[R] Problem with Integrate

[Spencer Graves]

      Have you done a search of "www.r-project.org" -> search -> "R site 
search" for "hermite quadrature"?  I just got 11 hits on this, the 
second of which referred to "gauss.quad {statmod}".  This said, "See 
also ... gauss.quad.prob {statmod}".  I haven't tried it, but it looks 
like what you want. 

      Hope this helps. 
      spencer graves

Anon. wrote:

> The background: I'm trying to fit a Poisson-lognormal distrbutuion to 
> some data.  This is a way of modelling species abundances:
> N ~ Pois(lam)
> log(lam) ~ N(mu, sigma2)
> The number of individuals are Poisson distributed with an abundance 
> drawn from a log-normal distrbution.
>
> To fit this to data, I need to integrate out lam.  In principle, I can 
> do it this way:
>
> PLN1 <- function(lam, Count, mu, sigma2) {
>   dpois(Count, exp(lam), log=F)*dnorm(LL, mu, sqrt(sigma2))
> }
>
> and integrate between -Inf and Inf.  For example, with mu=2, and 
> sigma2=2.8 (which are roughly right for the data), and Count=73, I get 
> this:
>
> > integrate(PLN1, -10, 10, Count=73, mu=2, sigma2=2.8)
> 0.001289726 with absolute error < 2.5e-11
> > integrate(PLN1, -20, 20, Count=73, mu=2, sigma2=2.8)
> 0.001289726 with absolute error < 2.5e-11
> > integrate(PLN1, -100, 100, Count=73, mu=2, sigma2=2.8)
> 2.724483e-10 with absolute error < 5.3e-10
> > integrate(PLN1, -500, 500, Count=73, mu=2, sigma2=2.8)
> 1.831093e-73 with absolute error < 3.6e-73
> > integrate(PLN1, -1000, 1000, Count=73, mu=2, sigma2=2.8)
> Error in integrate(PLN1, -1000, 1000, Count = 73, mu = 2, sigma2 = 2.8):
>         non-finite function value
> In addition: Warning message:
> NaNs produced in: dpois(x, lambda, log)
>
> So, the integral gets smaller, and then gives an error.
>
> I then tried entering the formula directly:
> PLN2 <- function(LL, Count, mu, sigma2) {
> exp(-LL-(log(LL)-mu)^2/(2*sigma2))*LL^(Count-1)/(gamma(Count+1)*sqrt(2*pi*sigma2)) 
>
> }
>
> > integrate(PLN2, 0, 100, Count=73, mu=2, sigma2=2.8)
> 0.001287821 with absolute error < 2.6e-10
> > integrate(PLN2, 0, 1000, Count=73, mu=2, sigma2=2.8)
> 0.001289726 with absolute error < 2.9e-08
> > integrate(PLN2, 0, 10000, Count=73, mu=2, sigma2=2.8)
> 0.001289726 with absolute error < 9.7e-06
> > integrate(PLN2, 0, 19100, Count=73, mu=2, sigma2=2.8)
> 1.160307e-08 with absolute error < 2.3e-08
> > integrate(PLN2, 0, 19200, Count=73, mu=2, sigma2=2.8)
> Error in integrate(PLN2, 0, 19200, Count = 73, mu = 2, sigma2 = 2.8) :
>         non-finite function value
>
> And the same thing happens.
>
> I assume that this is because for much of the range, the integral is 
> basically zero.
>
> Can anyone suggest a fix?  Preferably one that will work with 
> Count=320 and Count=0 (both of which I have in the data).
>
> Bob
>