  Modern surveys with large sample sizes and growing mixed-type questionnaires
require robust and scalable analysis methods. In this work, we consider
recovering a mixed dataframe matrix, obtained by complex survey sampling, with
entries following different canonical exponential distributions and subject to
heterogeneous missingness. To tackle this challenging task, we propose a
two-stage procedure: in the first stage, we model the entry-wise missing
mechanism by logistic regression, and in the second stage, we complete the
target parameter matrix by maximizing a weighted log-likelihood with a low-rank
constraint. We propose a fast and scalable estimation algorithm that achieves
sublinear convergence, and the upper bound for the estimation error of the
proposed method is rigorously derived. Experimental results support our
theoretical claims, and the proposed estimator shows its merits compared to
other existing methods. The proposed method is applied to analyze the National
Health and Nutrition Examination Survey data.
