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Hi Tom, Thanks for the quick reply. In reality, the time intervals would be days, i.e. there are differences between subjects, that's why I would like to regress out the effects, I also include the age and gender as covariates. Ping On Fri, Apr 17, 2009 at 9:28 AM, Thomas Nichols <[log in to unmask]> wrote: > Dear Ping-Hong, >> >> I have questions similar to this thread, if there are 3 subjects, >> all scanned at 3 timepoints, say baseline, 3months and 5months; and to >> test "3months vs baseline", "5months vs baseline" effects. Would the >> design matrix set up be like >> >> A0 A1 A ---B--- >> 0 0 0 1 0 0 >> 0 0 0 0 1 0 >> 0 0 0 0 0 1 >> 1 0 3 1 0 0 >> 1 0 3 0 1 0 >> 1 0 3 0 0 1 >> 0 1 5 1 0 0 >> 0 1 5 0 1 0 >> 0 1 5 0 0 1 >> >> A0 is "3months vs baseline", A1 for "5months vs baseline", and A1-A0 >> for "5months vs 3months" contrasts. > > Yes and no. Yes, this is the spirit of my previous answer, but, no, it > doesn't make sense in your setting. In the previous question each > individual was scanned at a slightly different time, there was interest in > finding variation related to these small timing differences. In your > example, everyone is scanned at exactly the same time, and thus predictor A > is totally redundant (i.e. explains a subset of the variation that A0 and A1 > explain). > >> >> If there are another 2-level factor , say "disease and control" and 3 >> subjects in each group, then >> >> A0 A1 A01 A11 A ---B--- >> 0 0 0 0 0 1 0 0 0 0 0 >> 0 0 0 0 0 0 1 0 >> 0 0 0 0 0 0 0 1 >> 0 0 0 0 0 0 0 0 >> 0 0 0 0 0 0 0 0 >> 0 0 0 0 0 0 0 1 >> >> >> 1 0 3 1 0 0 >> 1 0 3 0 1 0 >> 1 0 3 0 0 1 >> 0 1 5 1 0 0 >> 0 1 5 0 1 0 >> 0 1 5 0 0 1 > > > I think there's a formatting error in what you're trying to show, but I > think the answer is no, you can't do this. The general set up with the > block variables for subjects is only useful for within subject designs. > I.e. the blocking variables soak up intersubject variability, but in a two > group design you're specifically interested in the differences between > groups of subjects. > If you have some *covariate* driven by within subject effects, then, yes, > you could split that by group and look for group differences in this > setting. > Hope this helps. > -Tom > >> >> >> >> >> >> >> >> >> >> On Mon, Nov 3, 2008 at 10:21 AM, Thomas Nichols <[log in to unmask]> >> wrote: >> > Hi, >> > >> > I think the answer is simpler than Steve implies. >> > >> > Ideally, this would be an easy model to fit. Say you have just 3 >> > subjects, >> > imaged 2, 5 and 3 months apart, the design matrix you'd like to fit >> > would >> > be... >> > >> > A ---B--- >> > 0 1 0 0 >> > 0 0 1 0 >> > 0 0 0 1 >> > 2 1 0 0 >> > 5 0 1 0 >> > 3 0 0 1 >> > >> > which consists of the linear effect of time relative to the 1st scan >> > (A), >> > and the 3 subject-pairing/blocking variables (which also model the grand >> > mean) (B). This is presumably not satisfying, since it measures the >> > linear >> > time effect as a whole (i.e. significance of A will be determined by >> > both an >> > over-all time effect and the individual differences in the time effect). >> > >> > BTW, due to the orthogonalizing magic of the GLM, the model above will >> > have >> > the same fit if you had replaced column A with >> > [ -1 -2.5 -1.5 1 2.5 1.5 ]. >> > >> > If you would like to dissociate the average Time1-vs-Time2 effect from >> > the >> > additional variation explained by exact scanning times, then you'd use >> > the >> > model >> > >> > A0 A ---B--- >> > 0 0 1 0 0 >> > 0 0 0 1 0 >> > 0 0 0 0 1 >> > 1 2 1 0 0 >> > 1 5 0 1 0 >> > 1 3 0 0 1 >> > >> > Where A0 is the Time1-vs-Time2 effect, and A is the exact scanning time >> > variable. I frankly can't see how A0 would ever be significant, but, >> > crucially, A will be significant whenever there is appreciable >> > inter-individual variation in FA explained by the precise scanning >> > intervals >> > *discounting* any variation explained by the average Time1-vs-Time2 >> > effect. >> > >> > Again, due to GLM magic, A0 and A can be specified as A0 = [-1 -1 -1 1 >> > 1 >> > 1 ] and A as above, though I find the way I have set it up to be >> > clearer. >> > >> > Hope this helps! >> > >> > -Tom >> > >> > __________________________________________________ >> > Thomas Nichols, PhD >> > Director, Modelling & Genetics >> > GlaxoSmithKline Clinical Imaging Centre >> > >> > Senior Research Fellow >> > Oxford University FMRIB Centre >> > >> > > > > -- > ____________________________________________ > Thomas Nichols, PhD > Director, Modelling & Genetics > GlaxoSmithKline Clinical Imaging Centre > > Senior Research Fellow > Oxford University FMRIB Centre >