Dear experts,

I am confused by demean during GLM model setup and would like someone here can help me. Thanks!

Suppose I have a continuous behavior data and I want to find out which brain region(s) correlated with it. The simple way is to calculate correltation between brain data and behavior data, or in GLM to set up a model Y=AX+B+e, A is slope, B is constent and e is error, Y is brain data and X is beahvior data. So this design matrix have two collumns: behavior data and ones.

or we can think of demean that dX=X-mean(X), dY=Y-mean(Y)

Y=A'dX+B'+e', A' should be the same a A and B' differed from B, and B' maybe more interpretatable.

I was told that -D opion in FSL randomise will demean X and Y at the same time. one can set up models like dY=A1dX+B1+e1, or dY=A2dX+e2. I simulated a data in SPSS and confirmed that A1,A2 is the same as A, B1 is 0. but t test for A1 A2 differed a little, A1 is the same as above models.

So it seems to me that include a constent in the model is always right, right?

My confusion is why Y also need to demean and how was it done in randomise? when one says "demean" or "mean centering", he/she means demean X only or demean X and Y both?

Thanks for any clarification!

2013-01-09

Chunhui Chen

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State Key Laboratory of Cognitive Neuroscience and Learning

Beijing Normal University

Beijing, China 100875