[R] unstable results of nlxb fit

[PIKAL Petr]

Dear all

I started to use nlxb instead of nls to get rid of singular gradient error.
I try to fit double exponential function to my data, but results I obtain
are strongly dependent on starting values. 

tsmes ~ A*exp(a*plast) + B* exp(b*plast)

Changing b from 0.1 to 0.01 gives me completely different results. I usually
check result by a plot but could the result be inspected if it achieved good
result without plotting?

Or is there any way how to perform such task?

Cheers
Petr

Below is working example.

> dput(temp)
temp <- structure(list(tsmes = c(31, 32, 32, 32, 32, 32, 32, 32, 33, 
34, 35, 35, 36, 36, 36, 37, 38, 39, 40, 40, 40, 40, 40, 41, 43, 
44, 44, 44, 46, 47, 47, 47, 47, 48, 49, 51, 51, 51, 52, 53, 54, 
54, 55, 57, 57, 57, 59, 59, 60, 62, 63, 64, 65, 66, 66, 67, 67, 
68, 70, 72, 74, 76, 78, 81, 84, 85, 86, 88, 90, 91, 92, 94, 96, 
97, 99, 100, 102, 104, 106, 109, 112, 115, 119, 123, 127, 133, 
141, 153, 163, 171), plast = c(50, 51, 52, 52, 53, 53, 53, 54, 
55, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 64, 64, 65, 65, 66, 
66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 75, 76, 76, 77, 77, 78, 
78, 79, 80, 81, 82, 83, 84, 85, 85, 86, 86, 87, 88, 88, 89, 90, 
91, 91, 93, 93, 94, 95, 96, 96, 97, 98, 98, 99, 100, 100, 101, 
102, 103, 103, 104, 105, 106, 107, 107, 108, 109, 110, 111, 112, 
112, 113, 113, 114, 115, 116)), row.names = 2411:2500, class = "data.frame")

library(nlsr)

fit <- nlxb(tsmes ~ A*exp(a*plast) + B* exp(b*plast), data=temp,
start=list(A=1, B=15, a=0.025, b=0.01))
coef(fit)
           A            B            a            b 
3.945167e-13 9.772749e+00 2.802274e-01 2.179781e-02 

plot(temp$plast, temp$tsmes, ylim=c(0,200))
lines(temp$plast, predict(fit, newdata=temp), col="pink", lwd=3)
ccc <- coef(fit)
lines(0:120,ccc[1]*exp(ccc[3]*(0:120)))
lines(0:120,ccc[2]*exp(ccc[4]*(0:120)), lty=3, lwd=2)

# wrong fit with slightly different b
fit <- nlxb(tsmes ~ A*exp(a*plast) + B* exp(b*plast), data=temp,
start=list(A=1, B=15, a=0.025, b=0.1))
coef(fit)
           A            B            a            b 
2911.6448377    6.8320597  -49.1373979    0.0261391 
lines(temp$plast, predict(fit, newdata=temp), col="red", lwd=3)
ccc <- coef(fit)
lines(0:120,ccc[1]*exp(ccc[3]*(0:120)), col="red")
lines(0:120,ccc[2]*exp(ccc[4]*(0:120)), lty=3, lwd=2, col="red")