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Interpretation of Behavioural PLS involving 2 groups
Eric
Posted on 01/07/21 08:50:39
Number of posts: 9
Eric posts:

Dear PLS team and users,

I have a question regarding interpreting the behavioural PLS results involving mulitple groups

I am interested in the association between a social measure and fMRI functional connectivity, and whether the association differs between male and female. I ran a behavioural PLS using the command line, feeding 2 datamats (Vectorized FC) and a concatenated social score vector into behavioural PLS. Results showed that the strength of the correlation may be different between sexes/ genders at some FC edges, being stronger in males. (the first LV was significant; CI of the correlation did not include zero for male but contained zero in female; the CIs did not overlap).

Then I did 2 separate Behavioural PLS, one for each gender. This time there was no significant association for male (but the FC salience has similar topography as the 2-group PLS), but a significant assoication in female (different topography than the 2-group PLS). I wonder if I have done something wrong? Regardless of the topograhpy, I was expecting the male group would at least indicate a significant LV as well.

If my procedure is sounded. I wonder how I should interpret the discrepancy. Right now I am a bit reluctant to say 'There is a strong negative correlation in males, but much weaker association in females' based on the 2-group PLS, despite the CIs looking 'nice'. What I am contemplating is that since (at least in task PLS) PLS often characterises differences between conditions, can I understand my results as we understand a regression model with gender as a moderator, i.e., the male's slope on FC-social score is reliably different from the female's, even though the male's slope does not necessarily different from zero when estimated separately?

I hope my questions make sense. Looking forward to any comment and suggestion.

Regards,

Eric

Replies:

Untitled Post
rmcintosh
Posted on 01/07/21 13:54:59
Number of posts: 385
rmcintosh replies:

Hi Eric - the outcome you have in not atypical in the sense of breaking down a higher-order analysis and getting a non-signifcant results on a subset of data. A few questions 

 

1) is you behaviour matrix a single vector? 

2) what's your sample size?

One thing that could be informative is the see the relation between the group results and the single group outcomes in terms of how the within group relations get split up.  This you can do by getting the dot product of the singular vector 'u' in the results arrray.

e.g., assume group results are called 'group' and 'male' and 'female' for the within group analysis

group.u'*male.u %the values are the cosine between the outcome for group vs male, 

what you want see is if one group is driving the full analysis or if it's pretty well split.

 



Untitled Post
Eric
Posted on 01/11/21 00:59:01
Number of posts: 9
Eric replies:

Hello Randy,

Thanks for your help.

1) Yes my behavioural measure is a single vector

2) I have 67 males and 74 females

3) How can I evaluate the contribution by each gender from the dot product?

Regards,

Eric



Untitled Post
rmcintosh
Posted on 01/11/21 16:05:53
Number of posts: 385
rmcintosh replies:

quote:

Hello Randy,

Thanks for your help.

1) Yes my behavioural measure is a single vector

2) I have 67 males and 74 females

3) How can I evaluate the contribution by each gender from the dot product?

Regards,

Eric

Hi Eric the sample size is decent but I assume there are a lot of edges in your FC matrix, which adds some instability.  There's not much you can do with the within-subject analysis for permutation. How do the confidence intervals look?

 

For the contribution, lets say I run an analysis similar to yours but with 4 FC values.  My U matrix (result.u) for a two group analysis is:

   -0.4271   -0.6439
    0.3848    0.0216
    0.7530   -0.0518
    0.3202   -0.7631
 
and result.v
 
    0.9988   -0.0489
   -0.0489   -0.9988
 
though this is an idealized example the U matrix for group 1 (result1.u)
   -0.4185
    0.3845
    0.7536
    0.3303
 
and group 2: 
 
    0.7096
   -0.0897
   -0.0829
    0.6940
 
if I do the cosine for group 1 (result.u'*result1.u)
    0.9999
   -0.0133
which tells me that almost all of the first column of result.u is driven by group 1
 
and then for group2 (result.u'*result2.u)
   -0.1778
   -0.9841
 
which tells me that almost all of the second column of result.u is driven by group 2.  Incidently if you square and sum these cosines they will be 1.0 :)
 

 




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