Surprisingly, I was unable to find an answer to the following question using Google:
I have some biological data from several individuals that show a roughly sigmoid growth behaviour in time. Thus, I wish to model it using a standard logistic growth
P(t) = k*p0*exp(r*t) / (k+p0*(exp(r*t)-1))
with p0 being the starting value at t=0, k being the asymptotic limit at t->infinity and r being the growth speed. As far as I can see, I can easily model this using nls (lack of understanding on my part: why can I not model something similar using standard logit regression by scaling time and data? EDIT: Thanks Nick, apparently people do it e.g. for proportions, but rarely http://www.stata-journal.com/article.html?article=st0147 . Next question on this tangent would be if the model can possibly handle outliers >1).
Now I wish to allow some fixed (mainly categorical) and some random (an individual ID and possibly also a study ID) effects on the three parameters k, p0 and r. Is nlme the best way of doing this? The SSlogis model seems sensible for what I am trying to do, is that correct? Is either of the following a sensible model to begin with? I cannot seem to get the starting values right and update() only seems to work for random effects, not fixed ones - any hints?
nlme(y ~ k*p0*exp(r*t) / (k+p0*(exp(r*t)-1)), ## not working at all (bad numerical properties?) data = data, fixed = k + p0 + r ~ var1 + var2, random = k + p0 + r ~ 1|UID, start = c(p0=1, k=100, r=1)) nlme(y ~ SSlogis(t, Asym, xmid, scal), ## not working, as start= is inappropriate data = data, fixed = Asym + xmid + scal ~ var1 + var2, ## works fine with ~ 1 random = Asym + xmid + scal ~ 1|UID, start = getInitial(y ~ SSlogis(Dauer, Asym, xmid, scal), data = data))
As I am new to non-linear mixed models in particular and non-linear models in general, I would appreciate some reading recommendations or links to tutorials / FAQs with newbie questions.