Diagnostic Test for Realized Missingness in Mixed-type Data

A frequent concern in analyzing incomplete multivariate measurements in mixed categorical and quantitative scales is whether missing completely at random (MCAR) is an appropriate model. Realized MCAR refers to constancy of conditional probability at realized missing data patterns and differs from always MCAR. We develop a scalable approach for diagnostics of realized MCAR in mixed-type data for which existing methods are lacking. We interestingly establish that the null framework may hold under the broader condition of observed at random (OAR) under component independence and the method cannot detect departure in the direction of OAR under independence but may do so under dependence. We demonstrate that the proposed method is easy to implement and scalable. In the special case of non-mixed type data, we face computational difficulties with existing methods whereas the proposed approach performs superiorly. The proposed approach is applied to analyze incomplete mixed-type data from the ARCAD metastatic colorectal cancer database.