Dear Darren,
Not to supplant Laura's response, but the issue is what the
appropriate error variance (or H0 mean square) estimator is for a
given effect, not per se what the full model is. Your model #2 is
correct for a design (without replications), but it does not
explicitly provide the correct H0 mean square estimator for the
different effects. More particularly, the mean squared residual error
for model #2 would not in general be the correct H0 mean square
estimator for the main effect of group.
I do not know if the module in SPM computes the correct H0 mean square
estimator for the effect of interest (does anyone know the answer?). I
know packages like SAS and SPSS do when the design is correctly
specified.
An aside that I think is not irrelevant to this discussion is the
parametrization of the model. Specifically, if the s_i(j) in model #2
are not constrained to be equal to zero within each group, then the
model might not be estimable. And if they are, then there might
(depending on the presence of constraints for the other terms) need to
be an overall grand mean term to the model. In any case, the specific
parametrization of the model will effect how one expresses expected
mean squares under H0.
Eric
Quoting Darren Gitelman <[log in to unmask]>:
> Laura:
>
> So are you suggesting that if modeling a repeated measures design with
> a group (between) and a condition (within) factor the equation (and by
> implication the design) should be
>
> (1) y_ijk = g_j + c_k + gc_jk + e_ijk
>
> and not
>
> (2) y_ijk = s_i(j) + g_j + c_k + gc_jk + e_ijk ?
>
>
> As far as I can tell looking at books on mixed model designs they say
> the 2nd equation is the correct one for a repeated measures mixed
> model design. I think the 1st equation would be correct for a standard
> factorial ANOVA if one assumes independence between all the measures,
> but I may be misunderstanding you or misunderstanding these designs.
>
> -----
> Darren Gitelman
>
>
>
> On Sat, Apr 4, 2009 at 2:18 PM, Laura Menenti
> <[log in to unmask]> wrote:
>> d
>
>
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