Multicollinearity: How common factors cause Type 1 errors in multivariate regression

Abstract

Research Summary: In multivariate regression analyses of correlated variables, we sometimes observe pairs of estimated beta coefficients large in absolute magnitude and opposite in sign. T-statistics are also large, suggesting meaningful findings. I found 64 recently published Strategic Management Journal articles with results exhibiting these characteristics. In this article, I demonstrate that such results may be Type 1 errors (false positives): If regressors are correlated via an unobservable common factor, estimated beta coefficients will misleadingly tend toward infinite magnitudes in opposite directions, even if the variables’ real effects are small and of the same sign. Diagnostics such as Variance Inflation Factors (VIF) will misleadingly validate Type 1 errors as legitimate results. After establishing general results via mathematical analysis and simulation, I provide guidelines for detection and mitigation. Managerial Summary: This article demonstrates mathematically how regression analyses with correlated independent variables may generate beta coefficients of opposite sign to the variables’ true effects. To assess the likelihood of this possibility, I propose that: if (a) absolute correlation of two independent variables is about ±0.3 or more (smaller correlations may be problematic for large data sets), (b) the two variables have beta coefficients of opposite sign, if correlated positively, and of the same sign, if correlated negatively, and (c) the bivariate correlation of one independent variable with the dependent variable is of the opposite sign from the beta coefficient, then the beta might be a false positive. To facilitate such analysis, authors should provide complete correlation tables, including dependent variables, interaction terms, and quadratic terms.