Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data

TL;DR

This paper introduces a novel nested hidden Markov chain model for capturing dynamic unobserved heterogeneity and correlations in multilevel longitudinal data, with an application to health benefit data.

Contribution

It proposes a new nested hidden Markov chain framework for modeling unobserved heterogeneity at multiple levels in longitudinal data.

Findings

Effectively captures unobserved heterogeneity and correlations

Provides a feasible inference method via composite likelihood

Demonstrates applicability on real health data

Abstract

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we propose an approach based on nested hidden (latent) Markov chains, which are associated to every sample unit and to every cluster. The approach allows us to account for the mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation which may arise between the responses provided by the units belonging to the same cluster. Given the complexity in computing the manifest distribution of these response variables, we make inference on the proposed model through a composite likelihood function based on all the possible pairs of subjects within every cluster. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed.