[R] Finding starting values for the parameters using nls() or nls2()

[David Winsemius]

> On Oct 25, 2016, at 9:29 AM, dave fournier <davef at otter-rsch.com> wrote:
> 
> 
> 
> Unfortunately this problem does not appear to be well posed.
> 
>    Retention = (b0*Area^(th+1))^b
> 
> If b0, th, and b are the parameter only the product (th+1)*b is determined.
> 
> This comes from noting that powers satisfy
> 
> 
> 
>    (a^b)^c  =  a^(b*c)
> 
> 
> 
> So your model can be written as
> 
> 
> 
>          (b0^b) * Area^((th+1)*b)
> 

... which nicely completes the thread since one model had:

th1   =  9.1180e-01
 b01=    5.2104e+00
 b11 =  -4.6725e-04
(th1+1)*b11
[1] -0.0008932885


 b0  = 5.2104466   ;    b1 =   -0.0004672   ;  th =  0.9118029
((th+1)*b1)
[1] -0.0008931943

So both the R's nls2 and AD_MOdel_Builder results yield that same predictions for any given data point at least up to four decimal places.

So perhaps there was some other physical interpretation of those parameters and there exists an underlying theory that would support adding some extra constraints? 

-- 
David Winsemius
Alameda, CA, USA