[R-sig-ME] deriv example for nlmer

[Helen Sofaer]

Hello modelers,
I am working on a growth rate analysis in lme4, where my goal is to test
for differences in growth rates between two populations of birds while
incorporating random effects for nests (to deal with the lack of
independence between siblings) and for each nestling (to deal with repeated
measures of individuals). 

I’d like to build a model that is parameterized slightly differently than
the SSlogis self-starting model, where K = 1/scal (this is simply due to
convention in the bird world). I can tweak the SSlogis code (given in the
help file for selfStart) and the model runs, but cannot test for
differences between populations. Since determining reasonable starting
values is not a problem, and I’d like to be able to easily adjust the
formula to incorporate additional covariates, I would like to avoid using a
self-starting function.

It is my understanding that nlmer requires a function, but not necessarily
a self-starting one. However, I can’t find an example of any code that does
this. 

I can build a very simple function that allows for differences between
populations (referred to as site, which is a 0 1 dummy variable) in both
the inflection point (xmid) and the growth rate (K). I’m trying to start
with the simplest reasonable model, so I didn’t allow for differences in
the asymptote. This function works in nls:

logisKsite = function(Age, site, Asym, xmid, K, Kdiff, middiff){
	Asym/(1 + exp((xmid+middiff*site - Age)*(K+Kdiff*site)))
	}

startsite = c(Asym = 9, xmid = 3, K = .5, Kdiff=0, middiff=0)
nls_logisKsite = nls(weight ~ logisKsite(Age, site, Asym, xmid, K, Kdiff,
middiff), growth, start = startsite)

The nlmer model I am trying to run is (for simplicity, this model includes
only a random effect of nest, only on the K parameter):
nlmer_logisKsite = nlmer(weight ~ logisKsite(Age, site, Asym, xmid, K,
Kdiff, middiff) ~ (K | Nest_ID), growth, start = startsite, verbose = TRUE)

Running this model in nlmer produces the error: gradient attribute of
evaluated model must be a numeric matrix
Dr. Bates’ posted lectures note that the model must provide derivatives,
via the deriv function. I haven’t been successful getting this to work,
even in the model without site effects.

If there is an example of how to run nlmer without a self-start function,
could someone please point me to it? Advise on how to implement the deriv
function would also be very helpful. 

Thank you very much,

Helen

Helen Sofaer, PhD Candidate in Ecology, Colorado State University