moving from aov() to lmer()

Hello,

I'm using this command to analyse changes in brain volume:

       mod1<-aov(Volume~Sex*Lobe*Tissue+Error(Subject/(Lobe*Tissue)),data.vslt)

I'm comparing males/females. For every subject I have 8 volume
measurements (4 different brain lobes and 2 different tissues
(grey/white matter)).

But I read that aov() results change with the order of the factors
(type I anovas). So I would like to use lmer() with type II, but I'm
struggling to find the right syntaxis...

How should I write the model I use with aov() using lmer()??

Specifying Subject as a random effect is straightforward

        mod2<-lmer(Volume~Sex*Lobe*Tissue+(1|Subject),data.vslt)

but I can't figure out the /(Lobe*Tissue) part...


Thank you very much in advance!

roberto

Hello,
I've used this command to analyse changes in brain volume:

mod1<-aov(Volume~Sex*Lobe*Tissue+Error(Subject/(Lobe*Tissue)),data.vslt)

I'm comparing males/females. For every subject I have 8 volume measurements
(4 different brain lobes and 2 different tissues (grey/white matter)).

As aov() provides only type I anovas, I would like to use lmer() with type
II, however, I have struggled to find the right syntaxis.

How should I write the model I use with aov() using lmer()??

Specifying Subject as a random effect is straightforward

mod2<-lmer(Volume~Sex*Lobe*Tissue+(1|Subject),data.vslt)

but I can't figure out the /(Lobe*Tissue) part...

You're trying to model a separate effect of lobe, of tissue, and of the
interaction between lobe and tissue for each subject, so you want

mod2<-lmer(Volume~Sex*Lobe*Tissue+(Lobe*Tissue|Subject),data.vslt)

...the resulting fixed effect for Lobe, Tissue, and L:T in the summary()
then corresponds to the within-subjects effect aggregated (but not exactly
AVERAGED) across subjects. So, it's not exactly providing you a Type II
ANOVA...it's doing a mixed-effects model (or HLM, if you prefer), which as
you've written it is a Type III analysis (though once again, not an ANOVA in
the classical sense).

To get something more akin to type II using the lmer function (and I trust
someone will pipe up if there is a better way), you could first fit

mod2.additive<-lmer(Volume~Sex*Lobe+Tissue+(Lobe+Tissue|Subject),data.vslt)

...and interpret the coefficients and effects provided by it, then fit the
crossed model to get the coefficients and effects for the higher-order
terms.

I hope this made sense and that I have understood you correctly.

--Adam