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Paul Bernal

2023-Aug-20 17:15 UTC

[R] Issues when trying to fit a nonlinear regression model

Dear friends,

This is the dataset I am currently working with:>dput(mod14data2_random)structure(list(index = c(14L, 27L, 37L, 33L, 34L, 16L, 7L, 1L,
39L, 36L, 40L, 19L, 28L, 38L, 32L), y = c(0.44, 0.4, 0.4, 0.4,
0.4, 0.43, 0.46, 0.49, 0.41, 0.41, 0.38, 0.42, 0.41, 0.4, 0.4
), x = c(16, 24, 32, 30, 30, 16, 12, 8, 36, 32, 36, 20, 26, 34,
28)), row.names = c(NA, -15L), class = "data.frame")

I did the following to try to fit a nonlinear regression model:

#First, Procedure to Find Starting (initial) Values For Theta1, Theta2, and
Theta3

mymod2 <- y ~ theta1 - theta2*exp(-theta3*x)

strt2 <- c(theta1 = 1, theta2 = 2, theta3 = 3)

trysol2<-nlxb(formula=mymod2, data=mod14data2_random, start=strt2,
trace=TRUE)
trysol2
trysol2$coefficients[[3]]

#Fitting nonlinear Regression Model Using Starting Values From Previous Part
nonlinearmod2 <- nls(mymod2, start = list(theta1 trysol2$coefficients[[1]],
                     theta2 = trysol2$coefficients[[2]],
                     theta3 = trysol2$coefficients[[3]]), data
mod14data2_random)

And I got this error:
Error in nlsModel(formula, mf, start, wts, scaleOffset = scOff, nDcentral
nDcntr) :
  singular gradient matrix at initial parameter estimates

Any idea on how to proceed in this situation? What could I do?

Kind regards,
Paul

	[[alternative HTML version deleted]]

Bert Gunter

2023-Aug-20 18:20 UTC

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[R] Issues when trying to fit a nonlinear regression model

I got starting values as follows:
Noting that the minimum data value is .38, I fit the linear model log(y -
.37) ~ x to get intercept = -1.8 and slope = -.055. So I used .37,
exp(-1.8)  and -.055 as the starting values for theta0, theta1, and theta2
in the nonlinear model. This converged without problems.

Cheers,
Bert


On Sun, Aug 20, 2023 at 10:15?AM Paul Bernal <paulbernal07 at gmail.com>
wrote:
> Dear friends,
>
> This is the dataset I am currently working with:
> >dput(mod14data2_random)
> structure(list(index = c(14L, 27L, 37L, 33L, 34L, 16L, 7L, 1L,
> 39L, 36L, 40L, 19L, 28L, 38L, 32L), y = c(0.44, 0.4, 0.4, 0.4,
> 0.4, 0.43, 0.46, 0.49, 0.41, 0.41, 0.38, 0.42, 0.41, 0.4, 0.4
> ), x = c(16, 24, 32, 30, 30, 16, 12, 8, 36, 32, 36, 20, 26, 34,
> 28)), row.names = c(NA, -15L), class = "data.frame")
>
> I did the following to try to fit a nonlinear regression model:
>
> #First, Procedure to Find Starting (initial) Values For Theta1, Theta2, and
> Theta3
>
> mymod2 <- y ~ theta1 - theta2*exp(-theta3*x)
>
> strt2 <- c(theta1 = 1, theta2 = 2, theta3 = 3)
>
> trysol2<-nlxb(formula=mymod2, data=mod14data2_random, start=strt2,
> trace=TRUE)
> trysol2
> trysol2$coefficients[[3]]
>
> #Fitting nonlinear Regression Model Using Starting Values From Previous
> Part
> nonlinearmod2 <- nls(mymod2, start = list(theta1 >
trysol2$coefficients[[1]],
>                      theta2 = trysol2$coefficients[[2]],
>                      theta3 = trysol2$coefficients[[3]]), data >
mod14data2_random)
>
> And I got this error:
> Error in nlsModel(formula, mf, start, wts, scaleOffset = scOff, nDcentral
> nDcntr) :
>   singular gradient matrix at initial parameter estimates
>
> Any idea on how to proceed in this situation? What could I do?
>
> Kind regards,
> 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]]

Ben Bolker

2023-Aug-20 18:28 UTC

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[R] Issues when trying to fit a nonlinear regression model

My answer is WAY longer than Bert Gunter's but maybe useful nonetheless.

   (Q for John Nash:  why does the coef() method for nlmrt objects 
return the coefficient vector **invisibly**?  That seems confusing!)

   Here's what I did:

* as a preliminary step, adjust the formula so that I don't have to 
think as hard to eyeball starting values from the plot: in particular, 
replace (x) with (x-8) so that the data start from x = 0

* with this adjustment, we can approximate as follows:
     * theta1-theta2 is the value at (x' = 0) (or x = 8)
     * theta1 is the value as x goes to infinity
     * so since y(0) approx. 0.5 and y(inf) approx 0.4, we can use 
theta1 = 0.4, theta2 = -0.1
     * theta3 gives the rate of decline. Since the curve drops by 
*approximately* a factor of e over the range from x'=0 to x'=5, 1/5 
should be a good starting value for this

n1 <- nlxb(y~theta1 - theta2*exp(-theta3*(x-8)),
      start = list(theta1 = 0.4, theta2 = -0.1, theta3 = 1/5),
      data = dd2)

residual sumsquares =  0.00076151  on  15 observations
     after  6    Jacobian and  9 function evaluations
   name            coeff          SE       tstat      pval      gradient 
    JSingval
theta1          0.391967      0.006128      63.96          0  -2.629e-11 
       4.085
theta2        -0.0997234      0.007897     -12.63  2.733e-08  -1.035e-12 
      0.9956
theta3          0.107376       0.02365       4.54  0.0006777  -1.327e-11 
      0.3276

   Now if the formula is

theta1 - theta2*exp(-theta3*(x-8))

this is equivalent to

theta1 - theta2*exp(-theta3*x)*exp(8*theta3) theta1 -
(theta2*exp(8*theta3))*exp(-theta3*x))

cc <- coef(n1)
start2 <- with(as.list(cc), list(theta1 = theta1, theta2 = 
theta2*exp(8*theta3), theta3 = theta3))
unlist(start2)
  theta1   theta2   theta3
  0.39197 -0.23543  0.10738

To confirm, rerun the fit with these starting values:

n1 <- nlxb(y~theta1 - theta2*exp(-theta3*x),
    start = start2,
   data = dd2)


nlmrt class object: x
residual sumsquares =  0.00076151  on  15 observations
     after  4    Jacobian and  5 function evaluations
   name            coeff          SE       tstat      pval      gradient 
    JSingval
theta1          0.391967      0.006128      63.96          0  -4.066e-12 
       4.228
theta2         -0.235429       0.04553     -5.171  0.0002328   3.151e-12 
      0.8508
theta3          0.107376       0.02365       4.54  0.0006777  -5.795e-12 
      0.1569



On 2023-08-20 1:15 p.m., Paul Bernal wrote:> Dear friends,
> 
> This is the dataset I am currently working with:
>> dput(mod14data2_random)
> structure(list(index = c(14L, 27L, 37L, 33L, 34L, 16L, 7L, 1L,
> 39L, 36L, 40L, 19L, 28L, 38L, 32L), y = c(0.44, 0.4, 0.4, 0.4,
> 0.4, 0.43, 0.46, 0.49, 0.41, 0.41, 0.38, 0.42, 0.41, 0.4, 0.4
> ), x = c(16, 24, 32, 30, 30, 16, 12, 8, 36, 32, 36, 20, 26, 34,
> 28)), row.names = c(NA, -15L), class = "data.frame")
> 
> I did the following to try to fit a nonlinear regression model:
> 
> #First, Procedure to Find Starting (initial) Values For Theta1, Theta2, and
> Theta3
> 
> mymod2 <- y ~ theta1 - theta2*exp(-theta3*x)
> 
> strt2 <- c(theta1 = 1, theta2 = 2, theta3 = 3)
> 
> trysol2<-nlxb(formula=mymod2, data=mod14data2_random, start=strt2,
> trace=TRUE)
> trysol2
> trysol2$coefficients[[3]]
> 
> #Fitting nonlinear Regression Model Using Starting Values From Previous
Part
> nonlinearmod2 <- nls(mymod2, start = list(theta1 >
trysol2$coefficients[[1]],
>                       theta2 = trysol2$coefficients[[2]],
>                       theta3 = trysol2$coefficients[[3]]), data >
mod14data2_random)
> 
> And I got this error:
> Error in nlsModel(formula, mf, start, wts, scaleOffset = scOff, nDcentral
> nDcntr) :
>    singular gradient matrix at initial parameter estimates
> 
> Any idea on how to proceed in this situation? What could I do?
> 
> Kind regards,
> 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.

Berwin A Turlach

2023-Aug-21 03:21 UTC

head link

[R] Issues when trying to fit a nonlinear regression model

G'day Paul,

On Sun, 20 Aug 2023 12:15:08 -0500
Paul Bernal <paulbernal07 at gmail.com> wrote:
> Any idea on how to proceed in this situation? What could I do?
You are fitting a simple asymptotic model for which nls() can find good
starting values if you use the self starting models (SSxyz()).  Well,
Doug (et al.) choose to parameterise the asymptotic model differently,
but you can easily change to your parameterisation if you want:

```
fm1 <- nls(y ~ SSasymp(x, Asym, R0, lrc), data=mod14data2_random)
theta1 <- coef(fm1)["Asym"]
theta2 <- coef(fm1)["Asym"] - coef(fm1)["R0"]
theta3 <- exp(coef(fm1)["lrc"])

fm2 <- nls(y ~ theta1 - theta2 * exp(-theta3*x), 
           start=list(theta1=theta1, theta2=theta2, theta3=theta3),
           data=mod14data2_random)
summary(fm2)
```

Cheers,

	Berwin

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