[R] gamm: problems with corCAR1()

[Simon Wood]

corCAR1 doesn't allow you to have the same value of Week appearing more 
than once within a level of Treatment. Maybe average these replicates, 
if that makes sense in this context?

The singularity problem relates to lack of identifiability in the GAM 
structure. Treatment appears too many times! The way you have things set 
up the smooths of Week will be confounded with the factor(Treatment) 
term, and with the smooth of Treatment. I'd be inclined to declare 
Treatment as a factor and use

richness ~ s(Week,by=Treatment) + Treatment

dropping the smooth of Treatment (using this syntax will give a smooth 
of Week for each level of Treatment, and the smooths will be centred, so 
not confounded with the Treatment term.)

best,
Simon



On 05/10/11 15:21, Karel V wrote:
> Dear all,
>
> I’m analyzing this dataset containing biodiversity indices, measured over
> time (Week), and at various contaminant concentrations (Treatment). We have
> two replicates (Replicate) per treatment.
> I’m looking for the effects of time (Week) and contaminant concentration
> (Treatment) on diversity indices (e.g. richness).
>
> Initial analysis with GAM models showed temporal autocorrelation of
> diversity. So now I’m trying to fit this gamm (gamm1):
>
> gamm1<- gamm(richness~
> s(Week,by=as.numeric(Treatment=="0"),k=6) +
> s(Week,by=as.numeric(Treatment=="0.5"),k=6) +
> s(Week,by=as.numeric(Treatment=="5"),k=6) +
> s(Week,by=as.numeric(Treatment=="15"),k=6) +
> s(Week,by=as.numeric(Treatment=="50"),k=6) +
> s(Week,by=as.numeric(Treatment=="150"),k=6) +
> s(Treatment,k=6,fx=FALSE) + factor(Treatment),
> correlation=corCAR1(form=~Week|factor(Treatment),data=indices,family=gaussian)
>
> I seem to be having difficulties with the correlation structure. An initial
> error occurred because replicates were taken at the same time:
>
> /Error in Initialize.corCAR1(X[[2L]], ...) :
> Covariate must have unique values within groups for corCAR1 objects /
>
> I solved this by selecting one replicate but is there another solution for
> this?
>
> Moreover, when analyzing the data of one replicate, I received following
> error:
>
> /Error in MEestimate(lmeSt, grps) :
> Singularity in backsolve at level 0, block 1
> /
> I have no idea how to solve this. It seems to be related with the complexity
> of the model because no error occurred when running a simpler gamm (gamm2):
>
> gamm2<- gamm(richness~
> s(Week,k=6,fx=FALSE) + factor(Treatment),
> correlation=corCAR1(form=~Week|conc.f), data=test,family=gaussian)
>
> Any help would be well appreciated!
>
> With kind regards,
> Karel
>
>
>
>
> --
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>
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-- 
Simon Wood, Mathematical Science, University of Bath BA2 7AY UK
+44 (0)1225 386603               http://people.bath.ac.uk/sw283