I have a number of dichotomous variables from a number of study participants, and I want to do some exploratory factor analyses and other things. However, my sample is too small to include all the dichotomous variables, so I have to select a subset of them. There are various ways in which they can be selected, such as by theoretical considerations, agreement with another particular variable which measures an underlying construct of interest etc.
But I also have an idea that variables with a more even distribution of 1:s and 0:s should be preferable to variables with a very uneven distribution. My thinking is that variables in which only 1% are 1:s, or 99% are 1:s, contribute with very little information regarding any underlying factors. It thus seems intuitive that the closer the distribution of the variable is to 50% of each, the more information the variable potentially may contain regarding any underlying factor structure. So it would then make sense to try an approach in which this relationship is maximized, i.e. selecting variables based on closeness to a 50/50 distribution.
Is my thinking about this issue correct - is this a viable approach? And if so, could anyone provide a reference in which this issue is discussed, so that I can reference it if I need to?