I have designed a rather long (250 Qn) survey designed to uncover user clusters. The questions are such that the pattern of answering should elicit user clusters, but I am having trouble uncovering these with my analyses to date.
For example, a typical Qn might be: 'Are you more of a dog or cat person?' Or, 'Chocolate or vanilla?' etc.
I'm coding these questions in a binary format. So, if the user answered the two questions above with 1. Dog and 2. Vanilla, the user's answer matrix would look like: [1 0 0 1] Signifying that the user chose the first and fourth answer, where the answer space is [Dog Cat Chocolate Vanilla]
I have roughly 300 respondents who have answered all 250 questions, giving around 800 possible answers, so my binary [user x answer] matrix is 300 x 800.
I have run SVD on this matrix. The first factor relates to the number of people who selected that answer (magnitude) as expected. The second factor clusters nicely into male / female (I know because I ask gender) respondents.
My problem is, all other factors are Gaussian and offer no way for me to split them into groups. A plot-matrix of the factors shows no grouping whatsoever. A clue: when I look at the highest and lowest factor values for factors 3, 4, & 5, I can determine that there are definite personality types represented. For example, cautious/risky or conservative/outgoing or frugal/outlandish. But these are just the tails of a Gaussian. I am completely unable to separate these questions by anything but a 'random' threshold to the Gaussian tail.
The goal is to have a subset of the 250 questions that would allow me to quickly characterize a respondent, but right now, the only clustering I am able to assign is that of gender.
Thanks in advance!