Hi Anouk,

In the GLM that we usually write as a single equation in matrix form as Y=X*b+e, we actually have, for N subjects, a set of N equations, each of them with as many unknowns as there are EVs. Without changing the model, we are allowed to compute additions and subtractions between these equations, as long as everything that we do is done on both sides of each of these N equations.

For the within-subject effects, we are interested in differences between pairs of equations (that are timepoints), whereas for the between-subject effects we are interested in averages of pairs of equations.

When we compute differences between equations, coefficients that are repeated (e.g., some score that doesn't change between visits) cancel out. If we still think the value of such score (e.g., its average between visits, which is the same as the score itself) is a potential nuisance for the difference between visits, we need to put the signs alternating, so that when the differences between equations are computed, instead of these coefficients being canceled out, their values remain (although multiplied by two, which doesn't affect the result).

Conversely, when we add equations together for the between-subject effects, coefficients that are repeated are also summed. If we actually want the difference as nuisance we'd add the signs alternating, This is rarely the case, though.

So, in short:

- For within-subject effects: keep the signs if it is the difference between the two values of the nuisance that needs to be considered in the design, or put the signs alternating if it is the average is what needs to be considered.

- For between-subject effects: do the opposite, although rarely we want the difference to be a nuisance, so in practice, the signs most often stay the same.

Of course, with the GLM in matrix form we don't do any of these additions or subtractions of equations, and instead everything is done at once with single matrix operations, which is a much faster shortcut.

Hope this helps.

All the best,

Anderson

On 17 December 2015 at 13:12, A.G.M. Schrantee <[log in to unmask]> wrote:

Dear Anderson,

Mant thanks for your reply, very helpful! Just one small question, what is exactly the reason that you use alternating signs for movement/nuisance regressors? Because both symptom severity and movement are covariates I would say; why would you then use alternate signs for one of both, but not the other?

Best wishes,
Anouk

 

Van: FSL - FMRIB's Software Library [mailto:[log in to unmask]] Namens Anderson M. Winkler
Verzonden: Thursday, December 10, 2015 9:04 AM
Aan: [log in to unmask]
Onderwerp: Re: [FSL] design matrix association 2 change scores Randomise

 

PS: The design1 uses within-block exchangeability (option -e in randomise, or -eb in PALM). The design2 uses whole-block exchangeability (options -e with --permuteBlocks in randomise, or -eb with -whole in PALM).

 

On 10 December 2015 at 08:02, Anderson M. Winkler <[log in to unmask]> wrote:

Hi Anouk,

 

Please see below:

 

 

On 9 December 2015 at 15:27, A.G.M. Schrantee <[log in to unmask]> wrote:

Dear FSL experts,

 

I had a question about  the design matrix for one of my analysis of ASL data in Randomise and I could not find this question in the previous posts.
We have cerebral blood flow (CBF) maps from two groups (between subjects factor) before and after acute medication (within-subjects factor).

 

So 2 groups and 2 timepoints, which means both things need to be represented in the design.

 

 

There was quite a lot of movement,  so we calculated a movement summary score (and of course corrected for motion on an individual level) and found that is explained quite some variance in the data. Obviously, this nuisance parameter is present at both timepoints and we would like to include this into our model as a nuisance regressor.

 

Additionally, we would like to see how the change from pre- to post- acute medication is associated with a change in symptom severity (measured at pre-medication and some weeks later) and whether this differs between the 2 groups.

Could I actually assign the PRE-symptom severity to the PRE-CBF scan and the POST-symptom severity to the POST-CBF scan even though the last two are not measured at the same time?

 

Yes. This has to do more with the interpretation, less with the statistic: it is assumed that the severity, measured much later (after hours or days) is still related to the blood flow measured in the post scan.

 

 

I created a mock design matrix below. What would the contrast be to assess the association between change in scan and change in symptom severity?

 

I don't see both groups and timepoints represented in this design. Please, see an alternative one here: https://dl.dropboxusercontent.com/u/2785709/outbox/mailinglist/design_anouk.ods

 

There are two designs inside. The design1 is for the effect of medication (timepoint) and interaction with group. It is also to assess whether changes in severity are associated with changes in CBF. Movement is entered as a nuisance (note the alternating signs). The design2 is for the effect of group, while taking symptoms and movement as nuisance (note the signs don't alternate for movement here).

 

Hope this helps.

 

All the best,

 

Anderson

 

 

 

 

Many thanks in advance!

Kind regards,

Anouk Schrantee

 

 

desgin:  

subject	designmatrix		WS_group	Symptoms	nuisance	SS_EV1	SS_EV2	SS_EV3	SS_EV4
1			1	20	0.24	1	0	0	0
1			-1	32	0.56	1	0	0	0
2			1	22	0.36	0	1	0	0
2			-1	27	0.45	0	1	0	0
3			1	27	0.32	0	0	1	0
3			-1	29	0.31	0	0	1	0
4			1	30	0.65	0	0	0	1
4			-1	28	0.87	0	0	0	1

 

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