Doug,
I have been attempting to learn a little bit about nlme without too
much documentation except the online help. The Latex file in the nlme
directory looks interesting but uses packages that I do not have so
that I have not been able to read it.
I have run the example from gnls to compare it with the results I
get from my libraries (code below - I have not included output as it
is rather long and easy to reproduce).
For the model with variance a power function of the mean (fm1), I
get very similar results with a slightly better log likelihood fit.
For the AR(1) (fm2), I get a very much better fit using a continuous
AR(1) with my elliptic function. At first, looking at the
autocorrelation produced, I thought this was because gnls was
erroneously assuming a discrete AR with equally-spaced unit time
intervals when the data are in fact unequally space. (Note that, in
contrast to dataframes, this kind of error is impossible with my data
objects because the times must be associated with the response values
for such models to be fitted.) So I tricked my data objects and
functions into fitting the discrete time AR. The resulting model fits
a lot worse than the (correct) CAR but still very much better than that
from gnls. Something else appears to be wrong but I am not sure what.
Fitting the AR(1) with gnls is also extremely slow: that one model
takes longer than the time fitting all of the others together in the
file below.
I shall continue exploring nlme... Jim
---------------------------------------------------------------------------
library(nlme)
library(growth)
#example from gnls
data(Soybean)
# variance increases with a power of the absolute fitted values
summary(fm1 <- gnls(weight ~ SSlogis(Time, Asym, xmid, scal), Soybean,
weights = varPower()))
# errors follow an auto-regressive process of order 1
summary(fm2 <- gnls(weight ~ SSlogis(Time, Asym, xmid, scal), Soybean,
correlation = corAR1()))
# lines commented out are for fitting a discrete time AR(1)
# construct data objects from dataframe
soybean <- list()
#ctimes <- list()
plot <- variety <- year <- NULL
for(i in as.character(unique(Soybean[1]))){
soybean <- c(soybean,list(as.matrix(Soybean[5:4][Soybean[1]==i,])))
# for discrete time AR(1), correct times must be stored as a
#time-varying covariate
# soybean <- c(soybean,list(cbind(Soybean[5][Soybean[1]==i],
# 1:length(Soybean[5][Soybean[1]==i]))))
# ctimes <- c(ctimes,list(as.matrix(Soybean[4][Soybean[1]==i])))
plot <- c(plot,Soybean[1][Soybean[1]==i][1])
variety <- c(variety,Soybean[2][Soybean[1]==i][1])
year <- c(year,Soybean[3][Soybean[1]==i][1])}
# unfortunately, category names of factor variables were lost here by c()
data <- rmna(restovec(soybean),
ccov=tcctomat(data.frame(plot,variety=variety-1,
year=as.factor(year)),dataframe=F))
# for discrete time AR(1)
#data <- rmna(restovec(soybean),
# ccov=tcctomat(data.frame(plot,variety=variety-1,
#
year=as.factor(year)),dataframe=F),tvc=tvctomat(ctimes,name="ctimes"))
#rm(Soybean,soybean,plot,variety,year,ctimes)
rm(Soybean,soybean,plot,variety,year)
# builtin four-parameter generalized logistic curve
elliptic(data,model="logistic",preg=c(-1,3,-10,3))
# with AR(1)
elliptic(data,model="logistic",preg=c(-1,3,-10,3),par=0.8)
# standard logistic growth curve
elliptic(data,model=~Asym/(1+exp((xmid-times)/scal)),preg=c(20,50,10))
# when variance depends on mean, must use functions instead of formulae
# same logistic growth curve
mu <- function(p) p[1]/(1+exp((p[2]-times)/p[3]))
elliptic(data,model=mu,preg=c(17,50,8))
# variance increases with power of absolute fitted values: model fm1
# note: function for log(variance) is fitted
shape <- function(p,mu) p[1]*log(abs(mu))+p[2]
elliptic(data,model=mu,preg=c(17,50,8),varfn=shape,pvar=c(1,2),shfn=T)
# CAR(1): model fm2
elliptic(data,model=~Asym/(1+exp((xmid-times)/scal)),preg=c(17,50,8),par=0.5)
# fit the discrete time AR(1)
#elliptic(data,model=~Asym/(1+exp((xmid-ctimes)/scal)),preg=c(17,50,8),par=0.5)
# CAR(1) and variance depending on mean
elliptic(data,model=mu,preg=c(19,55,8),varfn=shape,pvar=c(1,2),shfn=T,par=0.95)
# fix power of the mean at 2 in variance function
shape2 <- function(p,mu) 2*log(abs(mu))+p[1]
elliptic(data,model=mu,preg=c(19,55,8),varfn=shape2,pvar=-2,shfn=T,par=0.95)
# dependence of the variance on time with the same function as the mean but
# different parameters
elliptic(data,model=~Asym/(1+exp((xmid-times)/scal)),preg=c(17,50,8),
varfn=~log(Asym/(1+exp((xmid-times)/scal))),pvar=c(3,10,1),par=0.95)
# random intercept?
elliptic(data,model=mu,preg=c(17,51,7.5),varfn=shape,pvar=c(1.8,-2),
shfn=T,par=0.9,pre=1)
# check if thick tails
# multivariate Student t
elliptic(data,model=mu,preg=c(17,51,7.5),varfn=shape,pvar=c(1.8,-2),shfn=T,
par=0.9,dist="Student",pell=1)
# multivariate power exponential
elliptic(data,model=mu,preg=c(17,51,7.5),varfn=shape,pvar=c(1.8,-2),shfn=T,
par=0.9,dist="power exp",pell=1)
# the following could be more easily done with formulae if the variance
# did not depend on the mean
#asymptote depends on variety?
mu2 <- function(p) (p[1]+p[4]*variety)/(1+exp((p[2]-times)/p[3]))
elliptic(data,model=mu2,preg=c(17,52,7.5,0),varfn=shape,pvar=c(1.8,-2.2),
shfn=T,par=0.9,dist="Student",pell=6.5)
# also on year?
mu3 <- function(p) (p[1]+p[4]*variety+p[5]*year2+p[6]*year3)/
(1+exp((p[2]-times)/p[3]))
elliptic(data,model=mu3,preg=c(14.5,52,7.5,4.5,0,0),varfn=shape,
pvar=c(1.8,-2.2),shfn=T,par=0.9,dist="Student",pell=8)
# etc.
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