State‐space models for multivariate longitudinal data of mixed types

TLDR

The approach is based on Tweedie exponential dispersion models, which accommodate a wide variety of discrete, continuous, and mixed data. The study proposes a class of state‑space models for multivariate longitudinal data with components having different distributions. The model assumes a Markov latent process with conditionally independent observations, estimates time‑varying covariate effects via a Kalman‑smoother‑derived estimating equation, and analyzes residuals from both observation and latent processes. It offers a fully parametric alternative to Liang and Zeger's quasilikelihood approach.

Abstract

Abstract We propose a class of state‐space models for multivariate longitudinal data where the components of the response vector may have different distributions. The approach is based on the class of Tweedie exponential dispersion models, which accommodates a wide variety of discrete, continuous and mixed data. The latent process is assumed to be a Markov process, and the observations are conditionally independent given the latent process, over time as well as over the components of the response vector. This provides a fully parametric alternative to the quasilikelihood approach of Liang and Zeger. We estimate the regression parameters for time‐varying covariates entering either via the observation model or via the latent process, based on an estimating equation derived from the Kalman smoother. We also consider analysis of residuals from both the observation model and the latent process.