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WilDscOp

2004-Apr-14 12:21 UTC

[R] Non-Linear Regression Problem

Dear all,

	I was wondering if there is any way i could do a "Grid Search" on a 
parameter space using R (as SAS 6.12 and higher can do it) to start the 
Newton-Gauss Linearization least squares method when i have NO prior 
information about the parameter.
W. N. Venables and B. D. Ripley (2002) "Modern Applied Statistics with
S",
4 th ed., page 216-7  has a topic "Self-starting non-linear
regressions"
using negexp.SSival - but i can not solve my hypothetical problem using 
that - my problem is :

Y = EXP(-(THETA * t)) with data below for estimating THETA:

t    	Y
1	0.80
4 	0.45
16 	0.04

Whatever i could do, is in http://www.angelfire.com/ab5/get5/nonlinear.PDF

Any response / help / comment / suggestion / idea / web-link / replies will 
be greatly appreciated.

Thanks in advance for your time.

_______________________

Mohammad Ehsanul Karim <wildscop at yahoo.com>
Institute of Statistical Research and Training
University of Dhaka, Dhaka- 1000, Bangladesh

Spencer Graves

2004-Apr-14 16:26 UTC

head link

[R] Non-Linear Regression Problem

1.  For the equation you mentioned, have you considered the following: 

DF <- data.frame(t.=c(1, 4, 16), Y=c(.8, .45, .04))
# I do NOT use "t" as a name, as it
# may conflict with the matrix transpose function.
fit0 <- lm(log(Y)~t.-1, DF)
fit0
Call:
lm(formula = log(Y) ~ t. - 1, data = DF)

Coefficients:
     t. 
-0.2012 
################

      If this is the problem you really wanted to solve AND you honestly 
need NONLINEAR least squares, I would expect that (-0.2) should provide 
a reasonable starting value for nls: 

 > fit1 <- nls(Y~exp(-THETA*t.), data=DF, start=c(THETA=-0.2))
 > fit1
Nonlinear regression model
  model:  Y ~ exp(-THETA * t.)
   data:  DF
    THETA
0.2034489
 residual sum-of-squares:  0.0003018337
 >

      2.  Alternatively, you could compute the sum of squares for all 
values of THETA = seq(0, .01, 100) in a loop, then find the minimum by 
eye. 

      3.  If this is just a toy example, and your real problem has 
several parameters, "expand.grid" will produce a grid, and you can 
compute the value of your function and the sum of squares of residuals 
at every point in the grid in a single loop, etc. 

      hope this helps.  spencer graves

WilDscOp wrote:
> Dear all,
>
>     I was wondering if there is any way i could do a "Grid
Search" on
> a parameter space using R (as SAS 6.12 and higher can do it) to start 
> the Newton-Gauss Linearization least squares method when i have NO 
> prior information about the parameter.
> W. N. Venables and B. D. Ripley (2002) "Modern Applied Statistics with
> S", 4 th ed., page 216-7  has a topic "Self-starting non-linear 
> regressions" using negexp.SSival - but i can not solve my hypothetical
> problem using that - my problem is :
>
> Y = EXP(-(THETA * t)) with data below for estimating THETA:
>
> t        Y
> 1    0.80
> 4     0.45
> 16     0.04
>
> Whatever i could do, is in 
> http://www.angelfire.com/ab5/get5/nonlinear.PDF
>
> Any response / help / comment / suggestion / idea / web-link / replies 
> will be greatly appreciated.
>
> Thanks in advance for your time.
>
> _______________________
>
> Mohammad Ehsanul Karim <wildscop at yahoo.com>
> Institute of Statistical Research and Training
> University of Dhaka, Dhaka- 1000, Bangladesh
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html

Douglas Bates

2004-Apr-14 16:29 UTC

head link

[R] Non-Linear Regression Problem

WilDscOp <wildscop at yahoo.com> writes:
> 	I was wondering if there is any way i could do a "Grid Search"
> on a parameter space using R (as SAS 6.12 and higher can do it) to
> start the Newton-Gauss Linearization least squares method when i have
> NO prior information about the parameter.
> 
> W. N. Venables and B. D. Ripley (2002) "Modern Applied Statistics with
> S", 4 th ed., page 216-7  has a topic "Self-starting non-linear
> regressions" using negexp.SSival - but i can not solve my hypothetical
> problem using that - my problem is :
> 
> 
> Y = EXP(-(THETA * t)) with data below for estimating THETA:
> 
> t    	Y
> 1	0.80
> 4 	0.45
> 16 	0.04
> 
> Whatever i could do, is in http://www.angelfire.com/ab5/get5/nonlinear.PDF
> 
> Any response / help / comment / suggestion / idea / web-link / replies
> will be greatly appreciated.
> 
> 
> Thanks in advance for your time.
> angel = read.table("/tmp/angelfire.dat", header = TRUE)
> angel   t    Y
1  1 0.80
2  4 0.45
3 16 0.04> lm(log(Y) ~ t - 1, angel)
Call:
lm(formula = log(Y) ~ t - 1, data = angel)

Coefficients:
      t  
-0.2012  
> fm = nls(Y~ exp(-(theta*t)), angel, c(theta = 0.2012), trace = TRUE)0.0003229897 :  0.2012 
0.0003018397 :  0.2034108 
0.0003018337 :  0.2034484 
0.0003018337 :  0.2034489 > summary(fm)
Formula: Y ~ exp(-(theta * t))

Parameters:
      Estimate Std. Error t value Pr(>|t|)    
theta 0.203449   0.006002   33.90  0.00087 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1

Residual standard error: 0.01228 on 2 degrees of freedom

Christian Mora

2004-Apr-15 03:33 UTC

head link

[R] Non-Linear Regression Problem

Working on the same idea, Ive generated a data grid with 4 vars, two of
them with its own sequence and two with fixed values. As Spencer pointed
out one option is to get the values from a simple loop. My question is:
How can jump from one set of starting values to the next (on the data
grid) in case they cause an invalid value in the model Im evaluating? In
my example, Ive 12 possible combinations of the 4 vars and in the 6th
combination I get an error and the loop is terminated so what Im looking
for is to skip this problem and continue from the 7th to 12th
combination of starting points

Ill appreciate any comment

Code:

data<-expand.grid(alpha=100,delta=4,beta=seq(1,2,by=0.5),gamma=seq(.1,.4
,by=.1))
for(i in 1:12){
fit<-nls(y~delta+(alpha-delta)/(1+exp(beta*log(rate/gamma))),data=base,s
tart=c(alpha=data$alpha[i],delta=data$delta[i],beta=data$beta[i],gamma=d
ata$gamma[i]),trace=T)
}

Thanks
CMora



-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Spencer Graves
Sent: Wednesday, April 14, 2004 12:27 PM
To: WilDscOp
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] Non-Linear Regression Problem


1.  For the equation you mentioned, have you considered the following: 

DF <- data.frame(t.=c(1, 4, 16), Y=c(.8, .45, .04))
# I do NOT use "t" as a name, as it
# may conflict with the matrix transpose function.
fit0 <- lm(log(Y)~t.-1, DF)
fit0
Call:
lm(formula = log(Y) ~ t. - 1, data = DF)

Coefficients:
     t. 
-0.2012 
################

      If this is the problem you really wanted to solve AND you honestly

need NONLINEAR least squares, I would expect that (-0.2) should provide 
a reasonable starting value for nls: 

 > fit1 <- nls(Y~exp(-THETA*t.), data=DF, start=c(THETA=-0.2))
 > fit1
Nonlinear regression model
  model:  Y ~ exp(-THETA * t.)
   data:  DF
    THETA
0.2034489
 residual sum-of-squares:  0.0003018337
 >

      2.  Alternatively, you could compute the sum of squares for all 
values of THETA = seq(0, .01, 100) in a loop, then find the minimum by 
eye. 

      3.  If this is just a toy example, and your real problem has 
several parameters, "expand.grid" will produce a grid, and you can 
compute the value of your function and the sum of squares of residuals 
at every point in the grid in a single loop, etc. 

      hope this helps.  spencer graves

WilDscOp wrote:
> Dear all,
>
>     I was wondering if there is any way i could do a "Grid
Search" on
> a parameter space using R (as SAS 6.12 and higher can do it) to start 
> the Newton-Gauss Linearization least squares method when i have NO 
> prior information about the parameter.
> W. N. Venables and B. D. Ripley (2002) "Modern Applied Statistics with
> S", 4 th ed., page 216-7  has a topic "Self-starting non-linear 
> regressions" using negexp.SSival - but i can not solve my hypothetical
> problem using that - my problem is :
>
> Y = EXP(-(THETA * t)) with data below for estimating THETA:
>
> t        Y
> 1    0.80
> 4     0.45
> 16     0.04
>
> Whatever i could do, is in 
> http://www.angelfire.com/ab5/get5/nonlinear.PDF
>
> Any response / help / comment / suggestion / idea / web-link / replies
> will be greatly appreciated.
>
> Thanks in advance for your time.
>
> _______________________
>
> Mohammad Ehsanul Karim <wildscop at yahoo.com>
> Institute of Statistical Research and Training
> University of Dhaka, Dhaka- 1000, Bangladesh
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html
______________________________________________
R-help at stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html

WilDscOp

2004-Apr-16 12:24 UTC

head link

[R] Non-Linear Regression Problem

Dear all,

First of all i like to thank specially Spencer Graves and Douglas Bates for 
their kind help and suggestions. I estimated the parameter nicely.

But, for my previous posted problem, the rational of the following line
  R> fit0 <- lm(log(Y)~t-1, draper.data)
is not clear to me. How come this gives the initial value?

Any response / help / comment / suggestion / idea / web-link / replies will 
be greatly appreciated.

Thanks in advance for your time.

_______________________

Mohammad Ehsanul Karim <wildscop at yahoo.com>
Institute of Statistical Research and Training
University of Dhaka, Dhaka- 1000, Bangladesh

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