Hi,
I would like to use constrained splines in a GLM model (Poisson link)
to take into account the nonlinear effect of some covariate. The
constraints I need are described below.
I have several variables that I need concurrently in the same model.
I looked at package mgcv but I do not know if/how I can use it in GLM (not
GAM) : I could
not manage to adapt the mono.con(mgcv) example to GLM.
The help for package fda is not complete.
Not sure that backSpline(splines) does what I need.
isoreg (modreg) seems to do univariate regressions.
Some of my covariates are linear.
Three covariates (x1,x2 and x3) must be transformed in a decreasing and
convex way like
this:
|o
|o
| o
| o
| o
| o
| ooooo
|-----------------
Currently, I use exp(-x1/alpha1)+exp(-x2/alpha2)+exp(-x3/alpha3), I try
several alpha's
and choose the best according to log-likelihood.
One variable should have only one local maximum (that is, the derivative
should be zero
only once, which is at the top), like this:
|
| TOP
| oo
| o o
| o o
|o o o
| o o
|--------------------
with bs() or ns() and no constraint, I get:
|
| TOP
| oo
|o o o
| o o o
| o
| o o
|--------------------
which is nonsense (note there are very few observations on the left part)
I also tried some parametric forms, choosing via log-likelihood. But with
four covariates,
it is a lot of parameters to try (several hours with little flexible
functions).
I am looking for something similar to ns or bs (package splines), which
are very
convenient to place in the formula of a GLM model. I tried them, adjusting
knots, but
could not manage what I want. Constraints on some derivatives may do the
trick, but I do
not know how to implement them in R.
Any help or comment would be greatly appreciated !
Mayeul KAUFFMANN
Universit?? Pierre Mend??s France - Grenoble
France
