nlmer and the binomial distribution.

Just a point of note, that the repeated package is on CRAN

https://cran.r-project.org/web/packages/repeated/index.html

and the gnm package on CRAN might be able to handle this, too,

https://cran.r-project.org/web/packages/gnm/index.html

Good luck.

nlmer does *not* handle non-Gaussian (exponential family) models
(GNLMMs). I don't know of a mainstream, out-of-the-box solution for
frequentist fits of GNLMMs in R.

* brms can handle nonlinear models with non-Gaussian responses
<https://cran.r-project.org/web/packages/brms/vignettes/brms_nonlinear.html>

. It does Bayesian estimation only, but optimization *could* be hacked
if you wanted <https://github.com/paul-buerkner/brms/issues/115>

* you could try the gnlmm function in Jim Lindsey's repeated package;
you'll have to install it and the rmutils package from source available
at <http://www.commanster.eu/rcode.html>

* to my knowledge the TMB package would be the most
straightforward/modern way to fit GNLMMs in R, but you would have to
figure out how to write the TMB code.

On 2019-02-10 4:50 a.m., Rolf Turner wrote:

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. :-)

cheers,

v

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.

Thanks to Ben Bolker and Kenneth Knoblauch for their replies.  I have
already investigated the "repeated" package --- and got some mileage out
of it, thanks to the assistance of the maintainer, Bruce Swihart.

I was not entirely satisfied with the results, since the software in the
"repeated" package only accommodates a "random intercept", and there is
evidence from investigating the more standard models that can be fitted
using glmer() that a random *slope* is needed as well.  Bruce has said
that he *may* be able to incorporate the "random slope" idea, in a sense
that I can make precise in the context of the particular non-linear
model that I have in mind.  However it is slowly dawning on me that
making this modification is probably an overwhelmingly difficult task.

I guess that I was na?ve in thinking that nlmer might handle it for me.

cheers,

Rolf Turner

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

   I guess overwhelmingly difficult is in the eye of the beholder.  Any
chance of a small example of what you want to do? Although TMB is
written in an extended form of C++ rather than R, it might not be too
horrible. A version of the classic orange tree example is here:
https://kaskr.github.io/adcomp/orange_big_8cpp-example.html (it could
use more comments/there are a few slightly weird-looking things ...)