Richard Goldstein wrote:
>>A couple of comments about Jay's material below (some has been snipped):
>>1. Yes, Aitchison wrote an important book; users should note, however,
that there was a big controversy over this in the 1980's in Geology
between Aitchison and GM Philip/DF Watson. I have not delved into this
in sufficient detail to have an opinion on whether Aitchison was correct.<<<
Yes indeed there was a big conflict, but more current literature in the area seems to side with Aitchison so far as I can tell. From what I know of it, the conflict didn't involve the problem that is at hand here. In short I don't think anyone disputes Aitchison's technical results on the multivariate logistic normal distribution and his discussion of the zeros problem. (It's not hard to prove Aitchison's results on the MVLN yourself, for that matter, with a few hours of stubby pencil and scratch paper.) The Fry, Fry and McLaren article is a good read, too.
>>Regarding the Smithson/Verkuilen paper, note, if you try to match their
results (as I did), that they used one-sided p-values (I checked this
with Smithson and he agreed that they had).<<
I think I recall the correspondence but as I have switched e-mail systems since then I don't know what the result was. Did we make a mistake and write down something as a two-sided p-value?
There is also a large literature in envirometrics on the zeros problem, which goes under the guise of "non-detect analysis." Usually the solution is to use a censored regression model, for which Stata is admirably supplied with tools. Which solution you pick depends a lot on how you see the boundary observation and observed points nearby it (software concerns aside, which in Stata is nearly true, and sample size).
JV
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