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I have data for a large number of unique populations. In each population each individual is described by a number of categorical and numeric variables. I want to conduct an analysis on each population, and taking into account the descriptive variables, identify the most typical individuals in each population.

I'm hoping that someone can point me towards an R package that provides tools for identifying these individuals as described, or failing that, one or more indices that might be replicated in R to do the job. I've found some literature on exemplar sampling which looks like it may be what I'm looking for, but haven't found any links back to a working R package.

Any advice would be really appreciated.

Terry B
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  • Not sure this is clear. What does "most typical" mean? Can you give a precise definition? – lulu Feb 24 '19 at 12:47
  • If, say, each variable is numerical (like "age" or such) then you could create a penalty function which measures how far you are from the mean of each (let's just use the sum of the $\sigma-$ unit distances, as an example). Then you could give every member a score and take the one(s) with the least score (so somebody who hit the mean on every variable would be selected). But, I expect you'll get weird and undesirable results this way. – lulu Feb 24 '19 at 12:51
  • I'm afraid I don't have a precise definition of what I mean by "most typical" apart from the fact that it should be determined on the basis of multiple descriptors. I acknowledge this is open to a wide range of possible outcomes, but I was hoping there might be one or more existing indices with at least a clear rationale behind to them and that I could trial and choose from. – Terry B Feb 24 '19 at 13:31
  • Well, try my definition and see if you like the results. My guess is that you'll at least want to weight the variables, else you'll get pulled off by an outlier or two. I think that the "optimal" penalty function will strongly depend on context...what the data measures and what you want to select for/against. – lulu Feb 24 '19 at 13:37
  • To be clear: In my proposed penalty function, I'd take the sum of the absolute values of the z-scores of each variable. Or you could take the square of the z-scores (which might be more tractable analytically, though if you just getting a list of the penalty values, that might not be a significant issue). If you want to weight the variables (declaring that some matter more than others, you can just put in coefficients as desired. – lulu Feb 24 '19 at 13:42
  • Many thanks. I think you are right that there is an important layer in this about deciding weights that are contextually relevant. – Terry B Feb 25 '19 at 08:02
  • No problem. I realized I should have mention Clustering Algorithms in case you are unfamiliar. Maybe this is more what you want. These are excellent methods for looking at data and identifying regions in the field with lots and lots of data near them. That might be much better than insisting on some sort of optimal individual point. – lulu Feb 25 '19 at 10:47

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