Extend AdapDISCOM beyond MCAR to MAR and MNAR missingness mechanisms

Extend AdapDISCOM—currently developed under the missing completely at random (MCAR) assumption—to settings where missingness occurs under missing at random (MAR) or missing not at random (MNAR) mechanisms, while preserving its ability to handle multimodal block-wise missingness and measurement error.

Background

The current formulation of AdapDISCOM assumes MCAR, which simplifies estimation of multimodal covariance structures from incomplete data. Real-world datasets often exhibit missingness that depends on observed or unobserved variables (MAR or MNAR), making this a critical extension.

The authors explicitly identify the need to generalize AdapDISCOM to MAR and MNAR as an outstanding direction for future research.