On Sun, 5 Apr 2009 18:55:03 -0400, Eric Zarahn <[log in to unmask]>
wrote:
>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.
Exactly. The model is fine, with the caveat that the residual is not
necessarily the right error term to test against.
>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.
I'm pretty sure SPM always tests against the residual. Perhaps I'm mistaken,
but I thought this was the reason why most people using SPM in multifactorial
models use "pooled errors" rather than "partitioned errors" (cf the
Henson/Penny monograph and a few posts to the list). You actually _can_
correctly partition the error, but you have to do that on your own by setting
up different models such that, in each one, the residual is the correct error for
the effect you want to test. In more generic packages, this is taken care of
for you.
>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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