Print

Print
Hi Anderson,

Just a couple of (hopefully) final queries:

"Another point to consider is that polynomial fits as these are better with continuous data. Given that the 5 levels are, for practical means as it seems, categorical, and it appears you don't know which is larger than which, perhaps a better solution is to drop the idea of U- and N-shapes altogether, and use instead the model that tests for any difference among the 5 levels using a conventional F-test.”

In my case, the 5 levels increase systematically and I expect BOLD response to vary in different brain regions in relation to this increase. I am particularly interested in finding where response peaks in the middle of the continuum (i.e., Level 3). Following an F-test comparing the means of all 5 levels, what post-hoc tests/contrast would be appropriate to identify this?

Also, I have run an analysis modelling  individual differences in the contrasts as you suggested ([IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj24 0 ... 0]’). I get get very high Z-MAX values (up to 14). Is this worrying/normal?

"Just in case, remember to pay attention to the exchangeability blocks when running this in randomise. Some contrasts require whole-block exchangeability, others within-block (the last under some assumptions about compound symmetry).”

I was not sure if I needed to use <randomise> or if the cluster corrected images (z threshold: 2.3) were acceptable?  

If randomise is needed:
Would changing the <group> column in the GLM to the following do the trick? 1 2 3 … 24 1 2 3 …24 1 2 3 … 24 1 2 3 … 24 1 2 3 … 24
For 5 levels and 24 participants what would be an acceptable total number of permutations?
What would the input image be? 
Does this call look alright for my model? $ randomise -i 4D_input_data -o TwoSampT -d design.mat -t design.con -f design.fts -m mask -e design.grp -T

Many thanks,
Christophe


##############################

Hi Chris,

Please, see below:


On 20 February 2015 at 12:45, Christophe de Bezenac <[log in to unmask]> wrote:
Hi Anderson

Modelling linear and quadratic effects directly in EVs rather than in contrasts does seem like a better approach. Using this model could I not now also model individual differences (ID) (demeaned) related to the linear and quadratic trends in the contrasts as follows?

C1 Positive linear:  [0 0 0 ... 0 0 0 1 0]        
C2 Negative linear:  [0 0 0 ... 0 0 0 -1 0]  

These two contrasts are fine.
 
C3 U-shape quadratic:  [0 0 0 ... 0 0 0 0 1]  
C4 inverted-U-shape quadratic ID:  [0 0 0 ... 0 0 0 0 -1]  

No, these two contrasts aren't good. To test for a quadratic effect, define an F-test that includes both the linear EV and the squared EV. This F-test will test both directions (in fact, all possible combinations of positive and negative signs for the linear and quadratic), so there's no need to explicitly try to test one way or another.

Also, a quadratic fit means adjusting a parabola. It can have an U-shape or inverted-U if it happens to be that the area around the vertex fits well the data. The effect is still quadratic, but away from the vertex, and it won't look like an U anymore, just a curve.

Same applies to cubic effects. It may not have an N-shape for the same reason.

Another point to consider is that polynomial fits as these are better with continuous data. Given that the 5 levels are, for practical means as it seems, categorical, and it appears you don't know which is larger than which, perhaps a better solution is to drop the idea of U- and N-shapes altogether, and use instead the model that tests for any difference among the 5 levels using a conventional F-test.

 
C5 Positive linear ID: [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj 1 0]        
C6 Negative linear ID:  [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj -1 0] 

These contrasts aren't good I'm afraid, because their corresponding effect is a sum of the ID measurement with the levels (i.e., apples & oranges situation). Use instead something as:

C5: [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj24 0 ... 0]'
C6: [-IQsubj1 -IQsubj2 -IQsubj3 ... -IQsubj22 -IQsubj23 -IQsubj24 0 ... 0]'
 

C7 U-shape quadratic ID:  [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj 0 1]
C8 inverted-U-shape quadratic ID:  [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj 0 -1]

I'm not sure what you'd like to test here.
 

Also, am I right in thinking that an f-test between C1 and C3 would tell me where positive/negative linear/quadratic response occurred and that, provided it shows significance, I should be looking at contrasts to identify specific response functions/directions?   

I think that given these open hypotheses, the best thing to do is drop the idea of a polynomial fit. Use instead a conventional F-test, that will compare the means of all 5 levels; if that is significant, then you can go for the post-hoc tests to locate which levels differ and how.

 

With this approach could I still include measures that are scan-specific (not subject-specific) in EV columns modifying the contrasts, as you mentioned in the previous email?
 
C9 [0 0 0 ... 0 0 0    0 0 1]
C10 [0 0 0 ... 0 0 0    0 0 -1]

(a 0 would be added to each contrast above)

For either design, scan specific-measurements can be added as extra EVs and tested as usual, so it seems these two contrasts are fine.

Just in case, remember to pay attention to the exchangeability blocks when running this in randomise. Some contrasts require whole-block exchangeability, others within-block (the last under some assumptions about compound symmetry).

All the best,

Anderson


 

Thanks again for your input.

Chris

########################


PS: Btw, you mention n-shaped, which I think you mean a cubic relationship. It's possible to add yet another EV (the EV27), that would be the same EV25, but cubed (so, -8 -1 0 1 8). Then add one more contrast as [0 0 0 ... 0 0 0 0 0 1] and include it in the F-test.



On 19 February 2015 at 07:25, Anderson M. Winkler <[log in to unmask]> wrote:
Hi Chris,

Please, see below:

On 18 February 2015 at 15:45, Christophe de Bezenac <[log in to unmask]> wrote:
Hi Anderson,

Thanks for your reply. I was thinking of including subject-specific variables of interest (as opposed to nuisance variables). For instance, I wanted to include individuals’  performance on a behavioural task (demeaned) to examine how activation within contrasts of interest (linear/quadratic) is modulated by performance. Would this be possible/make sense in this context?

To test a subject-specific variable, then using the same design you have, the subject-specific measure can be coded in the contrast. For instance: you have the 24 subjects of your design, with EV1-EV24 for the subject-specific effects, and would like to test, say, whether IQ is associated with the imaging data. The contrast is then:

[IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj24 0 0 0 0]

Note that in this model it's not possible to test interactions, as the variable being tested (IQ in this example) is the same across all levels.

If, however, you'd like a measurement that isn't subject-specific, but that is specific for each scan (i.e., level within condition, such as if the performance at a certain fMRI task relates to the BOLD response), then it's much simpler: just add one extra column for the variable of interest, and modify the contrast so that it's tested. In this case, interactions are possible, as there are multiple measurements per subject.

 

Regarding the reference level, am I right in thinking that the results would be with L1 as reference instead of L5? 

The results won't really change, particularly for the F-tests. I only mentioned because in the design you labelled the contrast as with reference to L1. Which is the one used as reference doesn't really matter that much, so no worries.

 

To make sure that I understand the logic, do the contrasts below look right?

positive linear: [0 0 0 … 0 0 0 -48 -24 0 24]
negative linear: [0 0 0 … 0 0 0 48 24 0 -24]
n-shape quadratic [0 0 0 … 0 0 0 -48 24 48 24]
u-shape quadratic [0 0 0 … 0 0 0 48 -24 -48 -24]

The linear are fine, but the quadratic is not. The problem is that the GLM is "linear" in that the effects are treated as linear combinations of the regressors and regression coefficients. Coding a test as this with the contrast is fine as long as the hypothesised effect remains linear. To get around this, you'd have to change the design a bit:

- EV1-EV24: subject-specific EVs, just as you already have
- EV25: use a sequence of values in an arithmetic progression to represent the 5 levels (e.g., -2 -1 0 1 2)
- EV26: square the values from the previous EV for quadratic effects (in this example, 4 1 0 1 4)

For the contrasts, use:
C1: [0 0 0 ... 0 0 0 1 0] F1
C2: [0 0 0 ... 0 0 0 0 1] F1
(that is, define an F-test that includes C1 and C2).

In fact, the same design can be used for the linear effects too (just the C1 above), and it may be more powerful than the other that codes it with the contrast and has fewer degrees of freedom.

Hope this helps.

All the best,

Anderson

<design.png>


 


On 20 Feb 2015, at 12:45, Christophe de Bezenac <[log in to unmask]> wrote:

Hi Anderson

Modelling linear and quadratic effects directly in EVs rather than in contrasts does seem like a better approach. Using this model could I not now also model individual differences (ID) (demeaned) related to the linear and quadratic trends in the contrasts as follows?

C1 Positive linear:  [0 0 0 ... 0 0 0 1 0]        
C2 Negative linear:  [0 0 0 ... 0 0 0 -1 0]  
C3 U-shape quadratic:  [0 0 0 ... 0 0 0 0 1]  
C4 inverted-U-shape quadratic ID:  [0 0 0 ... 0 0 0 0 -1]  
C5 Positive linear ID: [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj 1 0]        
C6 Negative linear ID:  [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj -1 0] 
C7 U-shape quadratic ID:  [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj 0 1]
C8 inverted-U-shape quadratic ID:  [IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj 0 -1]

Also, am I right in thinking that an f-test between C1 and C3 would tell me where positive/negative linear/quadratic response occurred and that, provided it shows significance, I should be looking at contrasts to identify specific response functions/directions?   

With this approach could I still include measures that are scan-specific (not subject-specific) in EV columns modifying the contrasts, as you mentioned in the previous email?
 
C9 [0 0 0 ... 0 0 0    0 0 1]
C10 [0 0 0 ... 0 0 0    0 0 -1]

(a 0 would be added to each contrast above)

Thanks again for your input.

Chris

########################


PS: Btw, you mention n-shaped, which I think you mean a cubic relationship. It's possible to add yet another EV (the EV27), that would be the same EV25, but cubed (so, -8 -1 0 1 8). Then add one more contrast as [0 0 0 ... 0 0 0 0 0 1] and include it in the F-test.



On 19 February 2015 at 07:25, Anderson M. Winkler <[log in to unmask]> wrote:
Hi Chris,

Please, see below:

On 18 February 2015 at 15:45, Christophe de Bezenac <[log in to unmask]> wrote:
Hi Anderson,

Thanks for your reply. I was thinking of including subject-specific variables of interest (as opposed to nuisance variables). For instance, I wanted to include individuals’  performance on a behavioural task (demeaned) to examine how activation within contrasts of interest (linear/quadratic) is modulated by performance. Would this be possible/make sense in this context?

To test a subject-specific variable, then using the same design you have, the subject-specific measure can be coded in the contrast. For instance: you have the 24 subjects of your design, with EV1-EV24 for the subject-specific effects, and would like to test, say, whether IQ is associated with the imaging data. The contrast is then:

[IQsubj1 IQsubj2 IQsubj3 ... IQsubj22 IQsubj23 IQsubj24 0 0 0 0]

Note that in this model it's not possible to test interactions, as the variable being tested (IQ in this example) is the same across all levels.

If, however, you'd like a measurement that isn't subject-specific, but that is specific for each scan (i.e., level within condition, such as if the performance at a certain fMRI task relates to the BOLD response), then it's much simpler: just add one extra column for the variable of interest, and modify the contrast so that it's tested. In this case, interactions are possible, as there are multiple measurements per subject.

 

Regarding the reference level, am I right in thinking that the results would be with L1 as reference instead of L5? 

The results won't really change, particularly for the F-tests. I only mentioned because in the design you labelled the contrast as with reference to L1. Which is the one used as reference doesn't really matter that much, so no worries.

 

To make sure that I understand the logic, do the contrasts below look right?

positive linear: [0 0 0 … 0 0 0 -48 -24 0 24]
negative linear: [0 0 0 … 0 0 0 48 24 0 -24]
n-shape quadratic [0 0 0 … 0 0 0 -48 24 48 24]
u-shape quadratic [0 0 0 … 0 0 0 48 -24 -48 -24]

The linear are fine, but the quadratic is not. The problem is that the GLM is "linear" in that the effects are treated as linear combinations of the regressors and regression coefficients. Coding a test as this with the contrast is fine as long as the hypothesised effect remains linear. To get around this, you'd have to change the design a bit:

- EV1-EV24: subject-specific EVs, just as you already have
- EV25: use a sequence of values in an arithmetic progression to represent the 5 levels (e.g., -2 -1 0 1 2)
- EV26: square the values from the previous EV for quadratic effects (in this example, 4 1 0 1 4)

For the contrasts, use:
C1: [0 0 0 ... 0 0 0 1 0] F1
C2: [0 0 0 ... 0 0 0 0 1] F1
(that is, define an F-test that includes C1 and C2).

In fact, the same design can be used for the linear effects too (just the C1 above), and it may be more powerful than the other that codes it with the contrast and has fewer degrees of freedom.

Hope this helps.

All the best,

Anderson

<design.png>