An error in fitting a non linear regression

Hi

I have a data set with two variables "q" and "depth" as follows:

q<-c(tapply(weight[Soil=="Jy"], Depth[Soil=="Jy"], mean)). This commns
returns 7 "q" values:
0.687900000 0.845550000 0.405416667 0.152766667 0.033100000 0.031400000
0.005183333

The "depth" values are produced using this command whish "depth" shows 

soil depth: 
depth <--c(5,15,25,35,45,55,65). This return these values for "depth":
[1]  -5 -15 -25 -35 -45 -55 -65

I have uploaded the plot file in below:



http://www.nabble.com/file/p22118160/plot.doc plot.doc 

Now I want to fit the following decaying exponential model to our data
presented in the plot file such that depth is X and q is Y.
nreg<-nls(q~a*exp(-b*depth), start=list(a=1, b=0.5)). This command 

the following error:
Error in nls(q ~ a * exp(-b * depth), start = list(a = 1, b = 0.5)) : 
  singular gradient

However, if I use positive values of depth i.e. 
[1]  5 15 25 35 45 55 65

then I recieve the following error:
Error in numericDeriv(form[[3]], names(ind), env) : 
  Missing value or an infinity produced when evaluating the model

Notice that though in the plot depth is drawn on Y axis but in the
regression model "depth" in independent. Plot shows the real world of 

happne to the crop root growth.

Thank you.
Saeed Ahmadi

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Hi Saeed,

one approach is to try out several initial value combinations for a and b.

It often helps to find initial values of the same order of magnitude and
of the same sign
as the final estimates.

To get such initial values, you could linearize the model:

lm(log(q) ~ I(-depth))


and supply the estimated coefficients from the linear regression as
starting values:

nreg <- nls(q ~ a*exp(-b*depth), start = list(a = 0.76168, b = -0.08484))
summary(nreg)


Christian

Hi,

Thank you for the reply and suggestions.

I have two questions?
1) If I want to use log, it seems that I have to take log from both 

the model which will lead to lm(log(q)~log(-depth)). What is 

between this syntax and lm(log(q) ~ I(-depth))?

2) How can I calculate the R-squared of a fitted non linear model?

Regards
Saeed


Christian Ritz-3 wrote:

Hi Saeed,

one approach is to try out several initial value combinations for a 

It often helps to find initial values of the same order of magnitude 

of the same sign
as the final estimates.

To get such initial values, you could linearize the model:

lm(log(q) ~ I(-depth))


and supply the estimated coefficients from the linear regression as
starting values:

nreg <- nls(q ~ a*exp(-b*depth), start = list(a = 0.76168, b = 

summary(nreg)


Christian

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Hi

r-help-bounces at r-project.org napsal dne 24.02.2009 11:31:22:

Hi,

Thank you for the reply and suggestions.

I have two questions?
1) If I want to use log, it seems that I have to take log from both 

sides of

the model which will lead to lm(log(q)~log(-depth)). What is 

tehdifference

between this syntax and lm(log(q) ~ I(-depth))?

If you have 

y = a*exp(-b*x) then log of this equation is

log(y) = log(a) - b * x

at least I was told that by my teacher back at school some decades ago 
that log(exp(x)) = x.

You can prove it by

log(exp(whatever))

interactively in R

Regards
Petr

2) How can I calculate the R-squared of a fitted non linear model?

Regards
Saeed


Christian Ritz-3 wrote:

Hi Saeed,

one approach is to try out several initial value combinations for a 

and b.

It often helps to find initial values of the same order of magnitude 

and

of the same sign
as the final estimates.

To get such initial values, you could linearize the model:

lm(log(q) ~ I(-depth))


and supply the estimated coefficients from the linear regression as
starting values:

nreg <- nls(q ~ a*exp(-b*depth), start = list(a = 0.76168, b = 

-0.08484))

summary(nreg)


Christian

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Hi Peter,

You are totally right and it was a miscalculating and misunderstanding 

me.
Regarding the R-squared calculation of non linear model (question 2), is
there any way to do that?

Regards
Saeed 

Petr Pikal wrote:

Hi

r-help-bounces at r-project.org napsal dne 24.02.2009 11:31:22:

Hi,

Thank you for the reply and suggestions.

I have two questions?
1) If I want to use log, it seems that I have to take log from both 

sides of

the model which will lead to lm(log(q)~log(-depth)). What is 

tehdifference

between this syntax and lm(log(q) ~ I(-depth))?

If you have 

y = a*exp(-b*x) then log of this equation is

log(y) = log(a) - b * x

at least I was told that by my teacher back at school some decades ago 

that log(exp(x)) = x.

You can prove it by

log(exp(whatever))

interactively in R

Regards
Petr

2) How can I calculate the R-squared of a fitted non linear model?

Regards
Saeed


Christian Ritz-3 wrote:

Hi Saeed,

one approach is to try out several initial value combinations for a 

and b.

It often helps to find initial values of the same order of 

and

of the same sign
as the final estimates.

To get such initial values, you could linearize the model:

lm(log(q) ~ I(-depth))


and supply the estimated coefficients from the linear regression as
starting values:

nreg <- nls(q ~ a*exp(-b*depth), start = list(a = 0.76168, b = 

-0.08484))

summary(nreg)


Christian

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