Example of using nlsLM to fit an s-curve to data

nlsLM_s-curve.R

# Based on a post at \url{http://www.walkingrandomly.com/?p=5254}
library(dplyr)
library(ggplot2)
library(minpack.lm)

# The data to fit
my_df <- data_frame(x = c(0,15,45,75,105,135,165,195,225,255,285,315),
                    y = c(0,0,0,4.5,19.7,39.5,59.2,77.1,93.6,98.7,100,100))

# EDA to see the trend
ggplot(my_df, aes(x = x, y = y)) + geom_point()

# Set initial values for the parameters
p1 <- 100
p2 <- 0
p3 <- 175
p4 <- .01
#my_fn <- my_df$y ~ p1 / (1 + exp(-my_df$x)) + p2

# Fit the data with a sigmoid function
fit_nls <- nlsLM(formula = y ~ p1 / (1 + exp(-x * p4 + p3)) + p2, 
                 data = my_df, 
                 control = nls.lm.control(ftol = 1e-10, ptol = 1e-10), 
                 start = list(p1 = p1, p2 = p2, p3 = p3, p4 = p4), 
                 lower = c(p1 = -Inf, p2 = 0, p3 = -Inf, p4 = -Inf), 
                 upper = c(p1 = 100, p2 = Inf, p3 = Inf, p4 = Inf))

summary(fit_nls)

# Create a data set of fitted data
new_df <- data_frame(x = seq(min(my_df$x), max(my_df$x), length.out = 10*nrow(my_df)))
new_df$y = predict(fit_nls, new_df)

# Plot both original data and the fitted curve
ggplot() +
  geom_line(data = new_df) +
  geom_point(data = my_df) +
  aes(x = x, y = y)

fit_nls <- nlsLM(formula = y ~ p1 / (1 + exp(-x * p4 + p3)) + p2,

•              data = my_df, 
  

•              control = nls.lm.control(ftol = 1e-10, ptol = 1e-10), 
  

•              start = list(p1 = p1, p2 = p2, p3 = p3, p4 = p4), 
  

•              lower = c(p1 = -Inf, p2 = 0, p3 = -Inf, p4 = -Inf), 
  

•              upper = c(p1 = 100, p2 = Inf, p3 = Inf, p4 = Inf))
  

Error in nlsModel(formula, mf, start, wts) :
singular gradient matrix at initial parameter estimates

Thanks for reporting that. I think something must have changed in minpack.lm. I'll update when I figure it out.

Sir, how to superimpose nls plots, drawn by using easynls

Actually, I want to do a Non-linear growth curve study, where I want to draw many non-linear growth curve on the same data, e.g., logistic, Richard, von bertallanffy, Gompertz.

Thanks for reporting that. I think something must have changed in minpack.lm. I'll update when I figure it out.

Any update on this? I'm running into the same error with my own data.