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Markov and Semi-Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

BIOMETRICS 2010年第3期66卷 753-762页

作者： Chaubert-Pereira, Florence Guedon, Yann Lavergne, Christian Trottier, Catherine CIRAD UMR Dev & Ameliorat Plantes F-34398 Montpellier 5 France INRIA F-34398 Montpellier 5 France Univ Montpellier 3 Inst Math & Modelisat Montpellier Case Courrier 051 F-34095 Montpellier 5 France

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.

关键词： Individual random effect Markov switching model mcem algorithm Plant structure analysis Semi-Markov switching model

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A Wiener-based degradation model with logistic distributed measurement errors and remaining useful life estimation

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2018年第6期34卷 1289-1303页

作者： Shen, Yan Shen, Lijuan Xu, Wangtu Xiamen Univ Sch Econ Dept Stat 422 South Siming Rd Xiamen 361005 Peoples R China Natl Univ Singapore Dept Ind Syst Engn & Management Singapore Singapore Xiamen Univ Sch Architecture & Civil Engn Dept Urban Planning Xiamen Peoples R China

Degradation data analysis, which investigates degradation processes of products to extrapolate the lifetime properties, is an effective method for reliability analysis. But degradation data that reflect a product's inherent randomness of degradation are often contaminated by measurement errors. To deal with the problem, this paper proposes a Wiener-based model with an assumption of logistic distributed measurement errors and adopts the Monte Carlo expectation-maximization method together with the Gibbs sampling for parameter estimation. Based on the model and parameter estimates, an efficient algorithm is proposed for a quick calculation of maximum likelihood value. Also, the estimation of remaining useful lifetime is discussed. Simulation results show that the proposed model is relatively better and more robust in comparison with the Wiener process with Gaussian noises. Finally, the application of the proposed model is illustrated by an example.

关键词： Gibbs sampling logistic distribution maximum likelihood value measurement error mcem algorithm

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Assessing local influence for nonlinear structural equation models with ignorable missing data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2006年第5期50卷 1356-1377页

作者： Lee, SY Lu, B Song, XY Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China

A method is proposed in this paper to assess the local influence of minor perturbations for a nonlinear structural equation model with missing data that are missing at random. The main idea is to apply Zhu and Lee's (J. Roy. Statist. Soc. Ser. B 63 (2001) 111) approach to the conditional expectation of the complete-data log-likelihood function in the corresponding EM algorithm for deriving the conformal normal curvature. Building blocks for achieving the diagnostic measures are computed via latent variables that are generated by the Gibbs sampler and Metropolis-Hastings algorithm. It is shown that the proposed methodology is feasible for a wide variety of perturbation schemes. To illustrate the methodology, results that are obtained from analyses of some artificial examples, a simulation study, and a real example are presented. (C) 2004 Elsevier B.V. All rights reserved.

关键词： conformal normal curvature Gibbs sampler local influence mcem algorithm

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General Path Models for Degradation Data With Multiple Characteristics and Covariates

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TECHNOMETRICS 2021年第3期63卷 354-369页

作者： Lu, Lu Wang, Bingxing Hong, Yili Ye, Zhisheng Univ S Florida Dept Math & Stat Tampa FL 33620 USA Zhejiang Gongshang Univ Sch Stat Hangzhou 310018 Peoples R China Virginia Tech Dept Stat Blacksburg VA USA Natl Univ Singapore Dept Ind Syst Engn & Management Singapore Singapore

Degradation data have been broadly used for assessing product and system reliability. Most existing work focuses on modeling and analysis of degradation data with a single characteristic. In some degradation tests, interest lies in measuring multiple characteristics of the product degradation process to understand different aspects of the reliability performance, resulting in degradation data with multiple characteristics. The literature on modeling such data is scarce. Motivated by the photodegradation process of polymeric material, we propose a multivariate general path model for analyzing degradation data with multiple degradation characteristics (DCs). The model incorporates covariates for modeling the nonlinear degradation path. It also includes random effects that are correlated among the multiple DCs to capture the unit-to-unit variation in the individual degradation paths and to model the interdependence among the multivariate measurements. An expectation-maximization algorithm combined with the Markov chain Monte Carlo simulation is developed for estimating the model parameters and predicting system reliability with quantified uncertainty. The performance of the developed method is evaluated and compared with existing methods through a simulation study. The implementation of the method is illustrated through two examples with different forms of reliability functions. The main motivating example analyzes the coating degradation data with a closed-form reliability function, while the second example on analyzing the Device-B data demonstrates a more general simulation approach for dealing with analytically intractable reliability functions.

关键词： mcem algorithm Multivariate degradation Photodegradation Polymeric materials Random effects Service life prediction

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An optimal classification rule for multiple interval-screened scale mixture of normal populations

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2013年第2期42卷 191-203页

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

This paper considers a new classification case where K categories of the target variable are defined by disjoint intervals of an underlying variable and proposes an optimal rule for the classification. A parametric classification model, known as interval-screened scale mixture of normal model, is used to derive the rule that classifies individuals into K populations defined by K disjoint intervals of the variable (screening variable). The effectiveness of the rule is verified by the simulation and empirical studies that compare its performance with other existing classification rules. The cross-validation error rate is used as the measure of performance. Necessary theories for deriving the rule, an mcem algorithm for estimating the rule, and the interesting characteristics of the rule are also provided. (C) 2013 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Classification analysis mcem algorithm Screened scale mixture of normal distribution Optimal rule

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Geostatistical Modelling Using Non-Gaussian Matern Fields

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SCANDINAVIAN JOURNAL OF STATISTICS 2015年第3期42卷 872-890页

作者： Wallin, Jonas Bolin, David Gothenburg Univ Dept Math Sci S-41124 Gothenburg Sweden Chalmers Univ Technol Dept Math Stat SE-41258 Gothenburg Sweden

This work provides a class of non-Gaussian spatial Matern fields which are useful for analysing geostatistical data. The models are constructed as solutions to stochastic partial differential equations driven by generalized hyperbolic noise and are incorporated in a standard geostatistical setting with irregularly spaced observations, measurement errors and covariates. A maximum likelihood estimation technique based on the Monte Carlo expectation-maximization algorithm is presented, and a Monte Carlo method for spatial prediction is derived. Finally, an application to precipitation data is presented, and the performance of the non-Gaussian models is compared with standard Gaussian and transformed Gaussian models through cross-validation.

关键词： Laplace Markov random fields Matern covariances mcem algorithm normal inverse Gaussian SPDE variance Gamma

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Copula-frailty models for recurrent event data based on Monte Carlo EM algorithm

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2021年第17期91卷 3530-3548页

作者： Bedair, Khaled F. Hong, Yili Al-Khalidi, Hussein R. Tanta Univ Fac Commerce Tanta Egypt Univ Dundee Sch Med Dundee Scotland Virginia Tech Dept Stat Blacksburg VA 24061 USA Duke Univ Dept Biostat & Bioinformat Durham NC USA

Multi-type recurrent events are often encountered in medical applications when two or more different event types could repeatedly occur over an observation period. For example, patients may experience recurrences of multi-type nonmelanoma skin cancers in a clinical trial for skin cancer prevention. The aims in those applications are to characterize features of the marginal processes, evaluate covariate effects, and quantify both the within-subject recurrence dependence and the dependence among different event types. We use copula-frailty models to analyze correlated recurrent events of different types. Parameter estimation and inference are carried out by using a Monte Carlo expectation-maximization (mcem) algorithm, which can handle a relatively large (i.e. three or more) number of event types. Performances of the proposed methods are evaluated via extensive simulation studies. The developed methods are used to model the recurrences of skin cancer with different types.

关键词： Clinical trial mcem algorithm multi-type recurrences multivariate frailty skin cancers survival models

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A two-level structural equation model approach for analyzing multivariate longitudinal responses

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STATISTICS IN MEDICINE 2008年第16期27卷 3017-3041页

作者： Song, Xin-Yuan Lee, Sik-Yum Hser, Yih-Ing Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China Univ Calif Los Angeles Integrated Substance Abuse Program Los Angeles CA USA

The analysis of longitudinal data to study changes in variables measured repeatedly over time has received considerable attention in many fields. This paper proposes a two-level structural equation model for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables. The first-level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that are changed with time. The second level is defined for individuals to assess their characteristics that are invariant with time. The proposed model accommodates fixed covariates, nonlinear terms of the latent variables, and missing data. A maximum likelihood (ML) approach is developed for the estimation of parameters and model comparison. Results of a Simulation study indicate that the performance of the ML estimation is satisfactory. The proposed methodology is applied to a longitudinal study concerning cocaine use. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： latent variables longitudinal study on cocaine use maximum likelihood mcem algorithm model comparison ordered categorical variables

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MAXIMUM LIKELIHOOD ESTIMATION FOR SIMPLEX DISTRIBUTION NONLINEAR MIXED MODELS VIA AN EM algorithm

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INTERNATIONAL JOURNAL OF BIOMATHEMATICS 2009年第1期2卷 9-17页

作者： Wei, Hongjie Zhang, Wenzhuan Chinese Acad Trop Agr Sci Rubber Res Inst Danzhou 571737 Hainan Peoples R China Guizhou Coll Finance & Econ Sch Math & Stat Guiyang 550004 Guizhou Peoples R China

Longitudinal continuous proportional data is common in many fields such as biomedical research, psychological research and so on. As shown in [16], such data can be fitted with simplex models. Based on the original models of [16] which assumed a fixed effect for every subject, this paper extends the models by adding random effects and proposes simplex distribution nonlinear mixed models which are one kind of nonlinear reproductive dispersion mixed models. By treating the random effects in the models as hypothetical missing data and applying Metropolis-Hastings (M-H) algorithm, this paper develops an EM algorithm with Markov chain Monte-Carlo method for maximum likelihood estimation in the models. The method is illustrated with the same data from an ophthalmology study on the use of intraocular gas in retinal surgeries in [16] for ease of comparison.

关键词： Simplex distribution nonlinear mixed models maximum likelihood estimates mcem algorithm M-H algorithm Newton-Raphson iteration longitudinal proportional data

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Semiparametric analysis of longitudinal zero-inflated count data

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JOURNAL OF MULTIVARIATE ANALYSIS 2011年第1期102卷 61-72页

作者： Feng, Jiarui Zhu, Zhongyi Fudan Univ Dept Stat Shanghai 200433 Peoples R China

In this article, we consider a semiparametric zero-inflated Poisson mixed model that postulates a possible nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate in the longitudinal studies. A penalized log-likelihood function is proposed and Monte Carlo expectation-maximization algorithm is used to derive the estimates. Under some mild conditions, we establish the consistency and asymptotic normality of the resulting estimators. Simulation studies are carried out to investigate the finite sample performance of the proposed method. For illustration purposes, the method is applied to a data set from a pharmaceutical company where the variable of interest is the number of episodes of side effects after the patient has taken the treatments. (C) 2010 Elsevier Inc. All rights reserved.

关键词： ZIP regression Mixed model Penalized spline mcem algorithm

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