Multicollinearity in Marketing Models: Notes on the Application of Ridge Trace Estimation in Structural Equation Modelling

Abstract

Abstract: Multicollinearity in Structural Equation Modelling (SEM) is often overlooked by marketing scholars. This is unfortunate as multicollinearity may lead to fallacious path coefficient estimates or even bring about statistical non‑significance of the parameter estimates. Previous empirical illustrations on mitigating the effects of multicollinearity are virtually non‑existent in the literature. The purpose of this paper is to empirically illustrate the problem of multicollinearity in marketing models and the use of ridge trace estimation in mitigating the effects of multicollinearity in SEM, using the LISREL program. Two slightly differing ridge estimation procedures are illustrated using real data with a multicollinearity problem: Method A, in which the ridge constant is added manually to all diagonal elements of the correlation matrix of the variables in the model, and Method B, in which the ridge constant is added manually only to the diagonal elements of the correlation matrix of the exogenous and explanatory endogenous variables in the model. In evaluating suitable values of the ridge constant, the ridge trace method is used. It is concluded that ridge trace estimation is an effective way of mitigating the effects of multicollinearity in SEM. With same ridge constant values, both methods produce same point estimates of path coefficients, but Method B produces smaller standard errors of parameter estimates and larger squared multiple correlations than Method A.