Using mle2 for parameter estimates with error and predict - r

Question

I'm using mle2 to estimate a parameters for a non-linear model and I want estimates of error around the parameter estimates (std. error). As well, I'd like to use the model to then predict with newdata, and I'm having problems (errors) with a couple steps in this process.
Here's the data:
table<- "ac.temp performance
1 2.17 47.357923
4 2.17 234.255317
7 2.17 138.002633
10 2.17 227.545902
13 2.17 28.118072
16 9.95 175.638448
19 9.95 167.392218
22 9.95 118.162747
25 9.95 102.770622
28 9.95 191.874867
31 16.07 206.897159
34 16.07 74.741619
37 16.07 127.219884
40 16.07 208.231559
42 16.07 89.544612
44 20.14 314.946107
47 20.14 290.994063
50 20.14 243.322497
53 20.14 192.335133
56 20.14 133.841776
58 23.83 139.746673
61 23.83 224.135993
64 23.83 126.726493
67 23.83 246.443386
70 23.83 163.019896
83 28.04 4.614154
84 28.04 2.851866
85 28.04 2.935584
86 28.04 153.868415
87 28.04 103.884295
88 30.60 0.000000
89 29.60 0.000000
90 30.30 0.000000
91 29.90 0.000000
92 30.80 0.000000
93 28.90 0.000000
94 30.00 0.000000
95 30.20 0.000000
96 30.40 0.000000
97 30.70 0.000000
98 27.90 0.000000
99 28.60 0.000000
100 28.60 0.000000
101 30.40 0.000000
102 30.60 0.000000
103 29.70 0.000000
104 30.50 0.000000
105 29.30 0.000000
106 28.90 0.000000
107 30.40 0.000000
108 30.20 0.000000
109 30.10 0.000000
110 29.50 0.000000
111 31.00 0.000000
112 30.60 0.000000
113 30.90 0.000000
114 31.10 0.000000"
perfdat<- read.table(text=table, header=T)
First I have to set a couple of the fixed parameters for my non-linear model on performance of an animal with respect to temperature
pi = mean(subset(perfdat, ac.temp<5)$performance)
ti = min(perfdat$ac.temp)
define the x variable (temperature)
t = perfdat$ac.temp
create a function for non-linear model
tpc = function(tm, topt, pmax) {
perfmu = pi+(pmax-pi)*(1+((topt-t)/(topt-tm)))*(((t-ti)/(topt-ti))^((tm-ti)/(topt-tm)))
perfmu[perfmu<0] = 0.00001
return(perfmu)
}
create the negative log likelihood function
LL1 = function(tm, topt, pmax, performance=perfdat$performance) {
perfmu = tpc(tm=tm, topt=topt, pmax=pmax)
loglike = -sum(dnorm(x=performance, mean=perfmu, log=TRUE))
return(loglike)
}
model performance using mle2 - maximum likelihood estimator
m1<- mle2(minuslogl = LL1, start=list(tm=15, topt=20, pmax=150), control=list(maxit=5000))
summary(m1)
This gives me parameter estimates but not estimates of error (std. error) with the warning message: In sqrt(diag(object#vcov)) : NaNs produced. However, the parameters estimates are good and get me predictions that make sense.
Plot of non-linear curve using parameter estimates
I have tried many different optimizers and methods and get the same error about not being able to calculate std. error, usually with warnings about not being able to invert the hessian. OR I get really wonky estimates of my parameters that don't make sense.
IF I use:
confint(m1)
I get 95% intervals for each of my parameters, but I can't incorporate those into a prediction method that I could use for making a graph like below, which I made using an nls model and predict():
non-linear model with error graphed
If I recreate my mle2() model by embedding the model formula into the mle2 function:
tpcfun<- function(t, tm.f, topt.f, pmax.f) {
perfmu = pi+(pmax.f-pi)*(1+((topt.f-t)/(topt.f-tm)))*(((t-ti)/(topt.f-ti))^((tm.f-ti)/(topt.f-tm.f)))
perfmu[perfmu<0] = 0.00001
return(perfmu)
}
m2<- mle2(performance ~ dnorm(mean=-sum(log(tpcfun(t=ac.temp, tm.f, topt.f, pmax.f))), sd=1), method='L-BFGS-B', lower=c(tm.f=1, topt.f=1, pmax.f=1), control=list(maxit=5000, parscale=c(tm.f=1e1, topt.f=1e1, pmax.f=1e2)), start=list(tm.f=15, topt.f=20, pmax.f=150), data=perfdat)
summary(m2)
I get non-sensical estimates for my parameters and I still don't get estimates for error.
My question is, can anyone see anything wrong with either of my models (the model functions and likelihood functions) or anything else that I am doing wrong? I have a feeling that I may be writing the likelihood function wrong but I've tried all sorts of distributions and different ways but I may be totally screwing it up.
OR is there a way that I can get estimates of error around my parameters such that I can use them to visualize error around my model prediction in graphs?
Thanks,
Rylee
PS. I decided to make a graph with just point estimates and then the trend line without error around it, but I wanted to put the bars for 95% CI on each of the point estimates, but confint() is giving me redicylously small CI's which don't even show up on the graph because they are smaller than the point character I'm using, ha.

Answer 1

I think the problem is in the "maxint" arg. Try to use good start values and avoid high interations. The second problem is the algorithm "L-BFGS-B" unless the default. When we use confint function it's normal obtain the intervals whether the mle2 otimization converged. Check if the profiles can be made as a plot (plotprofmle function). It's more safe.
It's normal a "NaNs produced" error if your data contain zero values when apply log. I suggest use this sequence:
loglike = -sum(dnorm(x=performance, mean=perfmu, log=TRUE), na.rm=TRUE)
Verify if the result is plausible.