[R-sig-ME] non-linear mixed effects: polynomial

[Douglas Bates]

On Tue, Sep 20, 2011 at 8:17 AM, Ben Bolker <bbolker at gmail.com> wrote:
> On 09/20/2011 04:22 AM, Gabriel Yvon-Durocher wrote:
>> Thanks for the reply Ben. I have 16 subjects, however the number of
>> observations per subject is not even, which is why I opted for nlmer
>> rather than nlme. I presumed nlmer (as is the case for lmer) would be
>> better at handling unbalanced designs.
>
>  No, nlme is also intended for unbalanced designs.
>
>  nlmer is likely to be (a) faster and (b) better for crossed designs,
> but otherwise I would stick (for the time being) to nlme.

I don't think you need either nlme or nlmer though, do you?  A
polynomial model is linear in the coefficients so this could be fit by
lmer.  Ben's caution about over-specification of the random-effects
variance-covariance model still applies to the linear mixed-effects
model, however.  You are trying to estimate 15 variance-covariance
parameters, for which you would need a great deal of data.

>   A couple of other things occur to me:
>
> (1) what you got was a warning about false convergence (the PORT library
> algorithm built into lme4 is pretty finicky ...) If the result seems
> sensible and accords with your individual-level fits, I would probably
> proceed (with caution)
>
> (2) the random-effects specification (1+a+b+c+d|Subject) is likely to be
> quite tricky (I guess you have lots of data per individual?) because it
> will fit a full, unstructured 5 x 5 variance-covariance matrix for the
> random effects across individuals.  It's a pain, but maybe try
>
> (1|Subject)+(0+a|Subject)+(0+b|Subject)+(0+c|Subject)+(0+d|Subject)
>
>  (i.e. independent random effects) for comparison?  (Admittedly the
> among-subject correlations among parameters could be quite interesting,
> although probably more interpretable if you centered your Temperature
> variable (another thing worth trying to improve convergence) or used
> orthogonal polynomials (ditto).
>
>
>>
>> I will check out the suggested books. Thanks.
>>
>> Gabriel Yvon-Durocher
>>
>>> Gabriel Yvon-Durocher <g.yvon-durocher at ...> writes:
>>>
>>>>
>>>> Dear all,
>>>>
>>>> I am trying to fit a 3rd order polynomial to some rate and
>>>> temperature
>>> measurements, but am running into
>>>> problems. I would like to treat the parameter a,b,c,d as random
>>>> effects across
>>> subjects, and use the model
>>>> to estimate these parms for each experimental subject.
>>>>
>>>> Here is my model:
>>>>
>>>> resp.fun<-function(Temp,a,b,c,d)
>>>> -a*(Temp^3)+b*(Temp^2)-c*(Temp)+d
>>>>
>>>> then I build a gradient function:
>>>>
>>>> gr.model<- deriv(body(resp.fun), namevec = c('a','b','c','d'),
>>> function.arg = resp.fun)
>>>>
>>>> and then run the mixed effects model:
>>>>
>>>> model<-nlmer(log10.rate ~ gr.model(Temp,a,b,c,d) ~
>>>> 1+a+b+c+d|Subject, start = c(a=4.897e-05, b=3.198e-03,
>>>> c=3.569e-02, d=1), data = lab.analysis, na.action=na.omit)
>>>>
>>>> unfortunately I get the error message
>>>>
>>>> Warning message: In mer_finalize(ans) : false convergence (8)
>>>>
>>>> Any ideas on what I may be doing wrong? I have manually fit this
>>>> polynomial to the data for each subject and the fits are good,
>>>> but I want to run the mixed effects analysis to get the best
>>>> possible parameter estimates given the experimental design.
>>>>
>>>
>>> How many subjects?
>>>
>>> Can you do it in nlme instead, which is more mature/robust? If not,
>>> you may end up needing to do this in AD Model Builder, or BUGS, or
>>> rolling your own Laplace approximator (there is an example in
>>> Madsen and Thyregod's book) ...
>>>
>>> Ben Bolker
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
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