[R-sig-ME] nlmer and the binomial distribution.

Rolf Turner r@turner @end|ng |rom @uck|@nd@@c@nz
Sun Feb 10 10:50:15 CET 2019

It is not clear to me from the help file whether the nlmer() function 
from the lme4 package can be used to fit non-linear mixed models when 
the response has a discrete distribution, in particular a binomial 
distribution.  I'd like to fit a mixed binomial model in which the 
success probability *cannot* be expressed as "linkinv(linear predictor)" 
where "linkinv()" is the inverse of one of the "standard" link functions
(logit, probit, or cloglog) and the linear predictor is linear in the 
model parameters, but has to be expressed as a more complicated 
non-linear function of the parameters and the predictors.

If it is possible, how should the response appear in the formula? 
Should it be given in the form

   cbind(successes,failures) ~ ... ?

And how should the non-linear function be structured so as to 
accommodate the two-column nature of the response?

I *might* be able to figure all this out by experimenting, but the range 
of possible wrong approaches and wrong garden paths down which to lead 
myself kind of overwhelms me.

So I thought I'd ask here and maybe save myself a bit of time. :-)


Rolf Turner

P. S.  It's quite possible that my question makes no real sense at all. 
If so, please feel free to tell me so, but a bit of elaboration as to 
why would be appreciated.

R. T.

Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

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