Dear Gina,
You should set unequal variance for the 'grp' factor but not for the
'subject' one. This will model variability between subjects within
groups. You would also only model 'main effect' of factor 1 (and not [1
2 3]). This should simplify your model and its estimation.
That said, it is still not the model I would recommend: are you aiming
at testing for the group by treatment interaction?
Best regards,
Guillaume.
On 02/06/2021 15:59, Gina Joue wrote:
> Hi SPM experts,
>
> I am dabbling in the world of flexible factorial to test group
> differences in a longitudinal study following treatment only in the
> patient group (PT) and not in the healthy control group (HC) and have
> questions about variance setup.
>
>
> Flexible factorial setup
>
> Factor 1: subject (total n = 43)
> dept = 0 (no dependency between levels/independent)
> Factor 2: grp (2 levels: n_HC = 23, n_PT = 20)
> dept = 0
> variance = 1
> Factor 3: timept (within-subject factor; 2 levels)
> dept = 1 (dependent)
> Main effects: 1, 2, 3
> Interactions: [2;3]
>
> The factor "timept" corresponds to a difference between two testing
> conditions at two time points (contrasted in 1st-level models, i.e. 2
> con imgs/person -- and as I am not interested in any single
> between-subject condition against 0, such as a main group effect, I
> sidestep issues with SPM's pooled error variances -- is this correct?)
>
> Theoretically, as my subjects are drawn from two different populations
> AND that there is considerable interindividual variation on the task, I
> want to say that I want to allow for variances to differ by subject and
> by time -- I know this is not what is laid out in Gläscher & Gitelman's
> 2008 "Contrast weights in flexible factorial design with multiple groups
> of subjects". Or can I assume that the model is defined hierarchically
> and that the unequal variances in subjects is subsumed by the grp factor
> so the variance of the subject should be configured as "equal" which
> means equal within each group?
>
> Either way, specifying variance to be unequal for both "subjects" and
> "timept" seems to indicate model definition problems. I do not get any
> errors -- SPM completes model estimations, but I see that the model is
> ill-defined when I look at the whitened design matrix after
> non-sphericity estimation and see the highly correlated subject
> regressors (right-most panel in the attached image). The leftmost panel
> is the design matrix SPM.xX.X as I have set it up flexible factorial
> before any sort of correction, and the second from the left is when
> variance is configured to be equal for both "subject" and my
> within-subject factor "timept", as suggested by Gläscher & Gitelman
> (assuming subjects were sampled from the same group...).
>
> I guess the estimation problem is also because of the redundancy when I
> allow variance to be unequal for both subject and timept as there are
> only 2 timept levels? But naively judging the whitened design matrix, I
> want to say that I just don't have enough data or have too much variance
> in my data to take into account unequal variances for either subject or
> timept (counting from the left -- 3rd panel in img: non-equal variance
> only for timept, 4th panel: unequal variance only for subject) but then
> is that also an indication that my variances are far from being
> non-spherical?). Is the 3rd panel/model (indep var for timept only) a
> passable model? Can one conjecture that the data variances have been
> subsumed by the variances in the first 5 subjects? I guess part of my
> question is related to model troubleshooting and diagnostics.
>
> I'd very much appreciate if someone could set me right if any of this is
> incorrect and/or for any demystification/clarification/full enlightenment.
>
> Many thanks in advance!
> Gina
>
--
Guillaume Flandin, PhD
Wellcome Centre for Human Neuroimaging
UCL Queen Square Institute of Neurology
London WC1N 3BG
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