Estimated Coefficients, Information Sets, and 'Biases' in Nonlinear Models

Thomas Mroz, University of North Carolina at Chapel Hill
Yaraslau Zayats, University of North Carolina at Chapel Hill

Demographers often use logit and probit models when analyzing binary events. Many researchers, however, misinterpret how including or excluding additional regressors, heterogeneity corrections, and multi-level factors impact the interpretation of the estimated parameters. Such misinterpretations can result in incorrect inferences about the importance of incorporating additional features into statistical models. In this paper we derive how estimated coefficients in probit and logit models must change when one includes or excludes explanatory "variables" that are independent of the other explanatory variables in the model. We demonstrate how coefficient estimates change when one controls or fails to control for such independent factors. Reports of "biases" in such models can often be attributed to the fact that estimates in nonlinear models depend crucially on the inclusion or exclusion of factors that are independent of those already included in the statistical model. Unlike linear regression, the set of conditioning variables plays an important role.