Hi all,
I’m revising a task-fMRI paper using the stock market task from Lohrenz et al. (2007) : https://www.pnas.org/doi/abs/10.1073/pnas.0608842104, where participants place a bet (b), observe a market return (r), and receive a realized outcome (br = bet × return). Fictive error is defined as:
f = |r| − br
and is often interpreted as a computational measure of regret.
In the primary first-level fMRI model, we modeled f directly as a parametric modulator during the outcome/reveal event, following prior applications of this task. [nature.com]
A reviewer raised the concern that because fictive error is computed from market return and realized outcome, the neural effects attributed to f might instead reflect market-return magnitude. They suggested a sensitivity analysis accounting for market return.
To address this, I fit a first-level model including both |r| and f as parametric modulators in the same GLM (no orthogonalization). The group effects observed in the original f-only model were no longer significant.
My question is whether including r and f in the same model provides a meaningful way to “control for” market return, given that substantial shared variance between the two is an inherent feature of the fictive-error computation itself. Including r and f in the same fmri GLM model and looking at the effect of f may not really test the effect of fictive error.
Do you think there is a principled way to account for market-return magnitude in this setting, or would you consider the original model, which directly includes fictive error as the parametric modulator, to be the more appropriate implementation given the structure of the task?
Any thoughts would be greatly appreciated.
These models answer different questions. The f-only model includes the variance f shares with market magnitude. Adding |r| asks whether f explains anything beyond that magnitude.
For your stated f = |r| - br, the joint model can be rewritten exactly:
a|r| + c f = (a + c)|r| - c br.
So the f coefficient in that joint model is also the negative of the br coefficient when controlling for |r|, provided the columns are constructed and transformed consistently. That is a meaningful conditional association, but it does not isolate a uniquely psychological ‘regret’ component. Shared variance can also make the estimate less precise; losing significance alone does not tell you which explanation applies. I’d compare the coefficient estimates and standard errors, and inspect the actual convolved/filtered design columns.
One definition check first: are you pooling gains and losses? Lohrenz et al.'s main imaging regressor uses positive returns, r+(1-b); their gain/loss definitions differ. Your post also alternates r and |r|. Those choices change the question, so I’d settle them before choosing which sensitivity analysis to report.
Thank you so much for the prompt response. Your point is very much in line with what I have been thinking. My understanding is that including both |r| and f in the same model effectively turns the f coefficient into a reparameterization of the br coefficient once market-return magnitude is accounted for.
Regarding your question about the market-return term: in the behavioral model, I model positive and negative market returns (r+ and r−) separately, following Lohrenz et al. (2007). In the fMRI sensitivity analyses, I tried both approaches: (1) a single |r| regressor across all market events, and (2) separate r+ and r− regressors. The results were qualitatively similar, although I am not sure whether one approach is theoretically preferable in this context. Because the purpose of the sensitivity analysis is simply to account for market-return magnitude, I was initially inclined toward using a single |r| regressor.
As for my fictive error (f) regressor in the fMRI glm, I also separate them by f+ and f- (depending on the valence of market return).
That clarification helps. A single |r| term makes a substantive assumption: before separate scaling, |r| = max(r, 0) + max(-r, 0), so it gives market magnitude the same slope on gains and losses. Separate positive/negative terms allow those slopes to differ. If your negative-return regressor keeps its minus sign, the coefficient signs change, but the distinction remains.
Neither choice is universally preferable. If you want to allow valence-specific magnitude responses while estimating separate f+ and f- effects, the split control is more flexible. I’d explain that assumption and report the alternative as a sensitivity check, rather than choose according to which preserves significance. Keep the event definitions, scaling and other regressors explicit: two analyses with the same variable names can test different contrasts. Similar results across both specifications support that particular robustness statement; they still don’t identify a unique neural ‘regret’ signal.