EFA Analysis "RSTARTS =" command
Message/Author
 Lixin Ren posted on Wednesday, January 21, 2015 - 8:28 am
Dear Dr. Muthen,

I have a question about what the command "RSTARTS =" means under ANALYSIS when doing EFA. I found out that when I took this command out, it gave me one solution, while when I added it back in, it gave me a few sets of results. For instance, there are 22 sets of results for a 8-factor model (LOCAL MINIMUM # FOR ROTATION ALGORITHM WITH FUNCTION VALUE ###). Which set of results should I trust? Or none of them is trustworthy? How should I move forward?

Below is my syntax for the ANALYSIS section:
ANALYSIS:
TYPE = EFA 1 8;
ESTIMATOR = ML;
ROTATION = GEOMIN;
RSTARTS = 1000;
 Tihomir Asparouhov posted on Wednesday, January 21, 2015 - 10:45 am
Rotation is equivalent to minimizing a simplicity function. See page 401 in

Minimizing a function is tricky as the minimization algorithm has no way of knowing if a point is a local minimum (the best in the vicinity of the parameter space) or it is a global minimum (the best in the entire space). Random starting values are used in Mplus to ensure that the global minimum is found rather than a local minimum. By default we use only 30 random starting values however when the number of factors is large and the sample size is not more random starts should be used.

It is not unusual that multiple local solutions are found. We report the simplicity function value for each local minimum. If the best solution has much better simplicity function value you should use that. This should be an easy call since much better simplicity function means much easier interpretation of the rotated factors.

If the top few solutions have simplicity function values that are not that different a subjective call can be made and you should use the one solution that provides the best interpretation. If you have multiple local solutions that yield similar simplicity function value, that means that we can't quite determine which of these solutions would be the one if you had say 10 times more data than you have.

The above paper has further discussions and examples on that topic.