[R-sig-ME] GLMM with bounded parameters

[François Rousset]

Le 16/12/2016 à 13:43, Pierre de Villemereuil a écrit :
> Dear all,
>
> I'm trying to fit a predictive bell curve on count data with Poisson noise
> around the curve. The idea is to estimate the optimum of fitness according to
> some trait.
>
> The good news is that I don't need to resort to non-linear modelling to do
> that, because the exponential link combined with a polynomial formula can do
> the job as shown in the dummy example below:
> x <- runif(300,0,10)
> fitness <- rpois(300,10*dnorm(x,mean=5,sd=2))
>
> mod = glm(fitness ~ x + I(x^2),family="poisson")
> plot(fitness ~ x)
> points(predict(mod,type="response") ~ x,col="red")
>
> My problem is that I'd like to impose some constraints on the parameters to
> ensure that a bell-shape is fitted, e.g. that the parameter for x is positive
> and the parameter for I(x^2) is negative.
One can use offsets and a brute-force optim() over offsets that satisfy 
the constraints (and no mixed models in the present case)

x <- runif(300,0,10)
fitness <- rpois(300,10*dnorm(x,mean=5,sd=2))

objfn <- function(par) {
   off <- (par[1]+par[2]*x)*x
   fit <- glm(fitness ~ 1,family="poisson",offset=off)
   - logLik(fit)
}
opt <- optim(c(1,-1),objfn,lower=c(0,-Inf),upper=c(Inf,0),method="L-BFGS-B")

mod <- glm(fitness ~ 
1,family="poisson",offset=with(opt,(par[1]+par[2]*x)*x))

plot(fitness ~ x)
points(predict(mod,type="response") ~ x,col="red")

Best,

F.



>
> Is there a way to enforce such constraints in mixed models packages available
> in R? I'm currently using lme4, but I'm happy to switch to any other package.
>
> Cheers,
> Pierre.
>
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