Misleading interaction and curvilinear terms.

Abstract

This article examines the relationships between interaction (product) terms and curvilinear (quadratic) terms in regression models in which the independent vari-ables are correlated. The author uses 2 substantive xamples to demonstrate he following outcomes: (a) If the appropriate quadratic terms are not added to the estimated model, then the observed interaction may indicate a synergistic (offset-ting) relationship between the independent variables, whereas the true relationship is, in fact, offsetting (synergistic). (b) If the appropriate product terms are not added to the equation, then the estimated model may indicate concave (convex) relation-ships between the independent variables and the dependent variable, whereas the true relationship is, in fact, convex (concave). (c) If the appropriate product and quadratic terms are not examined simultaneously, then the observed interactive or curvilinear relationships may be nonsignificant when such relationships exist. The implications of these results for the examination ofinteraction and quadratic effects in multiple regression analysis are discussed. Hypotheses about interaction effects between con-tinuous variables are frequently examined in psycho-logical research using multiple regression analysis (e.g., Aiken & West, 1991; Jaccard, Turrisi, & Wan, 1990). However, despite the plethora of research con-cerning these hypotheses, the appropriate methods to test them remain a subject of debate. One issue that has received much attention in the recent literature is the relationship between interaction and curvilinear effects when there is a high multicollinearity between independent variables (e.g., Busemeyer & Jones,

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