R: Problem with 4 parameter hockeystick curve with nls

My dataset:

mydata<-structure(list(t = c(0.208333333, 0.208333333, 0.208333333, 0.208333333, 
1, 1, 1, 1, 2, 2, 2, 2, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 
16, 16, 0.208333333, 0.208333333, 0.208333333, 0.208333333, 1, 
1, 1, 1, 2, 2, 2, 2), parent = c(1.2, 1.4, 0.53, 1.2, 1, 0.72, 
0.93, 1.1, 0.88, 0.38, 0.45, 0.27, 0.057, 0.031, 0.025, 0.051, 
0.027, 0.015, 0.034, 0.019, 0.017, 0.025, 0.024, 0.023, 0.29, 
0.22, 0.34, 0.19, 0.12, 0.092, 0.41, 0.28, 0.064, 0.05, 0.058, 
0.043)), .Names = c("t", "Ct"), row.names = c(325L, 326L, 
327L, 328L, 341L, 342L, 343L, 344L, 357L, 358L, 359L, 360L, 373L, 
374L, 375L, 376L, 389L, 390L, 391L, 392L, 401L, 402L, 403L, 404L, 
805L, 806L, 807L, 808L, 821L, 822L, 823L, 824L, 837L, 838L, 839L, 
840L), class = "data.frame")

      

The function to be set is the hockeystick curve; that is, it flattens after the inflection point tb:

hockeystick<-function (t, C0, k1, k2, tb) 
{
  Ct = ifelse(t <= tb, C0 -k1 * t, C0 -k1*tb -k2*t)
}

      

Installation using nls:

start.hockey<-c(C0=3,k1=1,k2=0.1,tb=3)
nls(log(Ct)~hockeystick(t,C0,k1,k2,tb),start=start.hockey,data=mydata)

      

No matter what initial values ​​I use, I always get this error:

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

      

I tried both port

and standard nls methods. I tried both linearized (shown here) and normal model state but doesn't seem to work.

Edit: As per Karl's suggestion, I tried to fit the model to the dataset where I first averaged the Ct values ​​by the t value and still get the error.

edit: changed the model a bit, so the value is k2

positive, not negative. A negative value has no kinetic meaning.

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1 answer


I didn't quite solve the problem nls()

, but I have some tips.

First of all, I would suggest revisiting your hockey stick function a bit to make it continuous at a breakpoint:

hockeystick<-function (t, C0, k1, k2, tb) 
{
   Ct <- ifelse(t <= tb, C0 -k1 * t, C0 -k1*t -k2*(t-tb))
}

      

Eyeballing:

par(las=1,bty="l") ## cosmetic
plot(log(Ct)~t,data=mydata)
curve(hockeystick(x,C0=0,k1=0.8,k2=-0.7, tb=3),add=TRUE)

      

enter image description here

I've made it k2

negative here , so the decreasing slope of the second stage is less than the first stage.

start.hockey <- c(C0=0,k1=0.8,k2=-0.7, tb=3)
nls(log(Ct)~hockeystick(t,C0,k1,k2,tb),
                        start=start.hockey,data=mydata)

      



Models with breakpoints are often not differentiated by parameters, but I don't quite understand how this problem is here ...

It works:

library(bbmle)
m1 <- mle2(log(Ct)~dnorm(hockeystick(t,C0,k1,k2,tb),
                  sd=exp(logsd)),
          start=c(as.list(start.hockey),list(logsd=0)),
          data=mydata)

      

The options are reasonable (and different from the initial values):

coef(summary(m1))
##         Estimate Std. Error   z value        Pr(z)
## C0    -0.4170749  0.2892128 -1.442104 1.492731e-01
## k1     0.6720120  0.2236111  3.005271 2.653439e-03
## k2    -0.5285974  0.2400605 -2.201934 2.766994e-02
## tb     2.0007688  0.1714292 11.671108 1.790751e-31
## logsd -0.2218745  0.1178580 -1.882558 5.976033e-02

      

Estimated projections:

pframe <- data.frame(t=seq(0,15,length=51))
pframe$pred <- predict(m1,newdata=pframe)
with(pframe,lines(t,pred,col=2))

      

enter image description here

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