Dear Laura, Lennart, Stephen, Darren,
let me try to come back to my original question posted last week:
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0904&L=SPM&P=R12110
Following your discussion, and trying to sum things up, you recomend that I
should remove the subject factor from the model when testing for group
effect (i.e. use model 1 from Darrens posting below), and build a separate
model including the subject factor (model 2) to test for condition effects,
and for group x condition interactions?
But even if so, how can we explain the complex values of the
standarddeviation originiating from the square root of a negative number
that appears in a situation in SPM where numbers are not planned to be
negative? Is this a result from using the wrong model, or is it a bug in SPM?
Best,
Thomas
On Mon, 6 Apr 2009 02:32:38 +0100, Stephen J. Fromm <[log in to unmask]> wrote:
>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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