[R] Fitting data to a sigmoidal curve

[Rubén Roa-Ureta]

Greg Snow wrote:
> Sarah,
>
> Doing:
>
>   
>> RSiteSearch('gompertz', restrict='functions')
>>     
>
> At the command prompt gives several promising results.
>
> Hope this helps,
>
> --
> Gregory (Greg) L. Snow Ph.D.
>
>   
And you can also do:

nobs <- length(data$salam.size.observed)
fn<-function(p){
   salam.size.model <- 
salam.size.inf*exp(-G1*exp(-G2*data$age.observed)); # Gompertz model
   squdiff                <- 
(salam.size.model-data$salam.size.observed)^2; #vector of squared 
differences
   sigmasqu            <- sum(squdiff)/nobs; # nuisance sigma parameter 
profiled out
   minloglik            <- (nobs/2)*log(sigmasqu); #profile likelihood 
as approx. to true likelihood
   }
(salam.size.likfit <- nlm(fn,p=c(init. val. 4 salam.size.inf, init. val. 
4 G1, init. val 4 G2), hessian=TRUE))

where data is a dataframe with observed sizes and ages.
Invert Hessian to obtain measures of precision.
Note also that if you know the size at birth then you can 
re-parameterize, put size at birth instead of asymptotic size 
(salam.size.inf), and reduce model complexity to two parameters (but of 
course the Gompertz formula changes).
If the Gompertz model is not flexible enough, note that it is a 
particular case of another more flexible, and more complex model, 
Schnute's, which I have found often provides a better explanation of 
growth data (as measured by the AIC), especially if you have sizes of 
very young individuals.

HTH
Rubén