>>ALso consider using a beta distribution to model the fractions -
ssc describe betafit<<
Having written a paper on beta regression (and others in the works), I
obviously like it, but it's missing an important issue, namely the fact
that the time allocations are correlated due to a sum constraint. For
instance, let's say there are three tasks, A, B and C. Knowledge of how
much time is allocated to A and B automatically gives knowledge of C,
which in turn induces a negative correlation among the three
proportions.
Now, many people like the notion of using the Dirichlet distribution to
model this but it's got a serious issue: The Dirichlet's association
structure is completely determined by the marginals. This is highly
undesirable in general. Aitchison's book shows several examples of
datasets that cannot possibly be Dirichlet. He provides several options,
most notably one based on the multivariate Johnson family.
Thanks to Nick for the proper citation for Aitchison's book.
Jay
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