On the effects of predictor misclassification in multiple linear regression analysis

Abstract

Unweighted least squares regression analysis procedures are frequently used to model the relationship between a continuous response variable and one or more categorical predictor variables. Very commonly, these categorical predictors are subject to misclassification error. The majority of research in the area of mismeasurement of predictors in linear regression analysis has focused on continuous predictors (i,e., on errors-in-variables models). The theory developed for these situations relies on assumptions that do not apply to categorical predictors. We examine the impact of categorical predictor misclassification on unweighted least squares regression analysis results based on models that may also include any number of perfectly measured continuous or categorical predictors, Distributional properties of the response variable conditional on the potentially misclassified observed data are determined, These properties are used to examine the bias properties of estimators of regression coefficients and their estimated variances for models fitted using the observed data, In particular, we show that the bias of estimated regression coefficients based on the use of misclassified categorical predictors can be away from the null, The impact of predictor misclassification on certain test statistics is also explored.

Keywords:

• measurement error
• categorical variables
• least squares regression