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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 after light text normalization (handling dropped articles and pronouns, double-space artifacts, one typo, one paraphrase, and one verb-form difference in the source texts); all 144 of 144 items matched (100%).

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. Possible items appear as red dots in the Viability arm only; the Morality and Rationality arms did not include possible items.

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).