4. Regression with Missing Ys: An Improved Strategy for Analyzing Multiply Imputed Data

TLDR

In generalized linear modeling, analysts often face missing dependent variables and conventionally use multiple‑imputed Y values for analysis. This study proposes a modified multiple‑imputation‑then‑deletion (MID) strategy to obtain better estimates. MID imputes all cases but excludes those with imputed Y values from subsequent analysis. MID reduces noise from problematic imputations, protects estimates when Y imputations are flawed, and typically yields more efficient results than standard multiple imputation.

Abstract

When fitting a generalized linear model -- such as a linear regression, a logistic regression, or a hierarchical linear model -- analysts often wonder how to handle missing values of the dependent variable Y. If missing values have been filled in using multiple imputation, the usual advice is to use the imputed Y values in analysis. We show, however, that using imputed Ys can add needless noise to the estimates. Better estimates can usually be obtained using a modified strategy that we call multiple imputation, then deletion (MID). Under MID, all cases are used for imputation, but following imputation cases with imputed Y values are excluded from the analysis. When there is something wrong with the imputed Y values, MID protects the estimates from the problematic imputations. And when the imputed Y values are acceptable, MID usually offers somewhat more efficient estimates than an ordinary MI strategy.