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

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