Email discussion lists for the UK Education and Research communities

## SPM@JISCMAIL.AC.UK

#### View:

 Message: [ First | Previous | Next | Last ] By Topic: [ First | Previous | Next | Last ] By Author: [ First | Previous | Next | Last ] Font: Proportional Font
 LISTSERV Archives SPM Home SPM 2000

#### Options

Subject:

Re: baseline modelling

From:

Date:

Wed, 24 May 2000 16:31:07 +0100 (BST)

Content-Type:

text/plain

Parts/Attachments:

 text/plain (61 lines)
 ```Dear Ying, > After reading spm mailbase, I am still unclear about whether one should > model baseline explicitly and the resulting difference in activation > maps. > > Suppose I have a box-car experiment with two conditions A and B. Under > each condition I have two factors 1 and 2. A1 is the (assumed) > baseline. I could specify an overspecified design matrix with D1=[A1 > A2 B1 B2 mean] or a design matrix with D2=[A2 B1 B2 mean] which models > baseline implicitly. > > My understanding is that with design matrix D1, the contrast [-1 1 0 0 > 0] is equivalent to the contrast [1 0 0 0] for design matrix D2. I did > both for the same data set. The resulting activation maps were > different. It seems to me that the design which explicitly models the > baseline tends to produce more conservative activation maps. Is my > observation right? If so, why? Assuming you used a simple box-car convolved with the HRF the statistical models should be similar. Your contrasts are correct and you should get similar results, The only difference between the models implied by D1 and D2 relates to boundary effects after convolution with the HRF. Including the baseline explicitly models the difference between starting the baseline condition from a pre-scanning state. In other words if the sum of the 4 condition specific regressors was a conatant then the two models would be identical. If however you start with a basline condition there will be an initial transient that renders the two models slightly different. Cut and past this into the MatLab command window to see the differences incurred following convolution with the HRF X = toeplitz([1 0 0 0 1 0 0 0 1 0 0 0]); X = kron(X(:,1:4),ones(6,1)); HRF = spm_hrf(2); [n m] = size(X); for i = 1:4 x = conv(X(:,i),HRF); X(:,i) = x(1:n); end plot(sum(X,2)) In the absense of the HRF, or if you had started with another condition, this sum would be a constant over the time-series and it would not matter whether you modeled it or not. The same explanation applies to the interaction (for which your contrasts were correctly specified). > I would also be very grateful if someone could explain what SPM does > when the design matrix is overspecified like D1 above, i.e., if the > rank of D1 is 4, deos SPM still try to estimate the 5 parameters for > each voxel? This is not a problem. The least squares estimators use [effectively] a pseudoinverse that allows for redundancy or collinearity (i.e. rank deficient design matrices). I hope this helps - Karl %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ```