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help > RE: Interaction between continuous variables
Jan 31, 2019 01:01 PM | Alfonso Nieto-Castanon - Boston University
RE: Interaction between continuous variables
Hi Davide,
Regarding (1), to study the interaction between two continuous variables Scale_A and Scale_B you need to explicitly add that interaction term to your second-level model. You can do that, for example, by creating a new second-level covariate (e.g. named Scale_AB) and defining it as the product of Scale_A and Scale_B (e.g. enter in the values field "Scale_A.*Scale_B" without the quotes). Then, in the second-level results tab select the effects:
All_subjects, Age_covariate, Scale_A, Scale_B, Scale_AB
and enter a between-subjects contrast:
[0, 0, 0, 0, 1]
That will explicitly test the presence of a Scale_A-by-Scale_B continuous interaction. To clarify, the second-level analysis that you were mentioning (e.g. selecting All_subjects, Age_covariate, Scale_A, Scale_B and entering a [0,0,1,-1] contrast) evaluates whether the effect of ScaleA on connectivity is greater/smaller than the effect of ScaleB, in other words whether the change in connectivity per unit-change in ScaleA is greater/smaller than the change in connectivity per unit-change in ScaleB. In contrast the interaction analyses that we are referring to here evaluate whether the effect of ScaleA on connectivity is modulated by ScaleB (or viceversa), in other words whether the change in connectivity per unit-change in ScaleA is itself proportional/related to ScaleB.
And regarding (2), yes, for any significant area here it is important to plot the effects within those clusters in order to be able to interpret the directionality of these effects correctly, and your suggestion to binarize one of the Scale variables and show the changes in association between connectivity and the other Scale variable across the two groups is a perfectly reasonable way to do that.
Just as a side note, if you believe it makes more sense to evaluate the interaction in term of these "High-ScaleA" vs. "Low-ScaleA" groups you may also test that form of categorical-by-continuous interaction explicitly, and that works exactly in the same way as above but now using a categorical version of your Scale_A variable instead. For example, you could create a new Group_A second-level covariate containing 1's for the "High-ScaleA" subjects and 0's for the "Low-ScaleA" subjects, and then a new Group_AB covariate defined as "Groups_A.*Scale_B", and then define your second-level analysis by selecting All_subjects, Age_covariate, Group_A, Scale_B, Group_AB, and entering the same [0,0,0,0,1] contrast.
Hope this helps
Alfonso
Originally posted by Davide Fedeli:
Regarding (1), to study the interaction between two continuous variables Scale_A and Scale_B you need to explicitly add that interaction term to your second-level model. You can do that, for example, by creating a new second-level covariate (e.g. named Scale_AB) and defining it as the product of Scale_A and Scale_B (e.g. enter in the values field "Scale_A.*Scale_B" without the quotes). Then, in the second-level results tab select the effects:
All_subjects, Age_covariate, Scale_A, Scale_B, Scale_AB
and enter a between-subjects contrast:
[0, 0, 0, 0, 1]
That will explicitly test the presence of a Scale_A-by-Scale_B continuous interaction. To clarify, the second-level analysis that you were mentioning (e.g. selecting All_subjects, Age_covariate, Scale_A, Scale_B and entering a [0,0,1,-1] contrast) evaluates whether the effect of ScaleA on connectivity is greater/smaller than the effect of ScaleB, in other words whether the change in connectivity per unit-change in ScaleA is greater/smaller than the change in connectivity per unit-change in ScaleB. In contrast the interaction analyses that we are referring to here evaluate whether the effect of ScaleA on connectivity is modulated by ScaleB (or viceversa), in other words whether the change in connectivity per unit-change in ScaleA is itself proportional/related to ScaleB.
And regarding (2), yes, for any significant area here it is important to plot the effects within those clusters in order to be able to interpret the directionality of these effects correctly, and your suggestion to binarize one of the Scale variables and show the changes in association between connectivity and the other Scale variable across the two groups is a perfectly reasonable way to do that.
Just as a side note, if you believe it makes more sense to evaluate the interaction in term of these "High-ScaleA" vs. "Low-ScaleA" groups you may also test that form of categorical-by-continuous interaction explicitly, and that works exactly in the same way as above but now using a categorical version of your Scale_A variable instead. For example, you could create a new Group_A second-level covariate containing 1's for the "High-ScaleA" subjects and 0's for the "Low-ScaleA" subjects, and then a new Group_AB covariate defined as "Groups_A.*Scale_B", and then define your second-level analysis by selecting All_subjects, Age_covariate, Group_A, Scale_B, Group_AB, and entering the same [0,0,0,0,1] contrast.
Hope this helps
Alfonso
Originally posted by Davide Fedeli:
Hi Conn experts,
thank you for this amazing software and for listening to the growing community needs and questions.
I have a beginner's doubt regarding interactions effects between two continuous variables.
This is my study design (simplified with just 8 subjects):
All_subjects [1 1 1 1 1 1 1 1]
Age_covariate [45 50 54 49 47 42 43 52]
Scale_A [29 15 18 30 27 16 21 27]
Scale_B [8 9 12 6 6 5 7 3]
Scale_A and Scale_B are the scores in two different behavioural scales
1) I would like to see the effects of interaction of Scale_A and Scale_B on functional connectivity, and use age as a covariate of no interest. How should I set my contrast? [0 0 1 0; 0 0 0 1]? or maybe [0 0 1 -1; 0 0 -1 1]? or just [0 0 1 -1] and [0 0 -1 1] separately?
2) If the interaction is significant, then would it be ok to explore the relationship between the two variables by splitting the subjects in two groups (e.g. Scale_A high score; Scale_A low score) and then comparing the effect of Scale_B between them?
Many thanks for your kind help and support,
Davide
thank you for this amazing software and for listening to the growing community needs and questions.
I have a beginner's doubt regarding interactions effects between two continuous variables.
This is my study design (simplified with just 8 subjects):
All_subjects [1 1 1 1 1 1 1 1]
Age_covariate [45 50 54 49 47 42 43 52]
Scale_A [29 15 18 30 27 16 21 27]
Scale_B [8 9 12 6 6 5 7 3]
Scale_A and Scale_B are the scores in two different behavioural scales
1) I would like to see the effects of interaction of Scale_A and Scale_B on functional connectivity, and use age as a covariate of no interest. How should I set my contrast? [0 0 1 0; 0 0 0 1]? or maybe [0 0 1 -1; 0 0 -1 1]? or just [0 0 1 -1] and [0 0 -1 1] separately?
2) If the interaction is significant, then would it be ok to explore the relationship between the two variables by splitting the subjects in two groups (e.g. Scale_A high score; Scale_A low score) and then comparing the effect of Scale_B between them?
Many thanks for your kind help and support,
Davide
Threaded View
| Title | Author | Date |
|---|---|---|
| Davide Fedeli | Jan 30, 2019 | |
| Alfonso Nieto-Castanon | Jan 31, 2019 | |
| Davide Fedeli | Feb 1, 2019 | |