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Hello Tom, Thank you so much for your input. 1) Wouldn't one expect the covariance estimates to be more reliable? > > > The covariance estimates are based on the residuals, and if the models are > different you'll have different residuals. > Ah... I thought - silly me - that the covariance was estimated from the data. So I was thinking that different covariance estimates were a consequence of poor estimation, since I got two very similar W's and one with a different offset (see image in my original e-mail). 3) Is it OK to use the two out of three criterion to select a more correct > > whitening matrix? > > > I'm not sure what criterion you're referring to. To use R^2 or Extra Sums > of Squares for model comparisons the models must be nested. As you've > discovered, the different estimated W's means that the models are not > nested. Tools for non-nested model comparisons include AIC and BIC. It's a very unscientific criterion, actually. I was thinking the W matrix should be the same for all models, so getting two very similar W's on three models, I was guessing that the "true" W would be the one that came up twice! I now understand I was completely wrong... However, I don't quite understand why aren't the models nested. The "whole" design matrix includes movement parameters as covariates. I read somewhere on the list that the order of the regressors in the design matrix wasn't interchangeable, although it is not obvious to my why. If I hadn't included the movement parameters in the model, would the models be nested then? Perhaps a simpler way forward is to, just for the purposes of model > selection, is to turn off autocorrelation modeling, pick the best model, > then run it again with autocorrelation modeling. Indeed. Actually, I'm using SPMd to assess model validity and R^2 to assess model fit. When the model validity is not degraded by adding a regressor (time derivative, for instance) I go on and compare fits. Just thought you would like to know how SPMd is revealing itself useful! Thanks again. Rute