x <- 1:10
y <- x^2
f <- function(x,a,b,d) {(a*x^2) + (b*x) + d}
fit <- nls(y ~ f(x,a,b,d), start = c(a=1, b=0, d=0))
Error in nls(y ~ f(x, a, b, d), start = c(a = 1, b = 0, d = 0)) :
number of iterations exceeded maximum of 50
library(minpack.lm)
fit <- nlsLM(y ~ f(x,a,b,d), start = c(a=1, b=0, d=0))
summary(fit)
Formula: y ~ f(x, a, b, d)
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 1 0 Inf <2e-16 ***
b 0 0 NA NA
d 0 0 NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0 on 7 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 1.49e-08
Note that I had to adjust the starting values and the result is sensitive to starting values.
fit <- nlsLM(y ~ f(x,a,b,d), start = c(a=1, b=0.1, d=0.1))
Parameters:
Estimate Std. Error t value Pr(>|t|)
a 1.000e+00 2.083e-09 4.800e+08 < 2e-16 ***
b -7.693e-08 1.491e-08 -5.160e+00 0.00131 **
d 1.450e-07 1.412e-08 1.027e+01 1.8e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6.191e-08 on 7 degrees of freedom
Number of iterations to convergence: 3
Achieved convergence tolerance: 1.49e-08