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:

https://discuss.afni.nimh.nih.gov

Existing user accounts have been migrated, so returning users can login by requesting a password reset. New users can create accounts, as well, through a standard account creation process. Please note that these setup emails might initially go to spam folders (esp. for NIH users!), so please check those locations in the beginning.

The current Message Board discussion threads have been migrated to the new framework. The current Message Board will remain visible, but read-only, for a little while.

Sincerely, AFNI HQ

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Gang Chen
August 22, 2007 03:46PM
There are many (mathematically speaking, infinite) ways to get the matrices. Using 3x3 design as an example, the following is a simple way to obtain them for main effects and interactions.

First contruct common effect vectors for all the factors (A and B in this case):

A1 = [1 1 1] (number of elements corresponds to the number of levels for this factor)
B1 = [1 1 1]

Then differential effects for all the factors:

A2
=
[1 -1 0
0 1 -1]
B2
=
[1 -1 0
0 1 -1]

The main effects and interaction for A and B are the Kronecker products:

A main effect
A2 ⊗ B1 (⊗: Kronecker product in mathematical notation)
=
1 1 1 -1 -1 -1 0 0 0
0 0 0 1 1 1 -1 -1 -1

B main effect
A1 ⊗ B2
=
1 -1 0 1 -1 0 1 -1 0
0 1 -1 0 1 -1 0 1 -1

Interaction
A2 ⊗ B2
=
1 -1 0 -1 1 0 0 0 0
0 1 -1 0 -1 1 0 0 0
0 0 0 1 -1 0 -1 1 0
0 0 0 0 1 -1 0 -1 1

Gang
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Subject Author Posted

3dDeconvolve

John Christie August 22, 2007 11:18AM

Re: 3dDeconvolve

Gang Chen August 22, 2007 03:46PM