My team has recently used 3dDeconvolve paired with -stim_times_AM2 to model neural sensitivity to two continuous regressor during continuous listening of a podcast. These two variables are moderately correlated with each other (r2=0.37) and we want to make sure that the model is adequately capturing the variance associated with each continuous regressor.
Our questions are:
Is this moderate correlation an issue with how 3dDeconvolve fits the model? We had no warnings from AFNI when we ran the script and the output showed robust activation patterns for each regressor.
For -stim_times_AM2 that uses multiple regressors, does the order that the regressors are entered into the .txt file matter? We consistently used: time1regressor1, regressor2 time2regressor1, regressor2, etc. Is more variance assigned to each regressor sequentially or simultaneously?
A collaborator who was concerned with the collinearity recommended a stepwise approach to model the unique variance associated with each regressor. Is this something that is possible or even recommended with an amplitude modulated approach? It was our understanding that AFNI automatically calculates the partial F statistic for each regressor as part of the output of 3dDeconvolve
I am happy to provide the stimulus file and the 3dDeconvolve script code if needed!
Before we delve into any statistical concerns, could you provide the following background information?
What specific scientific questions are you aiming to address concerning these two covariates?
Could you elaborate on the scientific rationale behind including these two covariates?
What is prompting your concern about the correlation between these covariates? Are you considering dropping one or both of them for some reason?
I might not have detailed insights into the specifics of these two specific covariates, so my suggestions will be more general in nature.
Incorporating a covariate should be rooted in scientific rationale. Justifying the inclusion of these covariates with prior knowledge (e.g., from literature) would provide a strong foundation.
The popular notion of relying solely on statistical procedures like stepwise selection or similar measures (e.g., correlation) isn't a sufficient justification for the appropriateness of a covariate. In fact, these measures can sometimes be misleading. While resorting to a single measure (e.g., p-values, correlation, R^2) for covariate selection may seem understandably appealing, the decision should be driven by scientific principles. Letting the modeling outcomes solely determine the decision is akin to letting the tail wag the dog.
In your case, the specific degree of correlation between the two covariates shouldn't necessarily raise concerns. Even if the correlation approaches 1, it might indicate a need to revisit the domain knowledge or the understanding of these covariates' nature.
I will leave Gang to ponder the appropriateness of the regressors, but try to address the more simple aspects of the questions.
That is a bit high, but is not necessarily problematic. I would have expected afni_proc.py to warn about it though.
No, the order will not matter. The regression is not done stepwise or by projecting one regressor out of another.
Stepwise (or pairwise orthogonalized, if my understanding is correct) approaches will tend to favor one regressor over the other, and because of that does not usually seem appropriate. For example, if regressor A is projected out of regressor B, then the results for regressor B will be unchanged, but those of A will be inflated, as they will capture both A and B events (from the correlated part of the signal).
If you do not care about the independent effects of these regressors, then it should not matter at all. Projecting A out of B will not affect the rest of the results, it will only affect the betas for A. To be clear, yes, changing regressor B here only changes the betas for regressor A.
Thank you Rick and Gang.
Your answers were both very helpful and guided us towards our next steps!