[R-sig-ME] Model with interaction alone

[Pierre Montpied]

Hi list,

I could not find any answer to my problem thus I post it on this list.

I have a design where  sites (Site) are nested in different regions 
(Reg) and a pair of plots in each site
is assigned two levels of a treatment (Trait).

I fit this model with lme (or lmer)  with  two crossed fixed factors 
(Reg *Trait) and a random factor Site

All works fine when I fit the complete model "Response~Reg + Treat + 
Reg:Treat"t or equivalently "Response~Reg*Trait"

But when I try the interaction alone by "Response~Reg:Trait" I get the 
error message:
"Error in MEEM(object, conLin, control$niterEM) :   Singularity in 
backsolve at level 0, block 1".

When I replace "Reg:Trait" by "interaction(Reg,Trait)" or by 
"factor(Reg:Trait)" all works fine
whereas these should be equivalent to "Reg:Trait"

Any explanation ?

Below is a script simulating this

library(nlme)

Nrep<-10 # replicates = site number per region
Data<-data.frame(expand.grid(c("T1","T2"),rep(c("R1","R2"),each=Nrep)),
         Site=paste("S",rep(1:(Nrep*2),each=2),sep="")
         )
names(Data)<-c("Trait","Reg","Site")
Data$Trait<-factor(Data$Trait)
Data$Reg<-factor(Data$Reg)
Data$Site<-factor(Data$Site)
Data$RegTrait<-factor(paste(Data$Reg,Data$Trait,sep="."))
str(Data)
table(Data$Reg,Data$Trait,Data$Site)
table(Data$Site,Data$Trait,Data$Reg)


Mu<-20    # Intercept
Alpha2<-1    # Fixed effect Trait
Beta2<-2    # Fixed effect Region
Gamma22<-2    # Interaction Trait:Region
Sigi<-1.5    # Random effect Site
Sige<-1    # Residual

# Simulation:
Data$Rep<- Mu +
         Alpha2*(Data$Trait=="T2") +
         Beta2*(Data$Reg=="R2") +
         Gamma22*(Data$Reg=="R2")*(Data$Trait=="T2") +
         rep(rnorm(Nrep*2,0,Sigi),each=2) +
         rnorm(Nrep*4,0,Sige)


Modele.lme<-lme(Rep~Trait*Reg,
     random=~1|Site,
     data=Data)# OK

Modele.lme<-lme(Rep~Trait + Reg + Trait:Reg,
     random=~1|Site,
     data=Data)# OK

# Interaction alone:

Modele.lme<-lme(Rep~Trait:Reg,
     random=~1|Site,
     data=Data)# Error:

# Error in MEEM(object, conLin, control$niterEM) :
#  Singularity in backsolve at level 0, block 1


Modele.lme<-lme(Rep~interaction(Trait,Reg),
     random=~1|Site,
     data=Data)# OK

Modele.lme<-lme(Rep~factor(Trait:Reg),
     random=~1|Site,
     data=Data)# OK

Thank  in advance

-- 
=========================================================================
Pierre MONTPIED
INRA Université de Lorraine                     Tel : (33) 3 83 39 40 74
UMR EEF Ecophysiologie Ecologie Forestières     FAX : (33) 3 83 39 40 69
F-54280 CHAMPENOUX
http://www.nancy.inra.fr                        montpied at nancy.inra.fr