Antonio,

I'm left a bit confused by your question.  First, I've never seen a syntax for nls in which random effects are specified.  Your calls look more like nlme calls.  I'm guessing that you have typos for Model ii and iii?  Second, you may wish to test different random effect structures in which not all three parameters are assumed to vary across species or life form.  Third, to see if it did what you want, use the "ranef" function on the model - you should see the random variation for the random effect terms. 

Finally, regarding model selection, RMSR and log likelihood don't consider model complexity so they are inferior.  AIC and BIC preference varies as a function of the researcher's philosophy.  BIC is a bit more conservative than AIC, but the issues are deeper and may not be critical to your decision - if both metrics favor the same model, then no worries. 

Good luck,

Mike

Thanks for your reply Mike,

I agree with you, I never seen a syntax for nls in which random effects are specified. The model ii and iii are nlme calls. However, have you seen nlme models without randon effect?

Thank you again...

No - if you aren't specifying random effects, then you should be using nls, not nlme. 

Thank you again

A model without random effects in nlme is specified with the gls function.  Everything else works the same as lme.

AIC, AICc, BIC.

You might also look at a pseudo-r-square value and the p-value for the overall model.

But it looks like you have to decide if you want to go the nls route, or the linear mixed model route.

If I understand what you're getting at, my suspicion is that you're going to need to try the nls with everything included, and then an nls for each SP, and find a way to see which approach is better.  I don't know of a slick way to do this.  If you're lucky it will be obvious from the fits.

Pseudo-r-square example for nls here, at Nonlinear regression:

http://rcompanion.org/rcompanion/e_03.html

AIC, AICc, BIC.

You might also look at a pseudo-r-square value and the p-value for the overall model.

Sorry to disagree, but pseudo R2 is a flawed measure (and there are a bunch to choose from!).  For a fuller discussion, see http://www.ats.ucla.edu/stat/mult_pkg/faq/general/Psuedo_RSquareds.htm

Dear J, 

(1)There are ready functions for each sigmoid fit in R, for example (from help):

Self-Starting Nls Logistic Model

SSlogis(input, Asym, xmid, scal)=Asym/(1+exp((xmid-input)/scal))

So it is not necessary to define a function, like you did.

Type:

> ?selfStart

for help and presentation of all available sigmoid curves.

(2)If you are interested for finding the inflection point you can use my R - Package inflection:

>install.packages('inflection')

>library('inflection')

(3)You can upload a sample of your data in order to be able to help you in details.

https://cran.r-project.org/web/packages/inflection/index.html

Article Developing methods for identifying the inflection point of a...

Saeed,

Your function works fine for nls.  Example code is below.

I don't know how you intend to use nlme with a sigmoid curve.

The rest of your question is very similar to the original poster's. 

I don't know of any slick methods to choose between IND and SP. 

I think the reality is you're going to have to fit IND and SP, plot the models, and see what they look like.  You might be able to use confidence intervals for the parameters to see if they are significantly different from one another.  Or you may just need decide which you want to use (IND, SP, or LF), based on biological theory or based on what the data look like.  Maybe present all of them. 

It really depends what you trying to show  or  what question you are trying to answer.

Input = (

"x y

1 1

2 2

3 3

4 4

5 6

6 8

7 10

8 15

9 20

10 25

11 28

12 30

13 32

14 34

15 36

16 39

")

Data = read.table(textConnection(Input),header=TRUE)

model = nls(y ~ a/(1+exp(-(x-c)/b)),

data = Data,

start = c(a = 1,

b = 1,

c = 8),

trace = FALSE,

nls.control(maxiter = 10000)

)

summary(model)

plot(y~x, data=Data)

lines(Data$x, predict(model),

col = "blue",

lwd = 2)

Pinheiro and Bates "Mixed Models in S and S-Plus" discuss this issue very well so if you can get your hands on that book do so. What I would suggest is that you use gnls for your non-random model, then set up your nlme model this way: 

Model1