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

Bert Gunter bgunter@4567 @end|ng |rom gm@||@com
Sun Aug 20 21:39:46 CEST 2023

```Basic algebra and exponentials/logs. I leave those details to you or
another HelpeR.

-- Bert

On Sun, Aug 20, 2023 at 12:17 PM Paul Bernal <paulbernal07 using gmail.com> wrote:

> Dear Bert,
>
> Thank you for your extremely valuable feedback. Now, I just want to
> understand why the signs for those starting values, given the following:
> > #Fiting intermediate model to get starting values
> > intermediatemod <- lm(log(y - .37) ~ x, data=mod14data2_random)
> > summary(intermediatemod)
>
> Call:
> lm(formula = log(y - 0.37) ~ x, data = mod14data2_random)
>
> Residuals:
>     Min      1Q  Median      3Q     Max
> -0.7946 -0.0908  0.0379  0.1111  0.5917
>
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)
> (Intercept) -1.81693    0.25806   -7.04  8.8e-06 ***
> x           -0.05538    0.00964   -5.75  6.8e-05 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 0.323 on 13 degrees of freedom
> Multiple R-squared:  0.717, Adjusted R-squared:  0.696
> F-statistic:   33 on 1 and 13 DF,  p-value: 6.76e-05
>
> Kind regards,
> Paul
>
> El dom, 20 ago 2023 a las 14:07, Bert Gunter (<bgunter.4567 using gmail.com>)
> escribió:
>
>> Oh, sorry; I changed signs in the model, fitting
>> theta0 + theta1*exp(theta2*x)
>>
>> So for theta0 - theta1*exp(-theta2*x) use theta1= -.exp(-1.8) and theta2
>> = +.055 as starting values.
>>
>> -- Bert
>>
>>
>>
>>
>>
>> On Sun, Aug 20, 2023 at 11:50 AM Paul Bernal <paulbernal07 using gmail.com>
>> wrote:
>>
>>> Dear Bert,
>>>
>>> Thank you so much for your kind and valuable feedback. I tried finding
>>> the starting values using the approach you mentioned, then did the
>>> following to fit the nonlinear regression model:
>>> nlregmod2 <- nls(y ~ theta1 - theta2*exp(-theta3*x),
>>>                   start =
>>>                     list(theta1 = 0.37,
>>>                          theta2 = exp(-1.8),
>>>                          theta3 = -0.05538), data=mod14data2_random)
>>> However, I got this error:
>>> Error in nls(y ~ theta1 - theta2 * exp(-theta3 * x), start = list(theta1
>>> = 0.37,  :
>>>   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
>>> nlregmod2 <- nlxb(y ~ theta1 - theta2*exp(-theta3*x),
>>>                   start =
>>>                     list(theta1 = 0.37,
>>>                          theta2 = exp(-1.8),
>>>                          theta3 = -0.05538), data=mod14data2_random)
>>> summary(nlregmod2)
>>> Object has try-error or missing parameters
>>> nlregmod2
>>> And I get some NA values when retrieving the statistics for the fitted
>>> model:
>>> residual sumsquares =  0.0022973  on  15 observations
>>>     after  2235    Jacobian and  2861 function evaluations
>>>   name            coeff          SE       tstat      pval      gradient
>>>    JSingval
>>> theta1           9330.89            NA         NA         NA   5.275e-11
>>>      967470
>>> theta2           9330.41            NA         NA         NA  -5.318e-11
>>>       1.772
>>> theta3       -3.0032e-07            NA         NA         NA   1.389e-05
>>>   8.028e-12
>>>
>>> Kind regards,
>>> Paul
>>>
>>>
>>> El dom, 20 ago 2023 a las 13:21, Bert Gunter (<bgunter.4567 using gmail.com>)
>>> escribió:
>>>
>>>> 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 using 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]]
>>>>>
>>>>> ______________________________________________
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