I'm trying to analyze a survey and find the questions that are most often answered in the same way. There are 29 questions, and I have a matrix with the correlations between each pair of variables. I want to group them into clusters, but cluster analysis isn't something I've ever done, so I was hoping someone had some advice.
My idea was to look at each possible combination of variables, and for each variable in the group, calculate the average of the correlations between that variable and each other in that group, and the average of the correlations between that variable and each variable out of the group. Then take the difference between the in-group and out-group values, and then average the differences for each variable. The combination for which that value is maximized is my first cluster, and then I would repeat the process on the remaining variables a few times until I had several good clusters.
The first problem I see with that is practical -- there's 2^29 = ~537 million combinations, which might be a little much. The second is that I don't really know that this shows what I'm looking for, since like I said, I don't have much experience with cluster analysis, and there might be a better way. Any advice would be great! I'm working in R, and so if anyone had any thoughts about how to actually implement the method, that would also be welcome, though pseudocode is just fine too.