Multicollinearity in measurement error models

Abstract

The multicollinearity and error-prone variables in linear regression models cause problems in parameter estimation in that they both impair the estimation and statistical analysis. Consideration of both problems simultaneously has shown that the error-prone variables mask the multicollinearity. The variance inflation factor has been proven to be the most common diagnostic tool for multicollinearity. This paper theoretically gives valuable information on the variance inflation factor that it decreases as the reliability ratio decreases. The existence of the explanatory variables with measurement error affects the parameter estimation attenuated toward zero and the same time camouflage multicollinearity seriously as if there was no multicollinearity among the explanatory variables. This has been supported by a simulation study with two explanatory variables.

KEYWORDS:

• Error-prone variables
• linear regression
• measurement error
• multicollinearity