# Modelling with multiple-valued variables

I am about to start out analysis of a microbiological data set (ETEC: enterotoxic echerichia coli in children with diarrhea). The variables refer to the ETEC, not to the children. Some of the variables, like colonization factors (CF), may have none, one or multiple values; thus CF becomes a multiple-valued variable. I have ideas for the analysis, and I am not asking for such. I wonder if there is some literature about multiple-valued variables, which should be commonly occurring problem. But I can find little by googling, maybe I am using the wrong name?

I found one paper: "Correspondence Analysis for Symbolic Multi–Valued Variables" by Oldemar Rodrıguez R. (you will find that by googling) However this paper treats a similar but distinct problem: the multiple-valuedness of his variables represents only epistemic uncertainty. For instance, one object for variable A really has one of the values A1 or A2 (not both), and we do not know which. I am interested in ontological multi-valuedness: the object for that variable A can really have both values A1 and A2. As an example, the bacteria in my analysis can have two different colonization factors.

While I can think of many ways of treating this, my question is: Do any of you know about published papers/books discussing such problems? Or know of good terms to use for googling for it?

Thanks!

added after gung's comment: As for my example, all my variables refer to laboratory analysis of the bacteria, not the child. The goals is the epidemiology of etec itself, not its relation to characteristics of the children. One bacteria cell might have none colonization factors at all, some might have only one type like CFA/1 or CS6, others might have two CF present ( both CS1 and CS3), others might have three CF present (for instance, CS1, CS3 and CS21) and so on. Of course, how this should be treated must depend on the biological effect: does etec with both CS1 and CS3 share properties with etec which have only CS1, and at the same time share properties with etec having only CS3? Or is it completely different (that might be construed as a kind of interaction). If is is completely different, it might be modeled as simply another, new value of the variable CF, so the three values CS1, cS3, (CS1&CS3) now are three completely unrelated values. But if we had the first situation, sharing of properties, that would be a bad representation. There is lot of issues to discuss, and it seems likely it have been discussed already, somewhere ...

• Can you give a more concrete example of what you mean by CV having multiple values? Presumably you don't mean a factor that takes one of multiple levels or a number of colonization factors (eg, this kid has 2, that kid has 4). I'm not sure what you mean yet. – gung Oct 7 '13 at 1:19
• I will add some more explanation to the original Q – kjetil b halvorsen Oct 7 '13 at 1:28
• So, you have a factor with finite levels, but the bug might take more than one level? Is that correct? – gung Oct 7 '13 at 1:53
• yes, that is correct. It is formally similar to responses to MRC questionaires: "check all that might apply" but I cannot find theory addressing that! – kjetil b halvorsen Oct 7 '13 at 2:00
• Yes, that is of course one possibility, but tnere sure are others! references to discussions? – kjetil b halvorsen Oct 7 '13 at 2:13