help > RE: Question About Main Effects and Interaction in a Second-Level Regression Model (Warning Message)
Sep 21, 2023  10:09 AM | Alfonso Nieto-Castanon - Boston University
RE: Question About Main Effects and Interaction in a Second-Level Regression Model (Warning Message)

Dear Fei

Adding the regressor BehavioralScore does not modify the underlying model (as that effect was already being modeled by the combination of BehavioralScore_GroupA and BehavioralScore_GroupB, of course assuming that all of your subjects are either in GroupA or in GroupB). That said, that warning message should not appear for the contrast [0 0 0 0 1 -1], as that contrast is estimable even if the model has redundant terms. Could you please double-check that your second-level covariates are correctly defined? (e.g. GroupA should contain 1's for subjects in GroupA and 0's for all other subjects, similarly for GroupB, BehavioralScore_GroupA should contain the values of BehavioralScore for GroupA subjects and 0's for everybody else, similarly for BehavioralScore_GroupB, and GroupA+GroupB should equal AllSubjects).

To clarify (feel free to ignore this bit), the GLM equation for the first model would be:

Functional Connectivity = B1*GroupA + B2*GroupB + B3*Age + B4*BehavioralScore*GroupA + B5*BehavioralScore*GroupB

while for the second model it would be:

Functional Connectivity = B1*GroupA + B2*GroupB + B3*Age + B4*BehavioralScore*GroupA + B5*BehavioralScore*GroupB + B6*BehavioralScore

Since GroupA*BehavioralScore + GroupB*BehavioralScore = BehavioralScore, if the model regressors estimated from the data are B=[B1 B2 B3 B4 B5 B6], then any other set of model regressors of the form B=[B1 B2 B3 B4+A B5-A B6-A] would fit the same data equally well (for any arbitrary value A), which makes certain contrasts (any contrast where A does not cancel out, e.g. C=[0 0 0 0 1 0], where C*B=B5-A) non-estimable, which is what the warning message is indicating. That said, the contrast C=[0 0 0 0 1 -1] is estimable, as A cancels out here and C*B = B5-B6, so that contrast should not be giving you a warning message (unless there is something wrong with the model covariate definitions and GroupA*BehavioralScore + GroupB*BehavioralScore is not equal to BehavioralScore).

Hope this helps

Alfonso

Originally posted by I-Fei Chen:

Dear Alfonso and fellow forum users,

I have a question regarding the use of contrasts in a second-level setting. Here are the between-subjects factors and conditions in my study:

Between-subjects: "GroupA," "GroupB," "Age," "BehavioralScore_GroupA," "BehavioralScore_GroupB"
Conditions: "rest"

Based on previous discussions, the contrast for the interaction effect is specified as [0 0 0 1 -1], with control for age in the regression model. The regression equation looks like this:

Functional Connectivity = Beta0 + Beta1(Group) + Beta2(Age) + Beta3(BehavioralScore*Group)

Now, I'm wondering if I can include the main effect of "BehavioralScore" in the regression, as shown below:

Functional Connectivity = Beta0 + Beta1(Group) + Beta2(BehavioralScore) + Beta3(Age) + Beta4(BehavioralScore*Group)

In this case, the factors are defined as follows:

Between-subjects: "GroupA," "GroupB," "BehavioralScore," "Age," "BehavioralScore_GroupA," "BehavioralScore_GroupB"
Conditions: "rest"

The contrast for the interaction effect is [0 0 0 0 1 -1].

However, when I run this model, the GUI displays a warning message and suggests simplifying the second-level model. I'm wondering why is this warning happening?

Thank you for your assistance and valuable suggestions.

Sincerely,
Fei