Cross Validation in Factor Analysis I am trying to conduct an EFA with a sample size of 150 respondents. I would also like to use cross-validation but my professor says that the sample is not big enough for that. Is that true?
 A: This is definitely not true. Cross validation should always be done to avoid overfitting in the frequentist regime. In genetic analysis, there are cases where when studying a cancer the sample size is 40 so the split is 36 training 4 test in the 10 fold regime. See the example on pg. 245 of Hastie, Tibshirani and Friedman's book where they use CV where the number of predictors are 100 times the number of samples if you are still not convinced
A: I would even suggest the opposite. 
When you have enough data, you can simply do model selection/evaluation with simple splitting, e.g., to split your data in to train/development/test. 
When you do not have enough data, you should consider more advanced statistical procedures such as cross-validation and bootstrapping to make sure you get everything you can from the limited resources.
For example, in bioinformatics it is common to have a data sample with a very limited size. (There are often cases that the number of features is way larger than the number of data instances.) Leave-one-out cross validation is a popular choice in such situation, which can be seen in many publications in that field.  
