Substantive nonadditivity in social science research A note on induced collinearity and measurement and testing of effects

Abstract

Theories employed to explain regularities in social behavior often contain reference (explicit or implicit) to the presence of nonlinear and/or nonadditive (i.e., multiplicative) relationships among germane variables. While such nonadditive features are theoretically important, the inclusion of quadratic or multiplicative terms in structural equations to model such features can cause significant methodological problems. This paper estimates a set of equations and formally examines how the inclusion of quadratic terms and multiplicative interaction terms contribute to the level of collinearity or ill-conditioning of the input data matrix and the precision of the parameter estimates. Subsequently we examine how effects of explanatory variables in nonadditive models can be measured and tested for statistical significance. The results indicate that collinearity may not be as big a problem for linear structural social science models as is often believed. Further, although collinearity is increased by adding quadratic and/or multiplicative terms, the effects of the collinearity tend to be localized and entail only variables with a common base. The findings suggest the substantive insight gained from including theoretically appropriate nonlinear and nonadditive terms outweigh the methodological problems they create.