seeking input lme4::glmer with a gamma family: link = log or identity?

Hi Scott,

An incomplete answer?

1. Is a Gamma distribution best for my distance data? If so, which link
function is most appropriate? I explored two link functions: identity and
log. I have concerns and see potential issues with both (see my annotations
in the reproducible example below.

I don?t know (I haven?t run your code) but I?ve always somehow managed to avoid gamma regression for strictly positive data by logging the response and fitting a model with normal errors.

2.  If the log link is the best or most appropriate to use, then the
summary(mDist) produces a sd of the random effect = 0 with the bobyqa
optimizer. Switching to Nelder_Mead gives a reasonable sd, but throws a
convergence warning.

(For clarity, I assume that by "sd of the random effect? you mean the square root of the variance parameter that gauges residual inter-bird variation in mean distance and not the SD of the estimate of that parameter, which anyway isn?t output by glmer.)

Why is a random effect variance estimate of zero implausible? I would trust a converged estimate over a non-converged estimate, regardless of whether the estimate is zero. Also? you could compare the log-likelihoods using logLik() ?  you?d expect the converged fit to have a higher LL. For more general troubleshooting of convergence warnings:
http://rpubs.com/bbolker/lme4trouble1
Another quick check I often do is to fit the non-converged model with glmmTMB (which appears to be more robust than lme4), and compare likelihoods and estimates with lme4.

A quick and dirty model fit assessment is to simulate from the fitted model (which is as easy as simulate(my.fit)), and see if the simulated responses look more or less like the real responses.

Good luck,
Paul