On Fri, 17 Jul 2015, Bert Gunter wrote:> I believe John Aitchison's book and papers are the authoritative basic > resources. Have you read them?Bert, Yes, I have.> The problem is that the support of the distributions are (hyper)simplexes, > not Euclidean space, due to the requirement that the proportions must sum > to 1. This means that complicated animals like Dirichelet distributions > must be used to model populations, and the sampling theory is therefore > specialized. It's difficult for most folks to get their heads around this.That's true, When I read the math I move my lips and follow along with a finger. :-) My question is focused on presentation of graphic presentation of the data, such as a matrix of ternary diagrams that show the distribution of the response variables to the explanatory variables. The analysis of benthic macroinvertebrate functional feeding groups has 5 response variables which resulted in a 5-by-5 ternary diagram matrix. Anything larger than that would require the eyesight of a teenager to see any details. I'll keep searching the literature for a suitable example. Perhaps a CoDA SIG will develop on within the R mail list ecosystem in the not-too-distant future. Thanks, Rich
Hi Rich, Being in a position of relative ignorance on this topic, I'll offer some suggestions that may well be useless. You mention ternary diagrams, which use position to represent compositional proportions. These will not scale up to 46 values in any way that I can imagine. If you want to display relative concentration or the like, differentiate the components and display numeric information about each component, you may be looking for a variant of the Hinton diagram. This is a bit like a heatmap where the squares are of different sizes, representing relative numeric values. In the Hinton diagram, the colors represent sign (+-), but you would probably want more complex coloring. Finally, identifying labels and/or values could be displayed on each cell of the matrix. It would not be too difficult to program something like this, so if this idea is not completely useless, let me know. It is of course possible to go the interactive route and produce a "play with me" display if necessary. Jim