nls troubles: Missing value or an infinity produced when evaluating the model

Question

I am an R newbie trying to fit plant photosynthetic light response curves (saturating, curvilinear) to a particular model accepted by experts. The goal is to get estimated coefficient values for Am, Rd, and LCP. Here is the error I keep getting:

Error in numericDeriv(form[[3L]], names(ind), env) : Missing value or an infinity produced when evaluating the model

I have switched around the starting values a number of times, but still no luck. Help? Thanks you in advance. Example dataset below.

photolrc= c(3.089753, 6.336478, 7.737142, 8.004812, 8.031599)
PARlrc= c(48.69624, 200.08539, 499.29840, 749.59222, 1250.09363)
curvelrc<-data.frame(PARlrc,photolrc)
curve.nlslrc = nls(photolrc ~ Am*(1-((1-(Rd/Am))^(1-(PARlrc/LCP)))),start=list(Am=(max(photolrc)-min(photolrc)),Rd=-min(photolrc),LCP= (max(photolrc)-1)))
coef(curve.nlslrc)

Answer 1

minpack.lm to the rescue:

library(minpack.lm)
curve.nlslrc = nlsLM(photolrc ~ Am*(1-((1-(Rd/Am))^(1-(PARlrc/LCP)))),
                   start=list(Am=(max(photolrc)-min(photolrc)),
                              Rd=-min(photolrc),
                              LCP= (max(photolrc)-1)),
                   data = curvelrc)
coef(curve.nlslrc)
  #      Am         Rd        LCP 
  #8.011311   1.087484 -20.752957

plot(photolrc ~ PARlrc, data = curvelrc)
lines(0:1300, 
      predict(curve.nlslrc, 
              newdata = data.frame(PARlrc = 0:1300)))

If you pass start = list(Am = 8, Rd = 1, LCP = -20) to nls you also get a successful fit.

I don't know if the parameter values are sensible estimates considering the science behind this. Can LCP be negative?

Answer 2

The problems are:

• we need better initial values
• according to a comment by the poster we need to constrain LCP to be positive.

To do that we can use nls2 to get better starting values followed by using nls with the port algorithm to enforce a lower bound for LCP. Note that LCP hit the constraint boundary.

library(nls2)

# get starting value fit
st <- data.frame(Am = c(1, 10), Rd = c(-10, 10), LCP = c(0.5, 10))
fo <- photolrc ~ Am*(1-((1-(Rd/Am))^(1-(PARlrc/LCP))))
fm2 <- nls2(fo, start = st, alg = "brute")

# nls fit
fm <- nls(fo, start = coef(fm2), lower = c(-Inf, -Inf, 0.1), algorithm = "port")

giving:

> fm
Nonlinear regression model
  model: photolrc ~ Am * (1 - ((1 - (Rd/Am))^(1 - (PARlrc/LCP))))
   data: parent.frame()
       Am        Rd       LCP 
 7.919374 -0.007101  0.100000 
 residual sum-of-squares: 0.1858

Algorithm "port", convergence message: relative convergence (4)