Better predicted probabilities from linear probability models with applications to multiple imputation

Although logistic regression is the most popular method for regression analysis of binary outcomes, there are still many attractions to using least-squares regression to estimate a linear probability model. A major downside, however, is that predicted “probabilities” from a linear model are often greater than 1 or less than 0. That can be problematic for many real-world applications. As a solution, we propose to generate predicted probabilities based on a linear discriminant model, which Haggstrom (1983) showed could be obtained by rescaling coefficients from OLS regression. We offer a new Stata command, predict_ldm, that can be used after the regress command to generate predicted values that always fall within the (0,1) interval. We show that, for many applications, these values are very close to those produced by logistic regression. We also explore applications where there are substantial differences between logistic predictions and those produced by predict_ldm. Finally, we show that the linear discriminant method can be used to substantially improve multiple imputations of categorical data based on the multivariate normal model. We are currently developing a new mi impute command to implement this method.