R help - Apr 2010 - piecewise nls?

I am looking into fitting a so-called double von Bertalanffy function to fish
length-at-age data.  Attempting to simplify the situation, the model looks like
this ...

Y ~ f(X; a,b,c) if x <  Z
Y ~ g(X; a,d,e) if x >= Z

where

* f and g are non-linear functions (the "traditional"
"single" von Bertalanffy growth function),
* Y (length) and X (age) are observed variables,
* a,b,c,d,e are parameters to be estimated, and
* Z is not a parameter but is a constant computed from b,c,d,e.

I usually fit the "traditional" "single" model with nls()
but am unsure of how to fit this model with the "if" statement.  I
tried search the archives with "piecewise" and either "nls",
"nonlinear", or "regression" but did not find anything that
seemed to fit this situation.  One thought I had was to do something like this
(mostly pseudo-code) ...

nls(Y~ifelse(X<Z,1,0)*f(X;a,b,c)+ifelse(X>=Z,1,0)*g(X;a,d,e), ...)

but am unsure if this makes sense.

If anyone can offer some help I would be very appreciative.  Thank you in
advance.

Hi Derek,

have a look at the following made-up example:

f1 <- function(x){2*x}
f2 <- function(x){-10*x+1}

x<-rnorm(10)
x
(x<0)*f1(x)
(x>=0)*f2(x)
(x<0)*f1(x) + (x>=0)*f2(x)



Therefore I suggest you should specify the model as follows:

yourNLSmodel <- nls(Y ~ (X<Z) * f(X,a,b,c) + (X>=Z) * g(X,a,d,e), data
= myData, ...)



Christian

Christian,

Thank you for the response and hint.  This is essentially what I ended up doing
but I ran into several problems using nls().  I have since switched to optim()
and seem to be having better luck.  Again, thank you for your help.
> -----Original Message-----
> From: Christian Ritz [mailto:ritz at life.ku.dk]
> Sent: Saturday, April 17, 2010 2:45 PM
> To: Derek Ogle
> Cc: r-help at r-project.org
> Subject: Re: [R] piecewise nls?
> 
> Hi Derek,
> 
> have a look at the following made-up example:
> 
> f1 <- function(x){2*x}
> f2 <- function(x){-10*x+1}
> 
> x<-rnorm(10)
> x
> (x<0)*f1(x)
> (x>=0)*f2(x)
> (x<0)*f1(x) + (x>=0)*f2(x)
> 
> 
> 
> Therefore I suggest you should specify the model as follows:
> 
> yourNLSmodel <- nls(Y ~ (X<Z) * f(X,a,b,c) + (X>=Z) * g(X,a,d,e),
data
> = myData, ...)
> 
> 
> 
> Christian