help > RE: modeling interaction with continuous predictors
Dec 22, 2021  11:12 AM | Marius Gruber
RE: modeling interaction with continuous predictors
Hello Andrew,
first of all thanks for the toolbox and also for your help here in the forum! I am using this thread from Hamed as my questions are on the same topic.

I am currently working on a study which aims to investigate the association between structural connectivity on one side and the interaction of two continuous variables x and z on the other side. We are interested in both the main effects of x and z and the interaction effect of x*z. So, after some research here on the forum, I have created the following design matrix that includes all three effects as well as several covariates. Our sample includes more than 900 subjects (MDD patients and HCs) from 3 study sites, and I z-standardized all continuous variables. For simplicity, I present only a subset of the data:
Intercept   Sex   Site_2   Site_3   Group_MDD   Age        X           Z            X*Z
1              0       0          0             1                     0.86      -1.86     -0.83       1.56
1              1       0          0             1                     0.16       1.10       1.17       1.30
1              1       0          0             0                    -0.83       2.59      -0.16     -0.42
1              0       1          0             0                     1.63      -0.46      -0.29      0.13
1              1       1          0             1                     1.55      -1.53      -0.17      0.26
1              1       0          1             1                    -1.30      -0.13      -1.17      0.15
1              0       0          1             0                    -0.99       1.02      -0.37     -0.38

Test: F-test

Contrasts:
Main effect X: [0,0,0,0,0,0,1,0,0]
Main effect Y: [0,0,0,0,0,0,0,1,0]
Interaction X*Y: [0,0,0,0,0,0,0,0,1]

I have the following questions regarding these analyses:
As I understand the above posts, I can test the interaction from X and Y with this design matrix and the contrast given above. If NBS finds a network, then the structural connectivity within that network is associated with the interaction effect of X and Y. Is this correct?

Can I reliably test the simple main effects of X and Y with this design matrix and the contrasts given above, or should I create new design matrices for this that include only the variables X or Y (without their interaction)?

To ease the interpretation of the identified networks, I would perform post-hoc t-tests, using the following contrasts:
Main effect X: [0,0,0,0,0,0,1,0,0] and [0,0,0,0,0,0,-1,0,0]
Main effect Y: [0,0,0,0,0,0,0,1,0] and [0,0,0,0,0,0,0,-1,0]
Interaction X*Y: [0,0,0,0,0,0,0,0,1] and [0,0,0,0,0,0,0,0,-1]

I would use sqrt(threshold of the F-test) as the threshold in each test.
Is it possible to test these effects using the t-tests?

Thanks for your help in advance!

Best,
Marius

Threaded View

TitleAuthorDate
Hamed Zivari Dec 8, 2021
Selma Lugtmeijer Mar 10, 2022
Andrew Zalesky Mar 11, 2022
Selma Lugtmeijer Mar 11, 2022
Andrew Zalesky Mar 11, 2022
RE: modeling interaction with continuous predictors
Marius Gruber Dec 22, 2021
Andrew Zalesky Dec 22, 2021
Andrew Zalesky Dec 8, 2021