Multicolinearity and ridge regression: results on type I errors, power and heteroscedasticity

ABSTRACT

Let ${\beta }_1,\dots ,{\beta }_p$ be the slope parameters in a linear regression model and consider the goal of testing $H_0:{\beta }_j=0$ ($j=1,\dots ,p$). A well-known concern is that multicolinearity can inflate the standard error of the least squares estimate of ${\beta }_j$, which in turn can result in relatively low power. The paper examines heteroscedastic methods for dealing with this issue via a ridge regression estimator. A method is found that might substantially increase the probability of identifying a single slope that differs from zero. But due to the bias of the ridge estimator, it cannot reject $H_0:{\beta }_j=0$ for more than one value of j. Simulations indicate that the increase in power is a function of the correlations among the dependent variables as well as the nature of the distributions generating the data.

KEYWORDS:

• Regression
• multicolinearity
• heteroscedasticity

Disclosure statement

No potential conflict of interest was reported by the author.