crosseffects

Crosseffects is a term used in statistics and related disciplines to describe effects that arise from the interaction between two or more factors, rather than from their individual main effects alone. The concept is often rendered as cross-effects or described as interaction effects, reflecting how the influence of one variable on an outcome depends on the level of another variable.

In statistical modeling, cross-effects are most commonly represented by interaction terms. In a two-factor model with factors A and B, the regression or ANOVA term AB captures the cross-effect: the contribution of AB to the outcome indicates whether the effect of A changes when B changes, and vice versa. This idea also appears in more complex designs with multiple factors and in nonlinear models.

Detecting cross-effects involves including interaction terms in the model and assessing their significance. Graphical tools such as interaction plots, simple slopes analyses, and stratified estimates are often used to aid interpretation. Proper coding of factors and centering can affect the shape and interpretability of interaction terms, and large sample sizes are often required to reliably detect cross-effects.

Applications span diverse fields, including psychology, epidemiology, agriculture, economics, and engineering, wherever the joint influence of factors on an outcome is of interest. While cross-effects can illuminate nuanced dependencies, they also add complexity to interpretation and require careful consideration of model specification and measurement scales.

See also: interaction effect, factorial design, main effect, regression interaction, ANOVA.