Revisiting the statistical specification of near-multicollinearity in the logistic regression model

Abstract

This paper revisits the statistical specification of near-multicollinearity in the logistic regression model. We argue that the ceteris paribus clause, which assumes that the maximum likelihood estimator of β remains constant as the correlation ( ρ ) between the regressors increases, invoked under the traditional account of near-multicollinearity is rather misleading. We derive the parameters of the logistic regression model and show that they are functions of ρ , indicating that the ceteris paribus clause is unattainable. Monte Carlo simulations confirm these findings and further show that: coefficient estimates and related statistics fluctuate in a non-symmetric, non-monotonic way as | ρ |→1; that the impact of near-multicollinearity is centered on the estimates of β ; and that the impact on substantive inferences does not necessarily follow what the traditional account implies.