Correcting Misclassification Bias in Regression Models with Variables Generated via Data Mining

There is a surge of interest in social science studies in applying data mining methods to construct variables for regression analysis. For example, text classification was applied to classify whether the review is subjective or objective. The derived review subjectivity was used as an independent variable in the regression to examine its impact on review helpfulness. In the classification phase of these studies, researchers need to subjectively choose a classification performance metric for optimization. No matter which performance metric is chosen, the constructed variable still includes classification error because the variable cannot be classified perfectly. The misclassification of constructed variables will lead to inconsistent estimators of regression coefficients in the following phase. To correct the estimation inconsistency, we summarize and modify existing proofs in econometrics to derive theoretical formulas of consistent estimators in generalized linear models. The main implication of our theoretical result is that the inconsistency can be corrected by theoretical formulas, even when the classification accuracy is poor. Therefore, we propose that a classification algorithm should be tuned to minimize the standard error of the focal coefficient derived based on the corrected formula. As a result, researchers derive a consistent and most precise estimator in generalized linear models.

As a result of advances in data mining, more and more empirical studies in the social sciences apply classification algorithms to construct independent or dependent variables for further analysis via standard regression methods. In the classification phase of these studies, researchers need to subjectively choose a classification performance metric for optimization in the standard procedure. No matter which performance metric is chosen, the constructed variable still includes classification error because those variables cannot be classified perfectly. The misclassification of constructed variables will lead to inconsistent regression coefficient estimates in the following phase, which has been documented as a problem of measurement error in the econometrics literature. The pioneering discussions on the issue of estimation inconsistency because of misclassification in these studies have been provided. Our study attempts to investigate systematically the theoretical foundation of this problem when a newly constructed variable is used as the independent or dependent variable in linear and nonlinear regressions. Our theoretical analysis shows that consistent regression estimators can be recovered in all models studied in this paper. The main implication of our theoretical result is that researchers do not need to tune the classification algorithm to minimize the inconsistency of estimated regression coefficients because the inconsistency can be corrected by theoretical formulas, even when the classification accuracy is poor. Instead, we propose that a classification algorithm should be tuned to minimize the standard error of the focal regression coefficient derived based on the corrected formula. As a result, researchers can derive a consistent and most precise estimator in all models studied in this paper.