Hi all,

I'm using the 'mgcv' library to fit mixed models to a data set. I'm  
used to the lme framework, however, when faced the gamm formulation  
I'm not quite sure I'm understanding part of the results and  
interpretation. As an example let's say we use the 'Soybean' data set:

library(nlme)
library(mgcv)
library(lattice)

data(Soybean)
head(Soybean)

plot(Soybean)

Soybean$logweight<-log(Soybean$weight)

xyplot(logweight~Time|Plot,data=Soybean)


I can run a model that includes an overall smooth function in 'Time'  
but allows the intercept to differ randomly by plot:

m1<-gamm(logweight~Year+Variety+s(Time,k=4,bs="cr"),
	random=list(Plot=~1),data=Soybean,method="REML")

summary(m1$gam)
intervals(m1$lme,which="var-cov")
plot(m1$gam)


However, I can also run a model that includes an overall smooth  
function in 'Time' but allows the intercept and slope to differ by plot:

m2<-gamm(logweight~Year+Variety+s(Time,k=4,bs="cr"),
	random=list(Plot=~Time),data=Soybean,method="REML")

summary(m2$gam)
intervals(m2$lme,which="var-cov")
plot(m2$gam)


My question is that I do not know how to interpret the random 'Time'  
slope given that the covariate is modelled with a spline. I might say  
it allows the relationship between 'logweight' and 'Time' to vary  
among 'Plots', however, how can I obtain the population slope?

Thanks for your help.

Jaime







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