Hi,
Scaling of regressors (multiplying by some constant) in the GLM is unimportant for the statistical values such as t-stats or z-stats (they are unaffected by this scaling) but the actual parameter estimates (PEs or COPEs) would change.
If you have a set of regressors that model the mean (either a single regressor or several that add together to give a column of all ones) then it is not necessary to demean any _other_ regressors in the model (over and above the ones used to model the mean). However, this is true only for statistics associated with contrasts that do not include any of the regressors that model the mean (the entries for these regressors are zeros in the contrast vector).
If you do not have regressors that model the mean in the design matrix then it is important to demean all regressors and the data (as otherwise the mean affects the parameter estimates, the contrasts and the statistics).
I hope this makes things clear.
All the best,
Mark
On 28 Aug 2012, at 12:42, Ib <[log in to unmask]> wrote:
> Yes, that's clearer.
> The betas are originated in the regression analysis, and it's different from the rho coefficient if the regressors are not standardized.
>
> My last question. So then, for GLM, regressors must be standardized or demeaned (not the same thing)?
>
> Ib
>
>
> --------------------------
> Hi,
>
> The GLM only does regression.
> We talk loosely about "correlations" but that is inaccurate.
> Jeanette Mumford has written about this many times on the list before.
> Here is a quote from one of her emails:
> "The other contrast ... focuses on the slope of the regression fit, or some people like to call it a correlation. I try to not do this because technically the parameter estimate is not a correlation."
>
> So the mathematics of calculating correlations (as implemented in matlab and elsewhere) does actually take into account the mean and gets rid of it. However, this is not what the GLM is doing. The GLM is given you a slope, but one that results in the same statistical results for significance testing as if you did that on the correlation (and this is why people loosely refer to them as the same). However, the values produced by the GLM are not correlations, and the method of calculation is very different, and so you do need to make sure you deal with the means by either removing them or modelling them, as I said before. If you do not add the column of ones (or something equivalent) in the regression then it is a problem (the intercept is no longer separate from the slope).
>
> I hope this makes things clearer.
> All the best,
> Mark
>
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