Non Linear Regression Troubleshooting

Question

Following is an excerpt from my data set: relative frequency and size. As you can see from the open-circles, this is a Gaussian distribution. I am using the nls package in R to fit a nonlinear curve. My equation is

or in plain text: c * e^(-(x - z)^2/l)

Here is how I got here

fit <- as.formula(y~c*(exp((-(x-z)^2/l))))
preview(fit_partial, data=mydata, start=list(c=0.005, x=mydata$x_values, z=130,l=2000))

The starting values seem reasonable. So I try to get a non-linear fit

nls_fit <- nls(fit, data=mydata, start=list(c=0.005, x=mydata$x_values, z=130, l=2000))

However, I'm thrown with an error

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

This is likely because my starting values are poor. Something else must be the issue though. Appreciate any help.

Answer 1

As far as I can tell, your only problem is including x in your list of parameters, which is confusing R (I can't exactly tell you why ... something about the fact that it's not actually a parameter of the model ...). nls(fit, data=mydata, start=pars) works fine for me.

Simulate data:

fit <- as.formula(y~c*(exp((-(x-z)^2/l))))
mydata <- data.frame(x=80:200)
pars <- list(c=0.005, z=130,l=2000)
set.seed(101)
mydata$y_det <- eval(fit[[3]],
                     env=c(pars,as.list(mydata)))
mydata$y <- rnorm(nrow(mydata),mean=mydata$y_det,sd=0.0002)
plot(y~x,data=mydata) ## check

Try original fit:

nls_fit <- nls(fit, data=mydata, start=c(pars,list(x=mydata$x)))

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

Fit with parameters only (not x).

nls_fit <- nls(fit, data=mydata, start=pars)
lines(mydata$x,predict(nls_fit),col=2)
coef(nls_fit)
##           c            z            l 
## 4.963097e-03 1.302308e+02 2.035007e+03