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I am trying to find an optimal sigmoid functional that adjust to my data (at the end of this post). But there is an error: Error in nls(cumulativo ~ f(eixox, phi1, phi2, phi3), start = st, data = data, : singular gradient

Any suggestions ?

library("ggplot2")

data<-structure(list(cumulativo = c(2, 3, 17, 191, 819, 1699, 2679, 
                          3907, 5535, 7254, 9226, 11543, 13809, 15542, 16852, 17709, 18246, 
                          18661, 18976, 19256, 19412, 19539, 19639), eixox = 1994:2016), 
      class = "data.frame", row.names = c(NA, -23L))
plot(cumulativo~eixox, data=data)

st <- list(phi1=20000,phi2=-5,phi3=.0005)
f <- function(x,phi1,phi2,phi3) {phi1/(1 + exp(-phi3 * x - phi2))}
curvaS<-nls(cumulativo~f(eixox,phi1,phi2,phi3),start=st,data=data,trace=TRUE)

dvd.csv

Dave2e
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Antonio Abrantes
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    Please read the information at the top of the [tag:r] tag page. In particular questions should be reproducible. Do not use directory names that are specific to your platform or setup. Do not use images since they can only be used if tediously retyped.. Instead show the output of `dput(X)` where X is your input data. – G. Grothendieck May 09 '21 at 15:03

1 Answers1

3

You have an error in your function definition. It should be

f <- function(x, phi1, phi2, phi3) {phi1/(1 + exp(-phi3 * (x - phi2)))}

Where phi1 is the upper bound, phi2 is the midpoint of the sigmoid curve, and phi3 is the rate. Note the extra parentheses so that phi2 is subtracted from x and then multiplied by -phi3. Now pick reasonable starting values and run nls:

st <- list(phi1=20000, phi2=2005, phi3=.5)
curvaS <- nls(cumulativo~f(eixox, phi1, phi2, phi3), start=st, data=data, trace=TRUE)
# 20466691 :  20000.0  2005.0     0.5
# 1334673 :  19669.7851882  2004.2327533     0.4406048
# 902806.6 :  19566.0810794  2004.1449741     0.4639131
# 901808.4 :  19578.7102128  2004.1498061     0.4637724
# 901808.4 :  19578.7652076  2004.1498401     0.4637683
curvaS
# Nonlinear regression model
#   model: cumulativo ~ f(eixox, phi1, phi2, phi3)
#    data: data
#       phi1       phi2       phi3 
# 19578.7652  2004.1498     0.4638 
#  residual sum-of-squares: 901808
# 
# Number of iterations to convergence: 4 
# Achieved convergence tolerance: 0.000003139

Finally, plot:

plot(cumulativo~eixox, data=data)
pred <- predict(curvaS)
lines(data$eixox, pred)

Plot

dcarlson
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