# Cluster analysis not creating meaningful groups, just grouping together high/low scoring respondents

To better learn cluster analysis I'm playing around with some Likert scale (agree-disagree) data I have, but the results I'm getting are basically useless. As the title suggests, rather than grouping respondents in any meaningful way, I'm just getting clusters of people who scored high on all questions, low on all questions, and somewhere in the middle. (That's an oversimplification, but you get the point). I've factor analyzed the questions and found a pretty clean factor solution with five factors, so there's reason to believe the questions should indeed be capable of dividing up the respondents.

Nonetheless, I've tried a variety of things and the solution always exhibits the same problem (e.g. I've tried different cluster methods, I've standardized the scores, I've run it with just a handful of variables I figured should work well, and I've run it with the regressed factor scores even though I know that isn't recommended).

My assumption is just that some people tended to agree more strongly across the board and it's confusing the cluster analysis. Indeed, the one thing I did that produced a more logical result was standardizing the scores by case rather than by variable, even though this approach seems far less common.

Is there any other explanation or any other way to deal with this issue?

• I am puzzled why you seem puzzled here. People with similar scores will tend to be put in the same cluster, and all else is fine detail. Why is this surprising or disappointing? If you want to find different patterns you may need to work with other criteria. For example, finding black and white (5s and 1s) versus everything is grey (3s, etc.) needs some different approach. (Cf. @Matthieu Rouyer's answer, posted independently.) Nov 18 '15 at 20:24
• However, another way to think about it is that people classify themselves. if there are say 10 questions and you have 5 different answers, then there are $5^{10} \sim 10^7$ different profiles, whereas you presumably have many fewer respondents and it's unlikely that profiles that occur are equally common. So, that's a clustering with minimum technology requiring no assumptions. It might turn out to be a dead end, but it might also reveal some structure. Nov 18 '15 at 20:24
• Fair enough. I should be a bit clearer. As evidenced by the factor analysis, the scale seems to have several latent factors with which different respondents tend to agree/disagree. In other words, given the data, it makes more sense that respondents who agreed with certain variables would tend to disagree with others, rather than just showing strong agreement across the board. I strongly anticipated, for example, Cluster 1 to agree highly with variables 1, 3, 5, and 7, and to disagree with 2, 4, 6, and 8, with Cluster 2 being the opposite.
– DaGu
Nov 18 '15 at 20:33
• Indeed. Naturally I can't comment on your clusters or variables, least of all when they are just numbered! But suppose you ask me whether I am interested in statistics and in sport and my answers are 5 (strongly agree) and 1 respectively then I am similar to anyone who answers in the same way. By the way, I am not aware that there's universal endorsement of factor analysis for this kind of data. I'd tend to use correspondence analysis as a strong preference. No doubt you're aware of some debates along similar lines. Nov 18 '15 at 20:40
• More generally, clustering people [here] and clustering variables can't always be well served by the same technique but advocates of correspondence analysis seem positive that it can be. Nov 18 '15 at 20:40

Have you tried subtracting the average score of each respondent in all of that respondent's answers?

This would give you the "within variation" for every respondent, akin to the technique used in the fixed-effect estimator in multivariate regression.

EDIT: What you really have to think long and hard about is the question you want to answer with your analysis. For instance, Nick Cox's transformation in the comment to this post will lead to clustering people according to how strongly they express their opinion on some matter (in a way, the absolute interest they have in the subject regardless of which "side" they are on) whereas mine will lead to clustering according to the side they take.

• Hadn't tried that. I just gave it a quick test and it seemed to work well : ). Is this more common and/or preferable to taking the z-score for each respondent (by respondent, rather than by variable)?
– DaGu
Nov 18 '15 at 20:42
• Also, is there some sort of test I can use to demonstrate why this technique is useful (i.e., to overcome the noise of some people seemingly wanting to agree more strongly with everything)?
– DaGu
Nov 18 '15 at 20:48
• A variant of the same idea is to work with say $|\text{answer} - 3|$. Then (assuming a 5 point scale) everyone gets 0s, 1s or 2s. People with lots of 2s are going for the extremes; people with lots of 0s are going for the middle. I prefer this (at a distance) to subtracting means, because the numbers retain a closer link to the original scale. Nov 18 '15 at 20:52
• Interesting, I'll have to play around with this.
– DaGu
Nov 18 '15 at 20:56
• You can cluster statistical people into those who believe in cluster analysis and those who don't. There are many highly successful, or at least very often used, classifications in science (classifications of elements, species, diseases, industries). It is an interesting question which cluster analyses have been adopted outside the particular papers in which they were discussed. (Mind you, you could say the same of regressions, etc.) Nov 18 '15 at 21:02