Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Paul Bernal]

Dear Dr. Nash,

Thank you for your kind feedback. I was able to successfully find the
starting values for the nonlinear regression model parameters, here is my
code:
#Specifying Nonlinear Regression Model
mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)

strt <- c(Beta1 = 1, Beta2 = 2, Beta3 = 3)

trysol<-nlxb(formula=mymod, data=mod14data_random, start=strt, trace=TRUE)
trysol

#Examining structure of trysol model
str(trysol)

#Extracting Coefficients for Beta1, Beta2, and Beta3
trysol$coefficients[[1]]
trysol$coefficients[[2]]
trysol$coefficients[[3]]

The dataset is the same I shared previously, but for safety, I will share
it again below:
>dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")

I was able to get the results you shared:
> trysol
residual sumsquares =  1.5412e-05  on  20 observations
after  29Jacobian and  43 function evaluations
  namecoeff  SE   tstat  pval  gradient
 JSingval
Beta1 0.00629212 5.997e-06   1049  2.425e-42   4.049e-08
721.8
Beta2 0.00867741 1.608e-05  539.7  1.963e-37  -2.715e-08
56.05
Beta3 0.00801948 8.809e-05  91.03  2.664e-24   1.497e-08
10.81

Now my question is, how could I perform adequacy checking on this nonlinear
regression model? I was trying to use the deviance metric as follows:
#We will fit several models
nlregmod2 <- nls(y ~ 1/(Beta1*x1),
start =
  list(Beta1 = trysol$coefficients[[1]]),
data=mod14data_random)

nlregmod3 <- nls(y ~ 1/(Beta2*x2),
 start =
   list(Beta2 = trysol$coefficients[[2]]),
data=mod14data_random)

nlregmod4 <- nls(y ~ 1/(Beta3*x3),
 start =
   list(Beta3 = trysol$coefficients[[3]]),
data=mod14data_random)

nlregmod5 <- nls(y ~ 1/(Beta1*x1+Beta2*x2),
 start =
   list(Beta1 = trysol$coefficients[[1]],
Beta2 = trysol$coefficients[[2]]),
data=mod14data_random)


nlregmod6 <- nls(y ~ 1/(Beta1*x1+Beta3*x3),
 start =
   list(Beta1 = trysol$coefficients[[1]],
Beta3 = trysol$coefficients[[3]]),
data=mod14data_random)

nlregmod7 <- nls(y ~ 1/(Beta2*x2+Beta3*x3),
 start =
   list(Beta2 = trysol$coefficients[[2]],
Beta3 = trysol$coefficients[[3]]),
data=mod14data_random)




deviance(nlregmod)
deviance(nlregmod2)
deviance(nlregmod3)
deviance(nlregmod4)
deviance(nlregmod5)
deviance(nlregmod6)
deviance(nlregmod7)

However, for some models I get the following error:

nlregmod4 <- nls(y ~ 1/(Beta3*x3),
  start =
   list(Beta3 = trysol$coefficients[[3]]),
data=mod14data_random)
Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
  Missing value or an infinity produced when evaluating the model
 deviance(nlregmod5)
Error: object 'nlregmod5' not found
 deviance(nlregmod6)
Error: object 'nlregmod6' not found
 deviance(nlregmod7)
Error: object 'nlregmod7' not found

I spent a significant amount of time looking for a way to assess the
nonlinear regression model goodness of fit and to perform adequacy checking
using R (and in general) but was not able to find anything.

I would have thought that calculating the deviance for different models
would be a good way to perform adequacy checking, but got some errors. The
best I could find was this link
https://cran.r-project.org/web/packages/nlstools/vignettes/vignetteJSS.pdf.

Any help and/or guidance will be greatly appreciated.

Kind regards,
Paul

El El sáb, 19 de ago. de 2023 a la(s) 9:30 p. m., J C Nash <
profjcn...@gmail.com> escribió:

> The cautions people have given about starting values are worth heeding.
> That nlxb() does well in many cases is useful,
> but not foolproof. And John Fox has shown that the problem can be tackled
> very simply too.
>
> Best, JN
>
>
> On 2023-08-19 18:42, Paul Bernal wrote:
> > Thank you so much Dr. Nash, I truly appreciate your kind and valuable
> contribution.
> >
> > Cheers,
> > Paul
> >
> > El El sáb, 19 de ago. de 2023 a la(s) 3:35 p. m., J C Nash <
> profjcn...@gmail.com > escribió:
> >
> > Why bother. nlsr can find a solution from very crude start.
> >
> > Mixture <- c(17, 14, 

Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[J C Nash]

The cautions people have given about starting values are worth heeding. That 
nlxb() does well in many cases is useful,
but not foolproof. And John Fox has shown that the problem can be tackled very 
simply too.

Best, JN


On 2023-08-19 18:42, Paul Bernal wrote:

Thank you so much Dr. Nash, I truly appreciate your kind and valuable 
contribution.

Cheers,
Paul

El El sáb, 19 de ago. de 2023 a la(s) 3:35 p. m., J C Nash mailto:profjcn...@gmail.com>> escribió:

Why bother. nlsr can find a solution from very crude start.

Mixture <- c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23, 20, 6, 13, 21, 3, 18, 15, 
26, 8, 22)
x1 <- c(69.98, 72.5, 77.6, 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 
67.51, 77.63,
          72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48)
x2 <- c(29, 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 
32.47,
          20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5)
x3 <- c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
          3, 3, 0, 2)
y <- c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
         1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
         1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)
mydata<-data.frame(Mixture, x1, x2, x3, y)
mydata
mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)
library(nlsr)
strt<-c(Beta1=1, Beta2=2, Beta3=3)
trysol<-nlxb(formula=mymod, data=mydata, start=strt, trace=TRUE)
trysol
# or pshort(trysol)


Output is

residual sumsquares =  1.5412e-05  on  20 observations
      after  29    Jacobian and  43 function evaluations
    name            coeff          SE       tstat      pval      gradient   
 JSingval
Beta1         0.00629212     5.997e-06       1049  2.425e-42   4.049e-08    
   721.8
Beta2         0.00867741     1.608e-05      539.7  1.963e-37  -2.715e-08    
   56.05
Beta3         0.00801948     8.809e-05      91.03  2.664e-24   1.497e-08    
   10.81

J Nash


On 2023-08-19 16:19, Paul Bernal wrote:
 > Dear friends,
 >
 > Hope you are all doing well and having a great weekend.  I have data that
 > was collected on specific gravity and spectrophotometer analysis for 26
 > mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
 > nitrodiphenylamine).
 >
 > In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.
 >
 > The response variable is the specific gravity, and the rest of the
 > variables are the predictors.
 >
 > This is the dataset:
 > dput(mod14data_random)
 > structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
 > 20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
 > 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
 > 72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
 > 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
 > 20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
 >      x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
 >      3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
 >      1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
 >      1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names 
=
 > c(NA,
 > -20L), class = "data.frame")
 >
 > The model is the following:
 > y = 1/(Beta1x1 + Beta2x2 + Beta3x3)
 >
 > I need to determine starting (initial) values for the model parameters 
for
 > this nonlinear regression model, any ideas on how to accomplish this 
using
 > R?
 >
 > Cheers,
 > Paul
 >
 >       [[alternative HTML version deleted]]
 >
 > __
 > R-help@r-project.org  mailing list -- To 
UNSUBSCRIBE and more, see
 > https://stat.ethz.ch/mailman/listinfo/r-help 

 > PLEASE do read the posting guide 
http://www.R-project.org/posting-guide.html

 > and provide commented, minimal, self-contained, reproducible code.



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Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Ben Bolker]

  Adding one more method:

glm(y~ x1 + x2 + x3 - 1, family = gaussian(link = "inverse"), data = mydata)

  will fit the exact model (including the desired error structure). 
The default GLM starting values usually work OK, but it is true that 
inverse-links can sometimes be more finicky than more typical links.	


On 2023-08-19 6:48 p.m., John Fox wrote:

Dear John, John, and Paul,

In this case, one can start values by just fitting

 > lm(1/y ~ x1 + x2 + x3 - 1, data=mydata)

Call:
lm(formula = 1/y ~ x1 + x2 + x3 - 1, data = mydata)

Coefficients:
  x1   x2   x3
0.00629  0.00868  0.00803

Of course, the errors enter this model differently, so this isn't the 
same as the nonlinear model, but the regression coefficients are very 
close to the estimates for the nonlinear model.


Best,
  John



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Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[John Fox]

Dear John, John, and Paul,

In this case, one can start values by just fitting

> lm(1/y ~ x1 + x2 + x3 - 1, data=mydata)

Call:
lm(formula = 1/y ~ x1 + x2 + x3 - 1, data = mydata)

Coefficients:
 x1   x2   x3
0.00629  0.00868  0.00803

Of course, the errors enter this model differently, so this isn't the 
same as the nonlinear model, but the regression coefficients are very 
close to the estimates for the nonlinear model.


Best,
 John

--
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://www.john-fox.ca/

On 2023-08-19 6:39 p.m., Sorkin, John wrote:

Caution: External email.


Colleagues,

At the risk of starting a forest fire, or perhaps a brush fire, while it is 
good to see that nlxb can find a solution from arbitrary starting values, I 
think Paul’s question has merit despite Professor Nash’s excellent and helpful 
observation.

Although non-linear algorithms can converge, they can converge to a false 
solution if starting values are sub-optimally specified. When possible, I try 
to specify thought-out starting values. Would it make sense to plot y as a 
function of (x1, x2) at different values of x3 to get a sense of possible 
starting values? Or, perhaps using median values of x1, x2, and x3 as starting 
values. Comparing results from different starting values can give some 
confidence that the solution obtained using arbitrary starting values are 
likely “correct”.

I freely admit that my experience (and thus expertise) using non-linear 
solutions is limited. Please do not flame me, I am simply urging caution.

John

John David Sorkin M.D., Ph.D.
Professor of Medicine
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology and Geriatric 
Medicine
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to 
faxing)

On Aug 19, 2023, at 4:35 PM, J C Nash 
mailto:profjcn...@gmail.com>> wrote:

Why bother. nlsr can find a solution from very crude start.

Mixture <- c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23, 20, 6, 13, 21, 3, 18, 15, 26, 
8, 22)
x1 <- c(69.98, 72.5, 77.6, 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 
67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48)
x2 <- c(29, 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5)
x3 <- c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
3, 3, 0, 2)
y <- c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
   1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
   1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)
mydata<-data.frame(Mixture, x1, x2, x3, y)
mydata
mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)
library(nlsr)
strt<-c(Beta1=1, Beta2=2, Beta3=3)
trysol<-nlxb(formula=mymod, data=mydata, start=strt, trace=TRUE)
trysol
# or pshort(trysol)


Output is

residual sumsquares =  1.5412e-05  on  20 observations
after  29Jacobian and  43 function evaluations
  namecoeff  SE   tstat  pval  gradient
JSingval
Beta1 0.00629212 5.997e-06   1049  2.425e-42   4.049e-08   
721.8
Beta2 0.00867741 1.608e-05  539.7  1.963e-37  -2.715e-08   
56.05
Beta3 0.00801948 8.809e-05  91.03  2.664e-24   1.497e-08   
10.81

J Nash


On 2023-08-19 16:19, Paul Bernal wrote:
Dear friends,
Hope you are all doing well and having a great weekend.  I have data that
was collected on specific gravity and spectrophotometer analysis for 26
mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
nitrodiphenylamine).
In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.
The response variable is the specific gravity, and the rest of the
variables are the predictors.
This is the dataset:
dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
 x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
 3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
 1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
 1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")
The model is the following:
y = 1/(Beta1x1 + Beta2x2 + Beta3x3)
I need to determine starting (initial) values for the model parameters for
this nonlinear regression model, any ideas on how to accomplish this using
R?
Cheers,
Paul
[[alternative HTML version deleted]]
__
R-help@r-project.org

Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Paul Bernal]

Thank you so much Dr. Nash, I truly appreciate your kind and valuable
contribution.

Cheers,
Paul

El El sáb, 19 de ago. de 2023 a la(s) 3:35 p. m., J C Nash <
profjcn...@gmail.com> escribió:

> Why bother. nlsr can find a solution from very crude start.
>
> Mixture <- c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23, 20, 6, 13, 21, 3, 18, 15,
> 26, 8, 22)
> x1 <- c(69.98, 72.5, 77.6, 79.98, 74.98, 80.06, 69.98, 77.34, 69.99,
> 67.49, 67.51, 77.63,
>  72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48)
> x2 <- c(29, 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49,
> 32.47,
>  20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5)
> x3 <- c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
>  3, 3, 0, 2)
> y <- c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
> 1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
> 1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)
> mydata<-data.frame(Mixture, x1, x2, x3, y)
> mydata
> mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)
> library(nlsr)
> strt<-c(Beta1=1, Beta2=2, Beta3=3)
> trysol<-nlxb(formula=mymod, data=mydata, start=strt, trace=TRUE)
> trysol
> # or pshort(trysol)
>
>
> Output is
>
> residual sumsquares =  1.5412e-05  on  20 observations
>  after  29Jacobian and  43 function evaluations
>namecoeff  SE   tstat  pval  gradient
>   JSingval
> Beta1 0.00629212 5.997e-06   1049  2.425e-42   4.049e-08
>  721.8
> Beta2 0.00867741 1.608e-05  539.7  1.963e-37  -2.715e-08
>  56.05
> Beta3 0.00801948 8.809e-05  91.03  2.664e-24   1.497e-08
>  10.81
>
> J Nash
>
>
> On 2023-08-19 16:19, Paul Bernal wrote:
> > Dear friends,
> >
> > Hope you are all doing well and having a great weekend.  I have data that
> > was collected on specific gravity and spectrophotometer analysis for 26
> > mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
> > nitrodiphenylamine).
> >
> > In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.
> >
> > The response variable is the specific gravity, and the rest of the
> > variables are the predictors.
> >
> > This is the dataset:
> > dput(mod14data_random)
> > structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
> > 20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
> > 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
> > 72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
> > 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
> > 20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
> >  x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
> >  3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
> >  1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
> >  1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names
> =
> > c(NA,
> > -20L), class = "data.frame")
> >
> > The model is the following:
> > y = 1/(Beta1x1 + Beta2x2 + Beta3x3)
> >
> > I need to determine starting (initial) values for the model parameters
> for
> > this nonlinear regression model, any ideas on how to accomplish this
> using
> > R?
> >
> > Cheers,
> > Paul
> >
> >   [[alternative HTML version deleted]]
> >
> > __
> > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>

[[alternative HTML version deleted]]

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Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Sorkin, John]

Colleagues,

At the risk of starting a forest fire, or perhaps a brush fire, while it is 
good to see that nlxb can find a solution from arbitrary starting values, I 
think Paul’s question has merit despite Professor Nash’s excellent and helpful 
observation.

Although non-linear algorithms can converge, they can converge to a false 
solution if starting values are sub-optimally specified. When possible, I try 
to specify thought-out starting values. Would it make sense to plot y as a 
function of (x1, x2) at different values of x3 to get a sense of possible 
starting values? Or, perhaps using median values of x1, x2, and x3 as starting 
values. Comparing results from different starting values can give some 
confidence that the solution obtained using arbitrary starting values are 
likely “correct”.

I freely admit that my experience (and thus expertise) using non-linear 
solutions is limited. Please do not flame me, I am simply urging caution.

John

John David Sorkin M.D., Ph.D.
Professor of Medicine
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology and Geriatric 
Medicine
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to 
faxing)

On Aug 19, 2023, at 4:35 PM, J C Nash 
mailto:profjcn...@gmail.com>> wrote:

Why bother. nlsr can find a solution from very crude start.

Mixture <- c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23, 20, 6, 13, 21, 3, 18, 15, 26, 
8, 22)
x1 <- c(69.98, 72.5, 77.6, 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 
67.51, 77.63,
   72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48)
x2 <- c(29, 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
   20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5)
x3 <- c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
   3, 3, 0, 2)
y <- c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
  1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
  1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)
mydata<-data.frame(Mixture, x1, x2, x3, y)
mydata
mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)
library(nlsr)
strt<-c(Beta1=1, Beta2=2, Beta3=3)
trysol<-nlxb(formula=mymod, data=mydata, start=strt, trace=TRUE)
trysol
# or pshort(trysol)


Output is

residual sumsquares =  1.5412e-05  on  20 observations
   after  29Jacobian and  43 function evaluations
 namecoeff  SE   tstat  pval  gradient
JSingval
Beta1 0.00629212 5.997e-06   1049  2.425e-42   4.049e-08   
721.8
Beta2 0.00867741 1.608e-05  539.7  1.963e-37  -2.715e-08   
56.05
Beta3 0.00801948 8.809e-05  91.03  2.664e-24   1.497e-08   
10.81

J Nash


On 2023-08-19 16:19, Paul Bernal wrote:
Dear friends,
Hope you are all doing well and having a great weekend.  I have data that
was collected on specific gravity and spectrophotometer analysis for 26
mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
nitrodiphenylamine).
In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.
The response variable is the specific gravity, and the rest of the
variables are the predictors.
This is the dataset:
dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")
The model is the following:
y = 1/(Beta1x1 + Beta2x2 + Beta3x3)
I need to determine starting (initial) values for the model parameters for
this nonlinear regression model, any ideas on how to accomplish this using
R?
Cheers,
Paul
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Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[J C Nash]

Why bother. nlsr can find a solution from very crude start.

Mixture <- c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23, 20, 6, 13, 21, 3, 18, 15, 26, 
8, 22)
x1 <- c(69.98, 72.5, 77.6, 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 
67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48)
x2 <- c(29, 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5)
x3 <- c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
3, 3, 0, 2)
y <- c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
   1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
   1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)
mydata<-data.frame(Mixture, x1, x2, x3, y)
mydata
mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)
library(nlsr)
strt<-c(Beta1=1, Beta2=2, Beta3=3)
trysol<-nlxb(formula=mymod, data=mydata, start=strt, trace=TRUE)
trysol
# or pshort(trysol)


Output is

residual sumsquares =  1.5412e-05  on  20 observations
after  29Jacobian and  43 function evaluations
  namecoeff  SE   tstat  pval  gradient
JSingval
Beta1 0.00629212 5.997e-06   1049  2.425e-42   4.049e-08   
721.8
Beta2 0.00867741 1.608e-05  539.7  1.963e-37  -2.715e-08   
56.05
Beta3 0.00801948 8.809e-05  91.03  2.664e-24   1.497e-08   
10.81

J Nash


On 2023-08-19 16:19, Paul Bernal wrote:

Dear friends,

Hope you are all doing well and having a great weekend.  I have data that
was collected on specific gravity and spectrophotometer analysis for 26
mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
nitrodiphenylamine).

In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.

The response variable is the specific gravity, and the rest of the
variables are the predictors.

This is the dataset:
dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
 x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
 3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
 1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
 1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")

The model is the following:
y = 1/(Beta1x1 + Beta2x2 + Beta3x3)

I need to determine starting (initial) values for the model parameters for
this nonlinear regression model, any ideas on how to accomplish this using
R?

Cheers,
Paul

[[alternative HTML version deleted]]

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[R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Paul Bernal]

Dear friends,

Hope you are all doing well and having a great weekend.  I have data that
was collected on specific gravity and spectrophotometer analysis for 26
mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
nitrodiphenylamine).

In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.

The response variable is the specific gravity, and the rest of the
variables are the predictors.

This is the dataset:
dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")

The model is the following:
y = 1/(Beta1x1 + Beta2x2 + Beta3x3)

I need to determine starting (initial) values for the model parameters for
this nonlinear regression model, any ideas on how to accomplish this using
R?

Cheers,
Paul

[[alternative HTML version deleted]]

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Re: [R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Bert Gunter]

" need to determine starting (initial) values for the model parameters for
this nonlinear regression model," ...

what nonlinear regression model? Did html get stripped?

-- Bert

On Sat, Aug 19, 2023 at 12:38 PM Paul Bernal  wrote:

> Dear friends,
>
> Hope you are all doing well and having a great weekend.  I have data that
> was collected on specific gravity and spectrophotometer analysis for 26
> mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
> nitrodiphenylamine).
>
> In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.
>
> The response variable is the specific gravity, and the rest of the
> variables are the predictors.
>
> This is the dataset:
> dput(mod14data_random)
> structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
> 20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
> 79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
> 72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
> 25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
> 20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
> x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
> 3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
> 1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
> 1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
> c(NA,
> -20L), class = "data.frame")
>
> I need to determine starting (initial) values for the model parameters for
> this nonlinear regression model, any ideas on how to accomplish this using
> R?
>
> Any help and/or guidance will be greatly appreciated.
>
> Thanks, beforehand, for your valuable and kindness.
>
> Best regards,
> Paul
>
> [[alternative HTML version deleted]]
>
> __
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

[[alternative HTML version deleted]]

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[R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Paul Bernal]

Dear friends,

Hope you are all doing well and having a great weekend.  I have data that
was collected on specific gravity and spectrophotometer analysis for 26
mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
nitrodiphenylamine).

In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.

The response variable is the specific gravity, and the rest of the
variables are the predictors.

This is the dataset:
dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")

I need to determine starting (initial) values for the model parameters for
this nonlinear regression model, any ideas on how to accomplish this using
R?

Any help and/or guidance will be greatly appreciated.

Thanks, beforehand, for your valuable and kindness.

Best regards,
Paul

[[alternative HTML version deleted]]

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