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Paul Bernal

2023-Aug-19 22:42 UTC

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

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

Cheers,
Paul

El El s?b, 19 de ago. de 2023 a la(s) 3:35 p. m., J C Nash <
profjcnash at gmail.com> escribi?:
> 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 at 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]]

J C Nash

2023-Aug-20 02:30 UTC

head link

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

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 s?b, 19 de ago. de 2023 a la(s) 3:35 p.?m., J C Nash <profjcnash
at gmail.com <mailto:profjcnash at gmail.com>> escribi?:
> 
>     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 at r-project.org <mailto:R-help at r-project.org>
mailing list -- To UNSUBSCRIBE and more, see
>      > https://stat.ethz.ch/mailman/listinfo/r-help
<https://stat.ethz.ch/mailman/listinfo/r-help>
>      > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>     <http://www.R-project.org/posting-guide.html>
>      > and provide commented, minimal, self-contained, reproducible
code.
>

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