Reliably reproducing a number of prior classes is assessed with classification error measures, such as accuracy, specificity, sensitivity, positive predictive value and negative predictive value. They are easily calculated, and you can find lots of information online. In your case, another measure which is more naturally tailored to the problem is Cohen's Kappa - a measure of concordance.

In other words, as the problem is put, the method of prediction seems to be irrelevant, it could be any algorithm. It just happens to be CFA for you. What is relevant is a vector of predictions compared to a vector of true facts, and the percentage of coincidence between them.

Hi,

For your question kindly see the following links:

http://www.iu.edu/~statmath/stat/all/cfa/cfa.pdf

Hi,

It depends on if your latent variable is categorical or quantitative.

If you are looking for profiles of gamers, you should perform a latent class analysis (LCA). You can use poLCA in R. I think is the most interesting option considering what you asked. This analysis allows to include covariables.

If you latent variable is quantitative, it could be useful to use NOHARM software, it is based on nonlinear factor analysis. It is a quite good approach to analyse dichotomous items which might have skewness. Also Full-information item factor analysis could be a good approach.

I suggest carrying out both analysis, first LCA, and then nonlinear factor analysis.

Please take a look at the attached files, I think both articles could be useful.

I hope this helps.

Good luck with your research! :)