Table 1 Interaction Detection.

From: Measurement of tourism eco-efficiency, spatial distribution, and influencing factors in China

Factor relationships

Mean

q(X1 ∩ X2) < Min(q(X1), q(X2))

Weaken-nonlinear: Effect of a single variable is nonlinearly weakened by the interaction of two variables.

Min (q(X1), q(X2)) < q(X1 ∩ X2) < Max (q(X1), q(X2))

Weaken-univariate: Effect of single variables are univariably weakened by the interaction.

q(X1 ∩ X2) > Max(q(X1), q(X2))

Enhance-bivariate: Effect of single variables are bivariably enhanced by the interaction.

q(X1 ∩ X2) = q(X1) + q(X2)

Independence: Effect of the variables are independent.

q(X1 ∩ X2) > q(X1) + q(X2)

Nonlinear enhance: Effect of the variables are nonlinearly enhanced.