[R] glmer with non integer weights

[Emmanuel Charpentier]

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 ?