[R-sig-ME] Model with variable number of arguments

[Daniel Kaschek]

On Sa, 2015-08-01 at 09:26 -0500, Paul Johnson wrote:
> On Thu, Jul 30, 2015 at 8:34 AM, Daniel Kaschek
> <daniel.kaschek at physik.uni-freiburg.de> wrote:
> > Dear all,
> >
> > I have the following model:
> >
> > y_ij = x_i/s_j + (eps_ij)/s_j
> >
> > where y_ij are the responses, x_i and s_j are the fixed effects and the
> > random effects follow a normal distribution
> >
> 1.  x_i and s_j are observed variables or parameters you need to
> estimate?  Why you have no betas?

Both, the x_i and s_j are parameters whereas the y_ij are the
observations. The background is that a time course of concentrations,
x_i (i corresponds to different time points) is measured several times,
but on a different scale, given by s_j. If you plot all y_ij together in
one plot, put i on the x-axis and group with respect to j, you would see
the same time course on different scales.


> 
> 2. the formulation using division is unfamiliar to me, but when you
> get to this part
> 
> > eps_ij ~ N(0, sigma0^2 + x_i^2 * sigmaR^2)
> >
> 
> Can't answer because I can't tell if x_i is observed or not.  If it is
> not, I don't know that lme4 will help.

The parameters x_i correspond to the "true" time course. The expected
variance at time point i has two contributions: 1. a constant
contribution, sigma0^2, and 2. a contribution relative to the
concentrations, (x_i * sigmaR)^2. Since each measured time course lives
on a different scale, the variance eps_ij needs to be divided by the
corresponding scaling factor s_j. 

> 
> How did eps get this way in the first place.  It appears it might be
> the sum of 2 separate random effects. If that's right, you are getting
> closer to the sort of model I would understand
> 
> It makes me wonder why you don't have s_j inside the variance term
> there,, or why you don't have both x_ and s_ outside.
> 
> Its pretty tough to read email with lots of x_i and such.  That part
> is bad about plain text mailing lists

Yes, I known :-(


Though, I hope, I could make things clearer. 

Best regards,
Daniel

> 
> > with error parameters sigma0 and sigmaR. In the end, I am interested in
> > the parameters x_i, s_j, sigma0 and sigmaR.
> >
> > First of all, is lme4 the right package to solve this problem? When
> > looking at nlmer(), I had problems to figure out what would be the
> > correct structure of the function in the middle of the 3-part-formula.
> >
> > Any help is appreciated.
> >
> > Thanks a lot in advance,
> > Daniel
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> 
> 
>