Sorry for this late answer (I've had a seriously nonmaskable interrupt).
Since I have technical questions not related to R, I take the liberty to
follow this up by e-mail.
I might post a followup summary if another R problem arises...
Emmanuel Charpentier
Le lundi 19 avril 2010 à 23:40 -0800, Kay Cichini a écrit :
> hello,
>
> it's the Morisita Horn Index, which is an ecological index for similarity
> between two multivariate objects (vegetation samples with species and its
> abundance) where a value of one indicates completely same relative
> importance of species in both samples and 0 denotes total absence of any
> same species.
>
> it can be expressed as a probability:
>
> (prob. that an individual drawn from sample j
> and one from sample k belong to the same species)
> ------------------------------------------------- = MH-INdex
> (prob. that two ind. drawn from either sample will
> belong to same species)
[ Technical rambling ]
Hmmm ... that's the *ratio* of two probabilities, not a probability.
According to http://www.tnstate.edu/ganter/B412%20Ch%2015&16%
20CommMetric.html, that I found in the first page of answers to a simple
google query, in can also be thought of the ratio of two "distances"
between sites : (maximal distnce - actual distance) / maximal distance
(with a massive (over-?) simplification). There is no reason to think a
priori that the logit transformation (or the asin(sqrt()) transformation
has better properties for this index than any other mapping from [0 1]
to R.
(BTW, a better mapping might be from [0 1] to [0 Inf] or conversely, but
"negative" distances have no (obvious) meaning. Here asin(sqrt()) might
make more sense that qlogis().)
[ End of technical rambling ]
But I have trouble understanding how a "similarity" or "distance" index
can characterize *one* site... Your data clearly associate a MH.Index to
each site : what distance or similarity do you measure at this site ?
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