The Link Function Problem in Psychological Interaction Testing

Equal differences on one scale become different differences on another scale. This is crucial for interaction testing because an interaction is a difference between differences, and in psychological research the observed response and the construct of interest are often expressed on different scales. Therefore, the same data can show an interaction on one scale and not on another.

Generalized Linear Models make this problem explicit: the link function defines the scale on which a model without an interaction term is additive. Choosing a link thus defines what no interaction means, while the family describes the nature of the response variable.

The paper has two connected parts. A preregistered review of recent articles from five leading psychology journals shows that interaction testing is routinely performed, that the link function is most often unspecified, and that constrained outcomes are routinely analyzed with identity-link models without justifying the assumption of equal effects on the observed scale. Worked examples and simulations then develop three common response formats — forced-choice accuracy with a chance floor, logit versus probit within the same family, and sum scores as a measurement case — and quantify how a plausible-looking link can turn an additive structure on one scale into a statistically significant interaction on another.

Read the full abstract and the paper (PDF)