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Modals: interactive response-surface explorer

Smooth GAM-predicted Pr("Impossible") in three rating-pair geometries, separately per experiment. Toggle between the response-space view (our data) and the difference-space view (our data minus the speeded baseline of Phillips and Cushman, 2017). Hover over an item dot to see its action text, event type, ratings, and per-item Pr("Impossible") in our experiment and in P&C 2017.

Data and methods

Our data: three preregistered between-subjects experiments using a 1,500 ms speeded forced-choice modal-judgment paradigm. Anonymized trial-level data are available on the OSF repository linked in the manuscript.

Phillips and Cushman 2017 baseline: the speeded condition of Study 1a, downloaded automatically from github.com/phillipsjs/implicitModality on first run; MD5 checksums are pinned, so any upstream change is caught.

Per-item ratings: the x- and y-axis values for each item come from Phillips and Cushman 2017 Study 1b. In that study, a separate sample of 61 raters scored each event on three dimensions, immorality, improbability, and irrationality, on a 1-5 scale; the per-item mean across raters is the value plotted here. Items in our experiments were matched to the rating set by exact action-text correspondence (134 of 144 items matched, 93%).

Surfaces: each panel is a generalized additive model (GAM) fit per experiment using the mgcv R package. A GAM is a regression that allows the relationship between the predictors and the outcome to be smooth and non-linear: rather than fitting a straight line or plane, the model learns a flexible surface from the data. We use a tensor-product smooth (basis dimension k = 5) over the two rating dimensions, which lets the surface bend independently along each axis. The fitted surface is then evaluated on a 60 × 60 grid for visualization. Item dots are positioned at the actual item ratings, and their colour encodes the item's event type.

View:
Rating pair:

Response surface: Pr('Impossible') as f(Immorality, Improbability)

Smooth GAM-predicted Pr("Impossible") in our data, fit per experiment. White contour lines mark the 0.1, 0.3, 0.5, 0.7, and 0.9 levels.

Response surface: Pr('Impossible') as f(Immorality, Irrationality)

Smooth GAM-predicted Pr("Impossible") in our data, fit per experiment.

Response surface: Pr('Impossible') as f(Improbability, Irrationality)

Smooth GAM-predicted Pr("Impossible") in our data, fit per experiment.

Difference surface: ours − P&C 2017 in (Immorality, Improbability)

Per-item signed difference between our Pr("Impossible") and the speeded condition of Phillips and Cushman (2017). Magenta = P&C called the item impossible more often than we did; orange = we called the item impossible more often.

Difference surface: ours − P&C 2017 in (Immorality, Irrationality)

Per-item signed difference between our Pr("Impossible") and the speeded condition of Phillips and Cushman (2017).

Difference surface: ours − P&C 2017 in (Improbability, Irrationality)

Per-item signed difference between our Pr("Impossible") and the speeded condition of Phillips and Cushman (2017).