4
$\begingroup$

I'm very new to cluster analysis. In papers such as Richette et al.1 (which tries to see which concomitant diseases cluster together), authors first cluster the variables and then the observations (i.e., patients). (Bevis et al.2, did the same thing.) They used SAS's PROC VARCLUS and factor analysis (others have used PCA) for clustering variables, and cluster analysis for the patients. I don't understand why they would (need to) do both? In the first paper, all their discussion centered on the latter.

  1. Richette P, Clerson P, Périssin L, et al. Revisiting comorbidities in gout: a cluster analysis. Annals of the Rheumatic Diseases 2015;74:142-147.
  2. Bevis, et al. (2018). Comorbidity clusters in people with gout: an observational cohort study with linked medical record review. Rheumatology (Oxford). 57(8): 1358-1363.
Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

From a mathematical point of view, a standard dataset is just a matrix of numbers organized into rows and columns. We attach meanings to these, and think of the rows as pertaining to patients and the columns as representing variables, but they're just numbers and you can perform mathematical operations on them. The question is whether any given operation is meaningful.

Variables can be understood to be manifestations of some underlying truth that we don't have direct access to. In such a case, people often seek to combine the variables to get a better picture of the reality. These are called latent variables. The standard is to determine them through factor analysis, but PCA will typically yield almost the same results, and clustering algorithms can be applied to the columns (variables) to do the same thing. The latter guarantees that the result will have simple structure, at the cost of (usually) a worse empirical fit. That's presumably what they were after. This is done first because there's no point in clustering patients on the wrong variables—that would bias the results.

Improve this answer
$\endgroup$
5
  • $\begingroup$ "This is done first because there's no point in clustering patients on the wrong variables" Please would you expand on this? I don't think the authors made it apparent from the way they've done their analysis/interpretation. So if they started with 20 variables, and 3 variables have no association with a latent construct (ie they don't "cluster" with anything) should they then remove these variables before proceeding to cluster the patients? Also, thank you for the edit. $\endgroup$
    – bobmcpop
    Commented Oct 10, 2018 at 19:31
  • 2
    $\begingroup$ @bobmcpop, having several redundant variables distorts the space (see, eg, Should one remove highly correlated variables before doing PCA?). It will lead to the redundant set dominating the cluster result (see, eg: Why does gap statistic for k-means suggest one cluster, even though there are obviously two of them?). $\endgroup$
    – gung - Reinstate Monica
    Commented Oct 10, 2018 at 19:41
  • $\begingroup$ thank you for the links. I assume these principles apply to k-mean/hierarchical and continuous/binary variables all the same? $\endgroup$
    – bobmcpop
    Commented Oct 10, 2018 at 20:04
  • $\begingroup$ SPSS also does a good job on cluster analysis. I recently used two stage cluster analysis in a paper with BIC used to select the best clustering. Cluster analysis obviates variable interaction problems, which explains why some people (in my case a reviewer) insist on it. $\endgroup$
    – Carl
    Commented Oct 10, 2018 at 20:21
  • $\begingroup$ @bobmcpop, k-means, eg, is actually just using (squared) euclidean distance. So the space is distorted in exactly the same way. k-means doesn't really make sense for binary variables. Hierarchical clustering can use different linkages, which imply different possible distances, so the effect may or may not be the same. Nonetheless, this is what they had in mind. (I didn't read it that thoroughly, they could be doing this incorrectly, but it's certainly the thinking behind cluster-variables first, then patients.) $\endgroup$
    – gung - Reinstate Monica
    Commented Oct 10, 2018 at 20:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.