Non linear mixed model

Question

As a R beginner, I am trying to fix a model given including a random factor. The formula is:

Temp ~ a - (b * exp(-c *rate))

Where Temp is temperature and rate is a measure of the variation (time/temp). For construct the model and get the initial parameters I use the nlme package:

data1<-groupedData((Temp~rate|Year), data=data)
fm1<-nlme(Temp ~ a - (b * exp(-c *rate)), data=data, fixed=Temp~rate, start=c(a=8.10,b=7.24,c=0.5))
    Error in eval(expr, envir, enclos) : object 'a' not found`

I have tried this as well:

`fm100<-selfStart(~a-(b*exp(-c*rate)),
function(mCall, data, LHS)
{
xy<-sortedXyData(mCall[["x"]], LHS, data)
tmp<-coef(lm(Temp~rate, data=data),
value<-c(exp(tmp[1],temp[2])
getInitial=c("a","b","c"))
}`

Error: unexpected symbol in:
"value<-c(exp(tmp[1],temp[2]) getInitial"

Perhaps is a simple question but I haven’t found anything useful yet.

Here are the data:

Temp<-c(9,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,17.1,17.6,17.6,19.6,20.6,21.3,21.3,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,23.5,23.8,11.4,11.4,11.4,11.4,11.7,11.7,12.6,13.6,13.6,14.6,14.6,14.6,14.6,15.7,15.7,15.7,16.1,16.1,16.7,16.7,11.6,12.6,12.6,12.6,14.5,14.5,14.7,15.8,15.8,15.8,15.8,16,16,16,16,16,16,16,16,16,16)
Rate<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
Year<-c(2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011) 
data<-data.frame(Temp, Rate, Year)

Thank you in advance!

Please check your code for typos, as well as unmatched parentheses! (restart your R session and rerun your code, you'll see what I mean) — Dominic Comtois, Mar 23 '15 at 12:38
Thank you Dominic. I have corrected the errors but it doesn't help me to fix the model. — dej, Mar 23 '15 at 13:56

score 0 · Answer 1 · answered Mar 23 '15 at 13:45

Firstly, there are a few typos Rate between rate.

Secondly, I think the model is over-parameterised in it's current form, perhaps try something like the following instead?

library(nlme)
Temp <- c(9,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,17.1,17.6,17.6,19.6,20.6,21.3,21.3,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,22.8,23.5,23.8,11.4,11.4,11.4,11.4,11.7,11.7,12.6,13.6,13.6,14.6,14.6,14.6,14.6,15.7,15.7,15.7,16.1,16.1,16.7,16.7,11.6,12.6,12.6,12.6,14.5,14.5,14.7,15.8,15.8,15.8,15.8,16,16,16,16,16,16,16,16,16,16)
Rate <- c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,0.0417,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
Year <- c(2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2006,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2010,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011,2011) 
data <- data.frame(Temp, Rate, Year)

fm1 <- nlme(Temp ~ a * exp(-b * Rate), 
    data = data, 
    fixed = a + b ~ 1, 
    random = a + b ~ 1 | Year, 
    start = c(a = 20.0, b = 0.5))

Thirdly, I changed the starting values to actually fit the data a little better, look at a plot of Temp against Rate:

f <- function(Rate) {
    a <- 20.0
    b <- 0.5
    a * exp(-b * Rate)
}

plot(Temp ~ Rate, data = data)
curve(f, add = TRUE, lwd = 2, col = "red")

plot to help with starting values

Lastly, I have taken a guess at the structure of your random effects, I think a good reference is in ?nlme for the fixed and random arguments, so you can see for yourself how these work and choose the correct structure.

Hope this is useful!

Thank you for the answer Jeff. In fact, the model you propose is my second model (next I will choose the better one by AIC). I tried to do the same using the first model but I get this error: > fm2<-nlme(Temp ~ a - (b * exp(-(c *Rate))), + data=data, + fixed=a+b+c~1, + random=a+b+c~1 | Year, + start = c(a = 20.0, b = 5, c =0.5)) Error en MEEM(object, conLin, control$niterEM) : Singularity in backsolve at level 0, block 1 — dej, Mar 23 '15 at 14:04
Yes I did exactly the same, and got the same error, which was why I then realised the model was over-parameterised. — Jeff, Mar 23 '15 at 14:15

Non linear mixed model

1 Answers1