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Formula and Start-values for simplest "non-linear" mixed model - nlmer (nlme??, lmer ?)

1 message · Ben Bolker

Original
Ben Bolker
# 
Here's a start (I hope) -- new examples for nlmer ...  for the naming
issue, I would consider brute force:  R has a feature that often annoys
me that the names of vectors get carried along ...
a.a
  1

instead try y<-c(a=unname(x[1]))
a
1

## nonlinear mixed models --- 3-part formulas ---
## 1. basic nonlinear fit. Use stats::SSlogis for its
## implementation of the 3-parameter logistic curve.
## "SS" stands for "self-starting logistic", but the
## "self-starting" part is not currently used by nlmer ... 'start' is
## necessary
startvec <- c(Asym = 200, xmid = 725, scal = 350)
(nm1 <- nlmer(circumference ~ SSlogis(age, Asym, xmid, scal) ~ Asym|Tree,
             Orange, start = startvec))
## 2. re-run with "quick and dirty" PIRLS step
(nm1a <- update(nm1, nAGQ = 0L))
## 3. Fit the same model with a user-built function:
## a. Define formula
nform <- ~Asym/(1+exp((xmid-input)/scal))
## b. Use deriv() to construct function:
nfun <- deriv(nform,namevec=c("Asym","xmid","scal"),
              function.arg=c("input","Asym","xmid","scal"))
nm1b <- update(nm1,circumference ~ nfun(age, Asym, xmid, scal)  ~ Asym |
Tree)
## 4. User-built function without using derivs():
##    derivatives could be computed more efficiently
##    by pre-computing components, but these are essentially
##    the gradients as one would derive them by hand
nfun2 <- function(input, Asym, xmid, scal) {
    value <- Asym/(1+exp((xmid-input)/scal))
    grad <- cbind(Asym=1/(1+exp((xmid-input)/scal)),
              xmid=-Asym/(1+exp((xmid-input)/scal))^2*1/scal*
                    exp((xmid-input)/scal),
              scal=-Asym/(1+exp((xmid-input)/scal))^2*
                     -(xmid-input)/scal^2*exp((xmid-input)/scal))
    attr(value,"gradient") <- grad
    value
}
stopifnot(all.equal(attr(nfun(2,1,3,4),"gradient"),
                    attr(nfun(2,1,3,4),"gradient")))
nm1c <- update(nm1,circumference ~ nfun2(age, Asym, xmid, scal)  ~ Asym
| Tree)
On 14-01-16 01:01 PM, Robert Chatfield wrote: