My team recently used 3dDeconvolve paired with -stim_times_AM2 to model neural sensitivity to a set of stimuli, each containing two different traits. Our goal is to figure out whether the two traits elicit different neural responses, which means we are interested in their independent effects. However, the two variables are highly correlated with each other (r2=0.8). It seems like that AM2 can not adequately capture the variance associated with these collinear regressors.

We are struggling to find the correct approach to address this issue in AFNI. Could you please help me?

Assume that the two traits for the stimuli are T_1 and T_2. The decision basis is not the extent of correlation between them, but rather their causal relationships with the stimuli. Firstly, what is the effect of interest in this context? Secondly, among the three variables (stimulus, T_1 and T_2 ), determining which causes which is of utmost importance? For a more general discussion, see here.

The two traits (T1 and T2) are fundamental properties of the stimuli and have been widely studied respectively in the past. We have obtained specific values for T1 and T2 in each stimulus. Therefore, our focus is on T1 and T2 rather than the stimuli themselves. We are trying to model brain signals based on the different values of these two traits. Given this, we believe that T1 and T2 should be treated as main variables rather than covariates.
However, we need to address the collinearity issue in order to obtain accurate beta estimates. We would like to know whether we can resolve this in AFNI using AM2 or any other methods.

The two traits (T1 and T2) are fundamental properties of the stimuli and have been widely studied respectively in the past.

The fact that an approach has been used in the past does not automatically grant it legitimacy. The causal relationships among the variables are crucial for model construction and result interpretation, whether the variable regarding the effect of interest is categorical or quantitative.

It seems like that AM2 can not adequately capture the variance associated with these collinear regressors.

Did you get any error messages or warnings during the modeling process? Does one trait influence the other (e.g., T_1 \rightarrow T_2), or are they both influenced by another variable?

There were no warnings or errors during the modeling process. However, we believe that potential collinearity between variables needs to be considered, and it’s unclear whether -AM2 has addressed this issue. We hope to resolve this problem by orthogonalizing the variables, possibly through a stepwise approach to amplitude modulation. Is there a better method in AFNI for addressing this?

T1 and T2 are fundamental properties of the stimuli and are influenced by the physical characteristics of the stimuli themselves.

We’ve been struggling with this problem for a long time and hope to resolve it effectively through AFNI.

There were no warnings or errors during the modeling process. However, we believe that potential collinearity between variables needs to be considered, and it’s unclear whether -AM2 has addressed this issue. We hope to resolve this problem by orthogonalizing the variables, possibly through a stepwise approach to amplitude modulation. Is there a better method in AFNI for addressing this?

It's unclear to me why there is concern or difficulty regarding collinearity. Since the task stimulus serves as a confounder (a common cause) for both traits, it's natural for the two traits to be correlated. By incorporating both traits as explanatory variables in the regression model—as implemented via the -stim_times_AM2 option in 3dDeconvolve—the model should appropriately attribute effects to each trait. There's no valid reason to orthogonalize the two trait variables; such a workaround might seem to address numerical issues but would actually ruin result interpretation.

Thanks for your help. We've determined that orthogonalizing the two traits is not necessary.
However, we've encountered a new issue: after applying -stim_times_AM2, the betas for the two traits are nearly opposites due to high linearity. Is there a method to address this problem?

after applying -stim_times_AM2, the betas for the two traits are nearly opposites due to high linearity. Is there a method to address this problem?

I apologize if I’m overlooking something, but could you clarify why you consider the nearly opposite regression coefficients for the two traits to be problematic or potentially in violation of a neurological or statistical principle?

Gang Chen

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National Institute of Mental Health (NIMH) is part of the National Institutes of
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