Indicator and Stratification Methods for Missing Explanatory Variables in Multiple Linear Regression
研究了多元线性回归中处理缺失解释变量的两种方法（指标法和分层法），推导了最小二乘估计的精确偏误，并数值评估发现指标法偏误过大，不建议使用。
Abstract The statistical literature and folklore contain many methods for handling missing explanatory variable data in multiple linear regression. One such approach is to incorporate into the regression model an indicator variable for whether an explanatory variable is observed. Another approach is to stratify the model based on the range of values for an explanatory variable, with a separate stratum for those individuals in which the explanatory variable is missing. For a least squares regression analysis using either of these two missing-data approaches, the exact biases of the estimators for the regression coefficients and the residual variance are derived and reported. The complete-case analysis, in which individuals with any missing data are omitted, is also investigated theoretically and is found to be free of bias in many situations, though often wasteful of information. A numerical evaluation of the bias of two missing-indicator methods and the complete-case analysis is reported. The missing-indicator methods show unacceptably large biases in practical situations and are not advisable in general.