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Hidden Markov Latent Variable Models with Multivariate Longitudinal Data

BIOMETRICS 2017年第1期73卷 313-323页

作者： Song, Xinyuan Xia, Yemao Zhu, Hongtu Chinese Univ Hong Kong Dept Stat Shenzhen Res Inst Shatin Hong Kong Peoples R China Nanjing Forestry Univ Dept Appl Math Nanjing Jiangsu Peoples R China Univ North Carolina Chapel Hill Dept Biostat Chapel Hill NC USA

Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderate dependence on, or swearing off cocaine. Given its reversible feature, cocaine use can be formulated as a stochastic process that transits from one state to another, while the impacts of various factors, such as treatment received and individuals' psychological problems on cocaine use, may vary across states. This article develops a hidden Markov latent variable model to study multivariate longitudinal data concerning cocaine use from a California Civil Addict Program. The proposed model generalizes conventional latent variable models to allow bidirectional transition between cocaine-addiction states and conventional hidden Markov models to allow latent variables and their dynamic interrelationship. We develop a maximum-likelihood approach, along with a Monte Carlo expectation conditional maximization (mcecm) algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimates and statistics for testing the heterogeneity of model parameters are investigated. The finite sample performance of the proposed methodology is demonstrated by simulation studies. The application to cocaine use study provides insights into the prevention of cocaine use.

关键词： Hidden Markov model Latent variables Log-continuation ratio model mcecm algorithm Multivariate longitudinal data

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Multivariate generalized hyperbolic laws for modeling financial log-returns: Empirical and theoretical considerations

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2020年第5期36卷 757-775页

作者： Fotopoulos, Stergios B. Paparas, Alex Jandhyala, Venkata K. Washington State Univ Dept Finance & Management Sci Pullman WA 99164 USA Washington State Univ Dept Math & Stat Pullman WA 99164 USA

The aim of this study is to consider the multivariate generalized hyperbolic (MGH) distribution for modeling financial log-returns. Beginning with the multivariate geometric subordinated Brownian motion for asset prices, we first demonstrate that the mean-variance mixing model of the multivariate normal law is natural for log-returns of financial assets. This multivariate mean-variance mixing model forms the basis for deriving the MGH family as a class of distributions for modeling the behavior of log-returns. While theory suggests MGH to be an appropriate family, empirical considerations must also support such a proposition. This article reviews various empirical criteria in support of the MGH family. From a theoretical perspective, we present an alternative form of the density for the MGH family. This alternative density for the MGH family is more convenient for deriving certain limiting results. Numerical study on the distributional behavior of six stocks from the US market forms the foundation of investigating the suitability of the MGH family and some of its well-known subfamilies. Along the way, we implement the multicycle expectation conditional maximization algorithm for estimating the parameters of the MGH family. Then adapting a recently developed algorithmic procedure, we develop a self-contained methodology for carrying out goodness-of-fit tests for the MGH distribution. The numerical study on the six stocks confirms the suitability of the MGH distribution for different time scales of the log-returns such as daily, monthly, and 6-monthly data.

关键词： conditional laws kurtosis mcecm algorithm multivariate generalized hyperbolic distribution non-Gaussian normal subordination AMS Subject Classification

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Application of EM-type algorithms to spatial data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 1997年第3期26卷 669-683页

作者： Alonso, FJ Angulo, JM Bueso, MC UNIV GRANADA DEPT ESTAD & IOE-18071 GRANADASPAIN

We consider the problem of maximum-likelihood estimation and smoothing for lattice processes using incomplete data. In a previous paper (Alonso et al., 1996) the authors developed a methodology based on an application of the EM algorithm on a state-space framework for this problem. Now, the procedure is extended using new versions of EM-type algorithms (ECM and mcecm). This has computational advantages, especially when there are many parameters to estimate. The problem of estimating the asymptotic covariance matrix for the parameter estimators is also considered (supplemented EM-type algorithms). The steps are described through an application considering the underlying state model to have an AR(1)xAR(1) structure and extension to more general models is commented on. As an example, we apply the method to the data presented by Kempton and Howes (1981).

关键词： ECM algorithm EM algorithm incomplete data lattice processes maximum likelihood mcecm algorithm prediction SECM algorithm smoothing

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Elliptical regression models for multivariate sample-selection bias correction

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2016年第3期45卷 422-438页

作者： Kim, Hea-Jung Kim, Hyoung-Moon Dongguk Univ Seoul Dept Stat Seoul South Korea Konkuk Univ Dept Appl Stat Seoul South Korea

In linear regression, a multivariate sample-selection scheme often applies to the dependent variable, which results in missing observations on the variable. This induces the sample selection bias, i.e. a standard regression analysis using only the selected cases leads to biased results. To solve the bias problem, in this paper, we propose a class of multivariate selection regression models by extending classic Heckman model to allow for multivariate sample-selection scheme and robustness against departures from normality. Necessary theories for building a formal bias correction procedure, based upon the proposed model, are obtained, and an efficient estimation method for the model is provided. Simulation results and a real data example are presented to demonstrate the performance of the estimation method and practical usefulness of the multivariate sample-selection models. (C) 2016 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Bias correction Heckman model mcecm algorithm Multivariate sample-selection regression Rectangle-screened scale mixture of normal

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Maximum likelihood estimation of nonlinear structural equation models

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PSYCHOMETRIKA 2002年第2期67卷 189-210页

作者： Lee, SY Zhu, HT Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China Univ Victoria Dept Math & Stat Victoria BC V8W 2Y2 Canada

The existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables. However, models with nonlinear relationships are often encountered in social and behavioral sciences. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model. To avoid computation of the complicated multiple integrals involved, the E-step is completed by a Metropolis-Hastings algorithm. It is shown that the M-step can be completed efficiently by simple conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis's formula. The methodology is illustrated with results from a simulation study and two real examples.

关键词： nonlinear structural equation models missing data mcecm algorithm Metropolis-Hastings algorithm standard errors estimates

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Segmented classification analysis with a class of rectangle-screened elliptical populations

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JOURNAL OF APPLIED STATISTICS 2015年第9期42卷 1877-1895页

作者： Kim, Hea-Jung Dongguk Univ Seoul Dept Stat Seoul 100715 South Korea

In many practical situations, a statistical practitioner often faces a problem of classifying an object from one of the segmented (or screened) populations where the segmentation was conducted by a set of screening variables. This paper addresses this problem, proposing and studying yet another optimal rule for classification with segmented populations. A class of q-dimensional rectangle-screened elliptically contoured (RSEC) distributions is considered for flexibly modeling the segmented populations. Based on the properties of the RSEC distributions, a parametric procedure for the segmented classification analysis (SCA) is proposed. This includes motivation for the SCA as well as some theoretical propositions regarding its optimal rule and properties. These properties allow us to establish other important results which include an efficient estimation of the rule by the Monte Carlo expectation-conditional maximization algorithm and an optimal variable selection procedure. Two numerical examples making use of utilizing a simulation study and a real dataset application and advocating the SCA procedure are also provided.

关键词： segmented classification rectangle-screened elliptically contoured distribution optimalrule variable selection mcecm algorithm 62E10 62F30

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Robust statistical modelling using the multivariate skew t distribution with complete and incomplete data

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STATISTICAL MODELLING 2011年第3期11卷 253-277页

作者： Lin, Tsung-I Lin, Tzy-Chy Natl Chung Hsing Univ Dept Appl Math Taichung 40227 Taiwan Natl Chung Hsing Univ Inst Stat Taichung 40227 Taiwan Ctr Drug Evaluat Div Clin Sci Taipei Taiwan

Missing data is inevitable in many situations that could hamper data analysis for scientific investigations. We establish flexible analytical tools for multivariate skew t models when fat-tailed, asymmetric and missing observations simultaneously occur in the input data. For the ease of computation and theoretical developments, two auxiliary indicator matrices are incorporated into the model for the determination of observed and missing components of each observation that can effectively reduce the computational complexity. Under the missing at random assumption, we present a Monte Carlo version of the expectation conditional maximization algorithm, which is performed to estimate the parameters and retrieve each missing observation with a single value. Additionally, a Metropolis-Hastings within Gibbs sampler with data augmentation is developed to account for the uncertainty of parameters as well as missing outcomes. The methodology is illustrated through two real data sets.

关键词： data augmentation mcecm algorithm missing at random MST model multiple imputation multivariate truncated t distribution

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Generalized linear latent models for multivariate longitudinal measurements mixed with hidden Markov models

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JOURNAL OF MULTIVARIATE ANALYSIS 2016年 152卷 259-275页

作者： Xia, Ye-Mao Tang, Nian-Sheng Gou, Jian-Wei Nanjing Forestry Univ Dept Appl Math Nanjing 210037 Jiangsu Peoples R China Yunnan Univ Dept Stat Kunming 650091 Peoples R China

This article presents a generalized linear latent variable model for analyzing multivariate longitudinal data within the hidden Markov model framework. The relationships among multiple items are captured by several common latent factors. The linear coregionalization method is adopted to model the temporal processes of latent variables. The merit of this modeling strategy lies in the fact that the processes among latent variables are nonseparate and codependent from each other. To account for possible heterogeneity and interrelationship among the longitudinal data, a hidden Markov model is introduced to model the transition probabilities across different latent states over time. The Monte Carlo expectation conditional maximization (mcecm) algorithm is developed to estimate unknown parameters in the proposed model. The Wald- and score-type statistics are proposed to test the related dependence of processes. A simulation study is conducted to investigate the performance of the proposed methodology. An example from a longitudinal study of cocaine use is taken to illustrate the proposed methodology. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Generalized linear latent variable model Hidden Markov model Linear coregionalization mold mcecm algorithm

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