R help - Apr 2003 - nls, gnls, starting values, and covariance matrix

Dear R-Help,

I'm trying to fit a model of the following form using gnls. I've fitted
it
using nlsList with the following syntax:

nlsList(Y~log(exp(a0-a1*X)+exp(b0-b1*X))|K,start=list
(a0=6,a1=0.2,b0=4.5,b1=0.001),data=data.frame(Y=y,X=X,K=k)))

which works just fine:

<snip>

Coefficients:
         a0        a1       b0            b1 
 1 5.459381 0.5006811 5.137458 -0.0040548687
 2 5.761496 0.1716723 6.359151 -0.0022802595
 3 5.683510 0.5436838 5.906742 -0.0007788076
 4 6.225745 0.2807003 5.875803 -0.0008351051
 5 6.558350 0.1388707 5.071080  0.0014594212
 6 5.483639 0.2757080 2.406683 -0.0003282243
 7 5.746064 0.4354105 5.883882 -0.0002577279
 8 5.448679 0.3385350 2.851571  0.0011627360
 9 5.259762 0.5654369 5.498967  0.0015381718
10 6.546022 0.8008781 4.913085  0.0051150166
12 5.602982 1.1538595 5.008253 -0.0006087786
13 6.452605 0.1752357 6.229393  0.0007899073
15 5.937199 0.2214811 4.980386  0.0081102533
16 5.998689 0.2925840 6.077816  0.0062388250

However, I'd like to be able to fit the model using gnls. The format is a 
little different, but I get an error when I use the following syntax:

gnls(Y~log(exp(a0-a1*X)+exp(b0-b1*X)),params=a0+a1+b0+b1~K,start=list(rep(c
(6.02,0.2,4.5,0.001),16)),data=data.frame(Y=y,X=x,K=k),control=list
(msVerbose=TRUE,apVar=FALSE,returnObject=TRUE))

Error in gnls(Y ~ log(exp(a0 - a1 * X) + exp(b0 - b1 * X)), params = a0 +  : 
        Approx. covariance matrix for parameter estimates not of full rank

I assume that I'm getting the format of my starting values wrong. Any 
suggestions would be greatly appreciated.

Best wishes
Simon

Simon  -

There's a symmetry in the model you are fitting, and the error
message returned sounds to me as though it is referring to that.

Could you try a model formula of the form

Y ~ a0 + log(exp(-c0-a1*X) + exp(+c0-b1*X))

Maybe you will need to make the two slopes identifiable in much
the same fashion that I've done for the two intercepts, in order
to get it to work.  Or maybe not.  I'll leave that up to you.

HTH  -  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Sat, 19 Apr 2003 sdfrost at ucsd.edu wrote:
> Dear R-Help,
>
> I'm trying to fit a model of the following form using gnls. I've
fitted it
> using nlsList with the following syntax:
>
> nlsList(Y~log(exp(a0-a1*X)+exp(b0-b1*X))|K,start=list
> (a0=6,a1=0.2,b0=4.5,b1=0.001),data=data.frame(Y=y,X=X,K=k)))
>
> which works just fine:
>
> <snip>
>
> Coefficients:
>          a0        a1       b0            b1
>  1 5.459381 0.5006811 5.137458 -0.0040548687
>  2 5.761496 0.1716723 6.359151 -0.0022802595
>  3 5.683510 0.5436838 5.906742 -0.0007788076
>  4 6.225745 0.2807003 5.875803 -0.0008351051
>  5 6.558350 0.1388707 5.071080  0.0014594212
>  6 5.483639 0.2757080 2.406683 -0.0003282243
>  7 5.746064 0.4354105 5.883882 -0.0002577279
>  8 5.448679 0.3385350 2.851571  0.0011627360
>  9 5.259762 0.5654369 5.498967  0.0015381718
> 10 6.546022 0.8008781 4.913085  0.0051150166
> 12 5.602982 1.1538595 5.008253 -0.0006087786
> 13 6.452605 0.1752357 6.229393  0.0007899073
> 15 5.937199 0.2214811 4.980386  0.0081102533
> 16 5.998689 0.2925840 6.077816  0.0062388250
>
> However, I'd like to be able to fit the model using gnls. The format is
a
> little different, but I get an error when I use the following syntax:
>
> gnls(Y~log(exp(a0-a1*X)+exp(b0-b1*X)),params=a0+a1+b0+b1~K,start=list(rep(c
> (6.02,0.2,4.5,0.001),16)),data=data.frame(Y=y,X=x,K=k),control=list
> (msVerbose=TRUE,apVar=FALSE,returnObject=TRUE))
>
> Error in gnls(Y ~ log(exp(a0 - a1 * X) + exp(b0 - b1 * X)), params = a0 + 
:
>         Approx. covariance matrix for parameter estimates not of full rank
>
> I assume that I'm getting the format of my starting values wrong. Any
> suggestions would be greatly appreciated.
>
> Best wishes
> Simon