R help - Oct 2013 - SSweibull() : problems with step factor and singular gradient

SSweibull() :  problems with step factor and singular gradient

Hello

I  am working with growth data of ~4000 tree seedlings and trying to fit 
non-linear Weibull growth curves through the data of each plant. Since  they
differ a lot in their shape, initial parameters cannot be set for  all plants.
That’s why I use the self-starting function SSweibull().
However, I often got two error messages: 

1)
# Example
days <- c(163,168,170,175,177,182,185,189,196,203,211,217,224)
height <- c(153,161,171,173,176,173,185,192,195,187,195,203,201)
dat <- as.data.frame(cbind(days,height))
fit <- nls(y ~ SSweibull(x, Asym, Drop, lrc, pwr), data = dat, trace=T,
control=nls.control(minFactor=1/100000))

Error in nls(y ~cbind(1, -exp(-exp(lrc)* x^pwr)), data = xy, algorithm =
“plinear”, :                          
step factor 0.000488281 reduced below `minFactor` of 0.000976562

I  tried to avoid this error by reducing the step factor below the  standard
minFactor of 1/1024 using the nls.control function (shown in  the example
above). However, this didn’t work, as shown in the example  (minFactor still the
standard).
Thus, does nls.control() not work for self-starting functions like SSweibull()?
Or is there another explanation?

2)
In other cases, a second error message showed up:

Error in nls(y ~cbind(1, -exp(-exp(lrc)* x^pwr)), data = xy, algorithm =
“plinear”, :                          
singular gradient

Is there a way to avoid the problem of a singular gradient?

I’d be very glad about helpful comments. Thanks a lot.
Aline
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I think you have chosen a model that is ill-suited to the data.

My initial thoughts were simply that the issue was the usual nls() 
"singular gradient" (actually jacobian if you want to be understood in
the optimization community) woes, but in this case the jacobian really 
is bad.

My quick and dirty tries give some insight, but do not provide a 
satisfactory answer. Note that the last two columns of the nlxb summary 
are the gradient and the Jacobian singular values, so one can see how 
bad things are.

days <- c(163,168,170,175,177,182,185,189,196,203,211,217,224)
height <- c(153,161,171,173,176,173,185,192,195,187,195,203,201)
dat <- as.data.frame(cbind(days,height))
fit <- try(nls(y ~ SSweibull(x, Asym, Drop, lrc, pwr), data = dat, 
trace=T, control=nls.control(minFactor=1/100000)))
## failed

fdata<-data.frame(x=days, y=height)

require(nlmrt)
strt2<-c(Asym=250, Drop=1, lrc=1, pwr=1)
fit2<-nlxb(y ~ Asym - (Drop * ( exp(-(exp(lrc)*(x^pwr))))), data=fdata, 
start=strt2, trace=TRUE)

strt3<-c(Asym=250, Drop=.5, lrc=.1, pwr=2)
fit3<-nlxb(y ~ Asym - (Drop * ( exp(-(exp(lrc)*(x^pwr))))), data=fdata, 
start=strt3, trace=TRUE)

strt4<-c(Asym=200, Drop=.5, lrc=.1, pwr=2)
fit4<-nlxb(y ~ Asym - (Drop * ( exp(-(exp(lrc)*(x^pwr))))), data=fdata, 
start=strt4, trace=TRUE, masked=c("Asym"))

d50<-days-160
fd2<-data.frame(x=d50, y=height)
fit5<-nlxb(y ~ Asym - (Drop * ( exp(-(exp(lrc)*(x^pwr))))), data=fd2, 
start=strt3, trace=TRUE)
fit5

John Nash


On 13-10-04 02:19 AM, r-help-request at r-project.org
wrote:
> Message: 40
> Date: Thu, 3 Oct 2013 20:49:36 +0200
> From:aline.frank at wsl.ch
> To:r-help at r-project.org
> Subject: [R] SSweibull() : problems with step factor and singular
> 	gradient
> Message-ID:
> 	<OF669FA420.9EF643ED-ONC1257BF9.00676B04-C1257BF9.00676B07 at
wsl.ch>
> Content-Type: text/plain
>
>   SSweibull() : ? problems with step factor and singular gradient
>
> Hello
>
> I  am working with growth data of ~4000 tree seedlings and trying to fit 
non-linear Weibull growth curves through the data of each plant. Since  they
differ a lot in their shape, initial parameters cannot be set for  all plants.
That???s why I use the self-starting function SSweibull().
> However, I often got two error messages:
>
> 1)
> # Example
> days <- c(163,168,170,175,177,182,185,189,196,203,211,217,224)
> height <- c(153,161,171,173,176,173,185,192,195,187,195,203,201)
> dat <- as.data.frame(cbind(days,height))
> fit <- nls(y ~ SSweibull(x, Asym, Drop, lrc, pwr), data = dat, trace=T,
control=nls.control(minFactor=1/100000))
>
> Error in nls(y ~cbind(1, -exp(-exp(lrc)* x^pwr)), data = xy, algorithm =
???plinear???, : ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?
> step factor 0.000488281 reduced below `minFactor` of 0.000976562
>
> I  tried to avoid this error by reducing the step factor below the 
standard minFactor of 1/1024 using the nls.control function (shown in  the
example above). However, this didn???t work, as shown in the example  (minFactor
still the standard).
> Thus, does nls.control() not work for self-starting functions like
SSweibull()? Or is there another explanation?
>
> 2)
> In other cases, a second error message showed up:
>
> Error in nls(y ~cbind(1, -exp(-exp(lrc)* x^pwr)), data = xy, algorithm =
???plinear???, : ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?
> singular gradient
>
> Is there a way to avoid the problem of a singular gradient?
>
> I???d be very glad about helpful comments. Thanks a lot.
> Aline
> 	[[alternative HTML version deleted]]

Dear John Nash

Thank  you very much for your inputs on how to fit a non-linear growth curve 
without running into "singular gradient". I wasn't aware of the
package  "nlmrt" which seems to provide very helpful functions,
indeed. I'll try  to figure out how nlxb() can be applied to my data (I am
not sure yet  wheter I can actually apply the same initial parameters for all of
my  plants) and also how plotting of the fitted curve works with nlxb(). The 
easy way of using predict(fit) did not work in this case.

In addition, I am still wondering if there is in fact no way of controlling the
step factor in SSweibull.

Best regards, 
Aline Frank


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