Problems running a Factor Analysis I'm given a data set to run factor analysis on. The number of variables was greater than the number of cases so I had to decide which variables to remove. I did it looking at the correlation matrix, removing those variables who were too highly (almost totally) correlated. So here are a couple of questions:
1) What's the best method to get rid of variables when dealing with such problem? The number of my cases is 48 while I have reduced the number of variables to 24. I know the ratio of number of observations to number of variables must be at least 5 but I'm lost as to decide what other variables I need to remove.
I ran the factor analysis on this data set and I got this error: 

No local minimum was found, extraction was terminated.

Which must have to do with my data set not being suitable for a factor analysis, I assume. So, what should I do now? 2) Do I get the error because I still have lots of variables for which I don't have sufficient number of observations?
 A: 1) The best method to reduce the number of variables is a combination of theory and examining the correlation matrix (both the data and the residual after fitting). When you're unsure of the number of factors to extract/which items load on which factors, then you usually take an exploratory factor analysis approach. This is then validated with a confirmatory factor analysis on a separate set of data. You seem to be doing both simultaneously, which will most certainly lead to problems of overfitting.
2) Depending upon the software you are using, you can specify new starting values or increase the iteration limit to help with convergence issues. However, these issues substantially increase with smaller sample sizes. Some rules of thumb (as per David Kenny) suggest N = 200 as a goal for fitting an SEM. Of course, this can be reduced for simpler models (i.e., models without latent variables, or in your case, no more than a one-factor CFA) or models with strong correlations. With N = 48 and 24 items, you're likely to have issues even with the simplest of latent variable models. I've had issues in the past with a one-factor CFAs with N = 100, despite having strong correlations in the dataset and the measure being one that was previously validated. 
