Hello,
I am new to the mixed model world and hope that my questions are not too trivial.  I have been reading up and exploring a dataset for the last week and have come to the point where I need some advice or direction.
I have an experimental design where I collected 48 observations across 12 (identical in theory) experimental streams.
I have 3 fixed factors.
A (3 levels)-4 streams per level
B (2 levels)-within each stream
C (2 dates)
I am interested in the effect of A, B and C on my response variable so I am considering them all as fixed factors.
If I am correct, the traditional anova code that accounts for the between-within effects design would be:
aov(response~A*B*C + Error(Stream/(B*C)),data=X)

Beacuse I have repeated measures and a covariate nested within each Stream and stream to stream natural variability may have random effects on the data should I be considering Stream as a random factor and computing a linear mixed model instead?
lmer(response~A*B*C+(1|Stream),data=X)
Is this simple model accounting for fixed factors B and C being non independent within A?  It seems like it should b/c there will be more than one value for each Stream*B and Stream*C combination in the model.

An alternative would be applying code that accounts for nested/crossed random effects.  I came up with :
lmer(response~A*B*C+(1|StmB)+(1|StmC),data=X)
where (based on Oct31 Bates reply):
StmB= X<-within(X,{StmB<-factor(Stream:B)}) and
StmC=X<-within(X,{StmC<-factor(Stream:C)})
It is not entirely clear to me why I would count B and C as fixed factors and nested random factors.  Actually the example I got this code from was for factors that were only random (multiple measurements within individual sampling units) so perhaps it is not appropriate after all.

One other formula I have seen that accounts for the grouping is:
lmer(response~A*B*C+(B|Stream)+(C|Stream),data=X)
This is a little confusing to me.  As I understand it this structure implies that the relationship between the response variable and B or C will vary with Stream (random intercept and slope model).  It makes sense in that the relationship between the response variable and A cannot vary with Stream as there is only one level of A in each stream but I am not sure this is describing the nested structure.

Any advice on whether I am on the right track here would be appreciated and please feel free to berate me if my particular design falls into the subject of previous posts.
Thanks,
Jason Taylor





	[[alternative HTML version deleted]]


