State space models for multivariate time series data with nonmonotone MNAR missingness

Thomas M. Menino Convention & Exhibition Center 

State-space models are widely used for analyzing multivariate time series with missing observations. In many longitudinal studies, the pattern of missingness is nonmonotone, and the probability of missingness depends directly on unobserved signal values, leading to nonmonotone Missing Not At Random (MNAR) mechanisms that induce systematic bias under the widely popular MAR-based state-space inferences developed in the literature so far. We propose linear-Gaussian state-space models with explicit MNAR modeling for such data, where the missingness process is governed by a logistic regression depending on latent states, current and lagged emissions, and historical missingness. By leveraging Pólya--Gamma augmentation, the MNAR mechanism is rendered conditionally conjugate. This enables closed-form posterior updates via Gibbs sampling and variational inference via Kalman filtering and Rauch--Tung--Striebel smoothing within a coordinate-ascent algorithm. Through simulation studies and an application on optical sensors for AQI in the Montana SmartFIRES study, we demonstrate the advantages of our method over existing state-of-the-art approaches.

State space models

nonmonotone MNAR

Kalman filtering and smoothing

Variational Inference 

Survey Research Methods Section