Hi Juergen,

My reply is very long, and possibly a bit dodgy in parts, but I hope 
it is nevertheless of some help to you. I'd recommend playing around 
with spm_ancova and some toy problems to investigate the effects, e.g.

  N = 10; y = randn(N, 1); W = eye(N);
  X = [your design matrix here!];
  c = [your contrast row vector]';
  [t df beta] = spm_ancova(X, W, y, c); beta, t

Remember to check unbalanced cases (e.g. more subjects in one group 
than another)

I think nominal covariates coded with dummy variables (in separate 
columns if more than two levels) are absolutely fine. E.g. including a 
covariate for gender which is 0/1=male/female coded simply gives a 
beta that is the average extra response for females, and the intercept 
term is then the average value of the response for males (I'm probably 
ignoring some complications here with correlated regressors 
though...). A t-contrast with a 1 on this covariate tests the 
null-hypothesis that male and female response is equal, against the 
alternative that female is greater.

Contrasts over other regressors (the most common thing to look at) 
will be modified to adjust for the sex differences. The gender 
covariate will explain some of the overall variance, so the standard 
error (noise) of the contrast of interest will be lower, but if gender 
is correlated with the effect of interest (e.g. if you had more men in 
group A and more women in group B and you were testing the group 
difference, adjusted for gender) then the contrast itself (the signal) 
will also be reduced.

Beta and the other terms would change if you coded male/female=27/42 
instead of binary, but the t-test on gender would remain the same, as 
would other t-contrasts except for a test of the grand mean (or e.g. 
the sum of both groups), because this is perfectly correlated with the 
change in the mean of the re-coded covariate.

If you have three or more levels, then you need multiple columns to 
code these, in order for the model to make sense. For example, if you 
wanted to adjust for first-language (to pick something random) it 
would not be correct to have a covariate that had something like 
Italian/French/German=0/1/2 since this wouldn't make sense. The beta 
would be a kind of slope, suggesting in some way that French response 
is expected to be between Italian and German. A t-contrast over this 
would not have null hypothesis that language made no difference, 
rather that the (meaningless) slope was not significant.

Instead, if you had three columns with ones for each language and 
zeros elsewhere, then an F-contrast of [-1 1 0; 0 -1 1] would have the 
null hypothesis that language made no difference.

Ordinal covariates in a single regressor sound slightly dodgy to me, 
but I think some people do this, e.g. with subjective scales of 
strength of some opinion/pain-response/whatever. I don't think the 
maths (and hence nor SPM) need to be altered specially for this, it's 
just a question of how much you can believe the results, I think. 
Treating such a variable as nominal and coding in separate columns 
sounds better to me, but I might be missing something...

Hope this makes sense, and helps, best regards,

Ged.


> we had a very intensive discussion about whether it is appropriate
> to use nominal or ordinal scaled covariates in SPM. In statistics,
> we had learnt that covariates have to be at least intervall scaled 
> in order to be used as a real covariate in a design because the regression
> model
> needs continnous values. But, there are many situations where the covariates
> used 
> are nominal scaled (e.g., gender, different scanners, other dichotome
> variables 
> like genetic mutations, SNPs (yes/no coded). 
> 
> Is there a special implementation in SPM that allows the use of nominal
> scaled
> variables as covariates?
> 
> If yes, how does the influence of a dichotome variable is computed out of
> the data
> (with a normal regression model)?
> 
> Outside of SPM, I had seen correlations where one variable is intervall
> scaled (e.g. brain volumes)
> and the other nominal scaled (e.g. gender). Are these correlations really
> appropriate? 
> 
> Thanks a lot in advance
> Best regards
> Juergen
> 
> ----------------------------------------------
> Juergen Haenggi, Ph.D. student
> Neuropsychology and Imaging
> Division of Psychiatry Research
> Psychiatric University Hospital
> University of Zurich, Switzerland
> P.O. Box 1931
> Lenggstrasse 31, 8032 Zurich
> 0041 44 384 26 10 (office phone)        
> 0041 76 445 86 84 (mobile phone)
> 0041 44 384 26 86 (fax)
> H 115 (office room number)                      
> [log in to unmask] (division email)
> http://www.dpr.unizh.ch/ (division website)   
> http://www.juergenhaenggi.ch (private website)    
> ----------------------------------------------
>  
>