Assessment of Multicollinearity

Abstract

Interdependence among explanatory variables is a common condition for sociological analyses. It may markedly affect the stability of estimates of parameters obtained from least-squares regression. Multicollinearity is viewed as a problem which poses two questions for the analyst: how severe is the multicollinearity and what is its effect on the analysis? The determinant of the correlation matrix of explanatory variables is a measure of the severity of multicollinearity. Haitovsky's chi-square statistic permits the assessment of the null hypothesis that the correlation matrix is singular. This paper demonstrates the need for this test through an examination of published correlation matrices. It is suggested that use of the Haitovsky test be routine in any analysis which attempts the estimation of parameters through regression analysis.