AFNI Message Board

Dear AFNI users-

We are very pleased to announce that the new AFNI Message Board framework is up! Please join us at:

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Sincerely, AFNI HQ

History of AFNI updates  

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January 21, 2004 12:03PM
Hi, KJ.
I think I have some ideas about your first question.

In your setup, you are actually using the model Y_ijk=AB_ij +E_ijk. with i=2 and j=5 and k is the length of your time series. Your parameters are AB_11,
AB_12, AB_13, AB_14, AB_15,AB_21, AB_22, AB_23, AB_24, AB_25.

To construct the -glt to test the main effects and interations, you can consider the problem in the following way.
You can transform your model to Y_ijk=MU+alpha_i+beta_j+r_ij+E_ijk. with i=1 and j=1,2,3,4. This is the equvalent to the model you have before.

To test main effect of A, it is the same as testing alpha_1=0.
To test main effect of B, it is the same as testing beta_1=beta_2=beta_3=beta_4=0.
To test interaction of factor A and factor B, it is the same as testing r_11=r_12=r_13=r_14=0.

It is classical to do this tranform. We know that Mu=average of (AB_ij)=AB..=(AB_11+AB_12+AB_13+AB_14+AB_15+AB_21+AB_22+AB_23+AB_24+AB_25)/10
and alpha_1=(AB)1.-Mu
=(AB_11+AB_12+AB_13+AB_14+AB_15)/5-Mu
=((AB_11+AB_12+AB_13+AB_14+AB_15)-
(AB_21+AB_22+AB_23+AB_24+AB_25))/10.

So the -glt file

1 1 1 1 1 -1 -1 -1 -1 -1
is just as you used.

Similarly you need find the expression of beta_1, beta_2, beta_3, beta_4 to construct the glt file to test factor B effect.
beta_j=(AB).j-Mu, here (AB).j mean avearage of AB_ij for the index i. For example (AB).1=(AB_11+AB_21)/2.
Using this way, you will get
beta_1=(4(AB_11+AB_21)-(AB_12+AB_22)-(AB_13+AB_23)-(AB_14+AB_24)-(AB_15+AB_25))/10

beta_2= =(4(AB_12+AB_22)-(AB_11+AB_21)-(AB_13+AB_23)-(AB_14+AB_24)-(AB_15+AB_25))/10

beta_3==(4(AB_13+AB_23)-(AB_11+AB_21)-(AB_12+AB_22)-(AB_14+AB_24)-(AB_15+AB_25))/10

beta_4==(4(AB_14+AB_24)-(AB_11+AB_21)-(AB_12+AB_22)-(AB_13+AB_23)-(AB_15+AB_25))/10

So the glt file to test factor B will be

4 -1 -1 -1 -1 4 -1 -1 -1 -1
-1 4 -1 -1 -1 -1 4 -1 -1 -1
-1 -1 4 -1 -1 -1 -1 4 -1 -1
-1 -1 -1 4 -1 -1 -1 -1 4 -1


For the interaction, r_ij=AB_ij-(AB)i.-(AB).j+(AB).. where (AB)..=Mu.
r_11=AB_11-(AB)1.-(AB).1-(AB)..
r_12=AB_12-(AB)1.-(AB).2-(AB)..
r_13=AB_13-(AB)1.-(AB).3-(AB)..
r_14=AB_14-(AB)1.-(AB).4-(AB)..

You can try to expend the above expressions, and you will get the glt file for testing the interactions

4 -1 -1 -1 -1 -4 1 1 1 1
-1 4 -1 -1 -1 1 -4 1 1 1
-1 -1 4 -1 -1 1 1 -4 1 1
-1 -1 -1 4 -1 1 1 1 -4 1

Actually there are more than this way to do it. They will be equivalent. If anything you find not quite right, let me know.

Subject Author Posted

anova interaction

KJ Jantzen January 19, 2004 02:27PM

Re: anova interaction

KJ Jantzen January 19, 2004 02:37PM

Re: anova interaction - DELAY

bob cox January 21, 2004 09:16AM

Re: anova interaction - DELAY

KJ Jantzen January 21, 2004 12:55PM

Re: anova interaction

yanqiong January 21, 2004 12:03PM

Re: anova interaction

KJ Jantzen January 21, 2004 12:49PM

Re: anova interaction

yanqiong January 21, 2004 02:33PM