[R] Non-constant variance and non-Gaussian errors with gnls

[Paul Suckling]

I have been using the nls function to fit some simple non-linear
regression models for properties of graphite bricks to historical
datasets. I have then been using these fits to obtain mean predictions
for the properties of the bricks a short time into the future. I have
also been calculating approximate prediction intervals.

The information I have suggests that the assumption of a normal
distribution with constant variance is not necessarily the most
appropriate. I would like to see if I can obtain improved fits and
hence more accurate predictions and prediction intervals by
experimenting with a) a non-constant (time dependent) variance and b)
a non-normal
error distribution.

It looks to me like the gnls function from the nlme R package is
probably the appropriate one to use for both these situations.
However, I have looked at the gnls help files/documentation and am
still left unsure as to how to specify the arguments of the gnls
function in order to achieve what I want. In particular, I am unsure
how to use the params argument.

Is anyone here able to help me out or point me to some documentation
that is likely to help me achieve this?

Thank you.