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I am looking for literature on what I call multivariate proportional data where a single observation is a vector of proportions that sum to 1. For example, each person weights their preferences for each of a fixed number of categories such that the total weight is fixed.

More generally this could be multivariate data with a linear constraint on the Ys.

Is this the proper term for such data and can anyone recommend references on the topic?

Search engines (naturally) key in on the case where the response is a proportion, which is not quite what I am looking for.

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The keyword is compositional data. Here is a link to a course note with links to other papers/books explaining the basic characteristic/challenges associated with this type of data (in particular for a textbook like reference see (1))

(1) Aitchison, J., 1986. The Statistical Analysis of Compositional Data.

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