Hi Helmut,
> Is this commonly applied or are there instances in one would want to turn to a
> lower order (and/or turn to other polynomials)?
It's a legitimate and interesting question. The suggestion of "1 + floor(dur/150 s)" for the order of polynomials or the default cut-off value 1/128 Hz for the Discrete Cosine Transform is purely empirical (and convenient for the general user). It probably works fine for most cases; but for other cases (e.g., model tuning/building), it may make sense to find a more appropriate fitting. To do so in AFNI, you can add option -bout (plus -tout and -fout) in 3dDeconvolve or -Rbuck in 3dREMLfit to output the baseline coefficients (including the polynomial coefficients) and their statistics, which should be able to assist the investigator in determining the order of the fitting polynomials. For example, if the highest-order polynomial coefficient is very small and not statistically significant (with liberal thresholding of, e.g., 0.1) in the whole brain, you may lower the original order in model specification. On the other hand, if the highest-order polynomial coefficient is large or statistically significant (with liberal thresholding of, e.g., 0.1) in the whole brain, a higher order polynomial fitting is warranted.
> Are there any additional calculations on the polynomial regressors before they
> enter the design matrix and/or at a latter step performed automatically in AFNI
> but possibly not in SPM (e.g. orthogonalization of the regressors, well, Legendre
> polynomials should be orthogonal anyway)?
No further manipulations are performed on the Legendre polynomials in AFNI.
Gang
Edited 3 time(s). Last edit at 06/18/2015 11:17AM by Gang.
