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?

Best,
Marius