On Sun, May 6, 2012 at 8:41 AM, Ce Mo <[log in to unmask]> wrote:

Dear Dr. Mclaren,

 

Thank you so much for pointing out my mistakes, but I still have some questions concerning this matter and I really appreciate some further insights.

 

1) I assume if we want to test for main effects of dose, i.e. group effect, the contrast would be

 

T1D1+T2D1+T3D1 = T1D2+T2D2+T3D2

T1D2+T2D2+T3D2 = T1D3+T2D3+T3D3

T1D3+T2D3+T3D3 = T1D4+T2D4+T3D4

 

did I understand it correctly?

Yes, but this is invalid in the flexible factorial. With GLM Flex, you could test this properly. In SPM, you'd need to average the three time points first and then use a one-way ANOVA.

 

 

2)  In your example "This is for a design with 18 subjects in group 1, 9 subjects in group 2, 2 group terms and 2 conditions", 

 

One way to setup the flexible factorial model is to use one main factor (subject) and one interaction between group and condition, and thus yields a design matrix containing: subject (27 columns)  group*condition (4 columns)

 

I assume there is an alternative way which uses 3 main factors( subject, condition and group) and one interaction between group and condition and results another design matrix containing: subject (27 columns) group (2 columns) condition (2 columns) and group*condition (4 columns)


I would say both ways seem to be correct but they in fact have different dfs. So the key questions are: 

Will they yield identical results if proper contrasts are defined? 

The degrees of freedom should be the same. The results will be slightly different because of how the variance correction works.
 

If not,  is there a way to tell which one is more appropriate under certain circumstance?


Both are correct. I prefer the full model though because I was always taught to include the main effects in the model if you include the interaction term. 

 

3) I had trouble understand the meaning of th contrasts


S1G1C1=[1 zeros(1,26) 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
S1G1C2=[1 zeros(1,26) 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]

 

I assume the first 27 columns are subject constants but I could not figure out what the following 23 columns stand for (In fact I was expecting 8 columns at most.)

27 subject columns, 2 group columns, 7 condition columns. NOTE: in the original email, it was stated that there were only 2 conditions. My mistake.

The contrast is getting the contrast for Subject 1 of Group 1 for Condition 1.
 

 

4) Is it possible to test for subject effects or interaction between subject and condition?

In the flexible factorial, between-subject effects can not be interpreted as the flexible factorial uses the wrong error term. You can test for group*condition though. Subject*condition cannot be tested. 
 

 

5) I had trouble linking the GLM based ANOVA with the "sum all subjects and average" contrast definition method here. Could you please elaborate a little bit more?

The example above illustrates how you get to the contrasts listed in Gitelman and Glascher. When I say "sum all subjects and average" - I meant that you should take all the pieces that go into the contrast, add them up, and divide by the number of pieces. For example, if you have 10 subjects, then you would add the 10 contrasts for S*G1C1 and then divide by 10. This would give you the contrast for G1C1. Hope this made it clearer.
 

 

6) Is it possible to actually look at the error terms used in SPM statistics?

Look at the ResMS image. This is the basis for the error term for each contrast. The actual equations can be found in the SPM book, which is available on the SPM website.
 

 

Many thanks and best regards,

Sincerely and respectfully yours,

            Ce

 

 

 

 



 

----- 原始邮件 -----
发件人："MCLAREN, Donald" <[log in to unmask]>

收件人：[log in to unmask]
主题：[SPM] Contrast for testing interactions in 3x4 flexible factorial
日期：2012年05月05日 22点50分