Tomarchio Salvatore D, Punzo Antonio, Maruotti Antonello
Dipartimento di Economia e Impresa, Università degli Studi di Catania, Catania, Italia.
Dipartimento di Giurisprudenza, Economia, Politica e Lingue Moderne, Libera Università Maria Ss. Assunta, Roma, Italia.
Stat Comput. 2022;32(3):53. doi: 10.1007/s11222-022-10107-0. Epub 2022 Jun 15.
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 balanced 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 eigen 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.
隐马尔可夫模型（HMMs）已在单变量和多变量文献中得到广泛应用。然而，近年来人们对矩阵变量数据的分析兴趣日益增加。在本论文中，我们通过假设每个隐藏状态下的矩阵正态分布，引入了用于矩阵变量平衡纵向数据的HMMs。此类数据排列成一个四维数组。为了解决可能的过度参数化问题，我们考虑协方差矩阵的特征分解，从而得到总共98个HMMs。讨论了一种期望条件最大化算法用于参数估计。首先在模拟数据上研究了所提出的模型，包括参数恢复、计算时间和模型选择。然后，将它们应用于一个关于意大利各省失业率的四维真实数据集，该数据集按性别和年龄组进行评估，时间跨度为过去16年。
