Re: Repeated measures analysis of fractions summing to a constant

Posted by Andy W on Apr 05, 2013; 12:21pm
URL: http://spssx-discussion.165.s1.nabble.com/Repeated-measures-analysis-of-fractions-summing-to-a-constant-tp5719257p5719279.html

Kirill,

This is a question that has come up on cross-validated a few times, see here for an example http://stats.stackexchange.com/q/24187/1036. A frequent recommendation seems to be a Stata library by the name of dirifit (see http://maartenbuis.nl/software/dirifit.html) or a synonymous R library DirichletReg. I do not know if the current GENLIN procedure can be wrangled to produce the same model.

A quick perusing of some of the materials floating around the web related to said packages suggest a quick and dirty way is to fit separate beta regression models for each of the subsets - although that doesn't constrain the total to be 1. (Smithson & Verkuilen (2006) A Better Lemon Squeezer has supplementary material on how to fit beta regression models in SPSS.)

Count data models are not appropriate here because of the ceiling effect. You can look up ways around that (like censored Poisson regression or Tobit models) - but those ignore the compositional nature of the data here. Another suggestion on the CV site recommends multinomial models - which I see the relationship but I don't quite understand how you turn this into discrete outcomes to feed into a multinomial logistic regression.

Looks like you will have some (hopefully fun) reading to do to sort through all these disparate recommendations!

Andy