# [R] error using nls with logistic derivative

John C Nash nashjc at uottawa.ca
Tue Apr 17 16:07:13 CEST 2012

```Peter Dalgaard has already given some indications. However, nls() is pretty fragile as a
solver in my experience. I'm in the process of putting some more robust (in the computing
and not statistical sense) solvers in the nlmrt package on the R-forge project at

https://r-forge.r-project.org/R/?group_id=395

See output below.  Best, JN

> source("ardila.R", echo=T)

> rm(list=ls())

> require(nlmrt)

> logis<- expression(a/(1+exp((b-x)/c)))

> D(logis, "x")
a * (exp((b - x)/c) * (1/c))/(1 + exp((b - x)/c))^2

> myY<-c(5.5199668, 1.5234525, 3.3557000, 6.7211704, 7.4237955, 1.9703127, 4.3939336,
+       -1.4380091, 3.2650180, 3.5760906, 0.2947972, 1.0569417)

> myX<-c(1,  0,  0,  4,  3,  5, 12, 10, 12, 100, 100, 100)

> mydata<-data.frame(X=myX, Y=myY)

> ratelogis <- try(nls(Y ~ a*(exp((b-X)/c)*(1/c))/(1 + exp((b-X)/c))^2,
+    start=list(a = 21.16322, b = 8.83669, c = 2.957765),trace=TRUE, data=myda ....
[TRUNCATED]
151.098 :  21.163220  8.836690  2.957765
127.1149 :  103.49326  11.43274  20.29663
111.344 :  833.02390 -45.86244 140.32986
111.3375 :  978.97105 -76.20547 159.90818
111.3374 :  1097.1336 -101.6763  174.2032
111.3227 :  1179.8406 -119.7406  183.3788
Error in nls(Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2,  :
step factor 0.000488281 reduced below 'minFactor' of 0.000976562

> print(ratelogis)
[1] "Error in nls(Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2,  : \n  step
factor 0.000488281 reduced below 'minFactor' of 0.000976562\n"
attr(,"class")
[1] "try-error"
attr(,"condition")
<simpleError in nls(Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2,     start =
list(a = 21.16322, b = 8.83669, c = 2.957765), trace = TRUE,     data = mydata): step
factor 0.000488281 reduced below 'minFactor' of 0.000976562>

> ratelogisn <- nlxb(Y ~ a*(exp((b-X)/c)*(1/c))/(1 + exp((b-X)/c))^2,
+    start=list(a = 21.16322, b = 8.83669, c = 2.957765),trace=TRUE, data=mydata ....
[TRUNCATED]
'data.frame':	12 obs. of  2 variables:
\$ X: num  1 0 0 4 3 5 12 10 12 100 ...
\$ Y: num  5.52 1.52 3.36 6.72 7.42 ...
NULL
formula: Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2
lower:[1] -Inf -Inf -Inf
upper:[1] Inf Inf Inf
\$watch
[1] FALSE

\$phi
[1] 1

\$lamda
[1] 1e-04

\$offset
[1] 100

\$laminc
[1] 10

\$lamdec
[1] 4

\$femax
[1] 10000

\$jemax
[1] 5000

Data variable  Y : [1]  5.5199668  1.5234525  3.3557000  6.7211704  7.4237955  1.9703127
[7]  4.3939336 -1.4380091  3.2650180  3.5760906  0.2947972  1.0569417
Data variable  X : [1]   1   0   0   4   3   5  12  10  12 100 100 100
Start:lamda: 1e-04  SS= 151.098  at  a = 21.16322  b = 8.83669  c = 2.957765  1 / 0
gradient projection0 =  -113.7506  gangle= -0.2949267
Stepsize= 1
<<lamda: 4e-05  SS= 127.1308  at  a = 102.7381  b = 11.32418  c = 20.15418  2 / 1
gradient projection0 =  -55.55629  gangle= -0.1594696
Stepsize= 1
lamda: 4e-04  SS= 129.9286  at  a = 378.4733  b = -71.39815  c = 50.21802  3 / 2
gradient projection0 =  -49.05021  gangle= -0.505497

[snip]

lamda: 2814.75  SS= 50.50144  at  a = 36.13314  b = 2.572373  c = 1.079811  42 / 25
gradient projection0 =  -5.685471e-20  gangle= -0.9954213
Stepsize= 1
lamda: 28147.5  SS= 50.50144  at  a = 36.13314  b = 2.572373  c = 1.079811  43 / 25
gradient projection0 =  -5.68707e-21  gangle= -0.9954364
Stepsize= 1
lamda: 281475  SS= 50.50144  at  a = 36.13314  b = 2.572373  c = 1.079811  44 / 25
gradient projection0 =  -5.687227e-22  gangle= -0.995437
Stepsize= 1
No parameter change

> print(ratelogisn)
\$resid
[1] -0.3897067  1.0662193 -0.7660282 -1.1606765  0.6222073  0.9203074
[7] -4.3885301  1.4723895 -3.2596145 -3.5760906 -0.2947972 -1.0569417

\$jacobian
a             b             c
[1,] 1.419821e-01 -2.954633e+00 -4.486669e-01
[2,] 7.167026e-02 -1.992780e+00  2.349023e+00
[3,] 7.167026e-02 -1.992780e+00  2.349023e+00
[4,] 1.538890e-01  2.981895e+00 -1.207117e+00
[5,] 2.226765e-01  1.456449e+00 -6.874521e+00
[6,] 7.999913e-02  2.165639e+00  2.191813e+00
[7,] 1.495441e-04  5.002498e-03  3.867174e-02
[8,] 9.514926e-04  3.177379e-02  1.867210e-01
[9,] 1.495441e-04  5.002498e-03  3.867174e-02
[10,] 6.050186e-40  2.024541e-38  1.806428e-36
[11,] 6.050186e-40  2.024541e-38  1.806428e-36
[12,] 6.050186e-40  2.024541e-38  1.806428e-36

\$feval
[1] 44

\$jeval
[1] 25

\$coeffs
[1] 36.133144  2.572373  1.079811

\$ssquares
[1] 50.50144

> ratelogis <- try(nls(Y ~ a*(exp((b-X)/c)*(1/c))/(1 + exp((b-X)/c))^2,
+    start=list(a = 36.133144, b= 2.572373, c=1.079811),trace=TRUE, data=mydat ....
[TRUNCATED]
50.50144 :  36.133144  2.572373  1.079811

> print(ratelogis)
Nonlinear regression model
model:  Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2
data:  mydata
a      b      c
36.133  2.572  1.080
residual sum-of-squares: 50.5

Number of iterations to convergence: 0
Achieved convergence tolerance: 4.818e-07
>

On 04/17/2012 06:00 AM, r-help-request at r-project.org wrote:
> Message: 112
> Date: Mon, 16 Apr 2012 23:23:07 -0500
> From: "Francisco Mora Ardila" <fmora at oikos.unam.mx>
> To: r-help at r-project.org
> Subject: [R] error using nls with logistic derivative
> Message-ID: <20120417035718.M33436 at oikos.unam.mx>
> Content-Type: text/plain;	charset=utf-8
>
> Hi
>
> I?m trying to fit a nonlinear model to a derivative of the logistic function
>
> y = a/(1+exp((b-x)/c)) (this is the parametrization for the SSlogis function with nls)
>
> The derivative calculated with D function is:
>
>> > logis<- expression(a/(1+exp((b-x)/c)))
>> > D(logis, "x")
> a * (exp((b - x)/c) * (1/c))/(1 + exp((b - x)/c))^2
>
> So I enter this expression in the nls function:
>
> ratelogis <- nls(Y ~ a*(exp((b-X)/c)*(1/c))/(1 + exp((b-X)/c))^2,
> start=list(a = 21.16322, b = 8.83669, c = 2.957765),
> )
>
> The data is:
>
>> > Y
>  [1]  5.5199668  1.5234525  3.3557000  6.7211704  7.4237955  1.9703127
>  [7]  4.3939336 -1.4380091  3.2650180  3.5760906  0.2947972  1.0569417
>> > X
>  [1]   1   0   0   4   3   5  12  10  12 100 100 100
>
> The problem is that I got the next error:
>
> Error en nls(Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2,  :
>   step factor 0.000488281 reduced below 'minFactor' of 0.000976563
>
> I trien to change the minFactor using the control argument inside nls
>
> control=nls.control(maxiter=50, tol=1e-5, minFactor = 1/2048
>
> but got a new error message:
>
>
> Error en nls(Y ~ a * (exp((b - X)/c) * (1/c))/(1 + exp((b - X)/c))^2,  :
>   step factor 0.000244141 reduced below 'minFactor' of 0.000488281
>
> So it seems that as I modify minFactor, the step factor reduces also and I can never
> reach a solution.
>
> Does anybody Know what am I doing wrong? Is there a problem with the formula? How can I
> solve it? I tried some suggestions on R-help related topics but did not work.
>
> Thanks
>
> Francisco

```