Updatable Estimation in Generalized Linear Models with Missing Data

This paper develops online updating methods for the generalized linear models with missing data in streaming datasets. For cases with missing response, we propose the updatable inverse probability weighting (UIPW) estimation, which is implemented via a two-step online updating algorithm. In the first step, we suggest an updatable estimation for the parameters in the propensity function, thereby providing an updatable estimation of the propensity function itself. In the second step, we derive the UIPW for estimating the parameter of interest by using the inverse of the updatable estimate of the propensity function valued at each observation as the weight. The UIPW estimation is highly versatile, as it relaxes constraint on the number of data batches. We demonstrate that the UIPW estimator is both consistent and asymptotically normal, sharing the same asymptotic variance as the oracle estimation, thereby fulfilling the oracle property. For cases with missing covariate, we propose the updatable multiple imputation (UMI) estimation based on the classical chained equations method. Through simulation studies and real data analyses, we show the finite sample performance of the UIPW and UMI estimators, confirming that their performance is comparable to traditional offline learners. Supplementary materials for this article are available online.