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

Ben Bolker bbo|ker @end|ng |rom gm@||@com
Sun Feb 10 16:38:10 CET 2019

  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
. 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,
> 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.

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