Parsimonious Hidden Markov Models for Matrix-Variate Longitudinal Data

TL;DR

This paper introduces parsimonious hidden Markov models tailored for matrix-variate longitudinal data, utilizing spectral decomposition to reduce overparameterization, and demonstrates their effectiveness through simulations and real-world unemployment data analysis.

Contribution

It develops a new class of HMMs for matrix-variate data using spectral decomposition to address overparameterization issues.

Findings

Models successfully recover parameters in simulations.

Computational efficiency is improved with spectral decomposition.

Applied to unemployment data, models reveal meaningful patterns.

Abstract

Hidden Markov models (HMMs) have been extensively used in the univariate and multivariate literature. However, there has been an increased interest in the analysis of matrix-variate data over the recent years. In this manuscript we introduce HMMs for matrix-variate longitudinal data, by assuming a matrix normal distribution in each hidden state. Such data are arranged in a four-way array. To address for possible overparameterization issues, we consider the spectral decomposition of the covariance matrices, leading to a total of 98 HMMs. An expectation-conditional maximization algorithm is discussed for parameter estimation. The proposed models are firstly investigated on simulated data, in terms of parameter recovery, computational times and model selection. Then, they are fitted to a four-way real data set concerning the unemployment rates of the Italian provinces, evaluated by gender and age classes, over the last 16 years.