by Gösta
Hägglund**

** Research
Report 1995:8**

Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden

**Abstract**

A number of theorems are proved for
the characterization of the optimal reference variables using the factor
analysis estimation methods FABIN based on instrumental variables due to
Hägglund (1982). The different theorems consider several alternative
situations with at most three non-optimal reference variables involved.
Cases with an arbitrary number of of factors are considered. A fundamental
definition called *FABIN-dominant diagonal* is introduced. The theorems
are based on this concept.

**Key words:** factor analysis,
instrumental variables, reference variables.

*Last update: 1997-12-16 / KH*