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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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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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The Monte Carlo EM method for estimating multivariate tobit latent variable models

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2009年第9期79卷 1095-1107页

作者： Zhou, X. C. Liu, X. S. Nanjing Univ Aeronaut & Astronaut Inst Nanosci Nanjing 210016 Jiangsu Peoples R China Tongling Univ Dept Math & Comp Sci Tongling Anhui Peoples R China

We propose a multivariate tobit (MT) latent variable model that is defined by a confirmatory factor analysis with covariates for analysing the mixed type data, which is inherently non-negative and sometimes has a large proportion of zeros. Some useful MT models are special cases of our proposed model. To obtain maximum likelihood estimates, we use the expectation maximum algorithm with its E-step via the Gibbs sampler made feasible by Monte Carlo simulation and its M-step greatly simplified by a sequence of conditional maximization. Standard errors are evaluated by inverting a Monte Carlo approximation of the information matrix using Louis's method. The methodology is illustrated with a simulation study and a real example.

关键词： multivariate tobit model factor analysis latent variable maximum likelihood estimates Gibbs sampler mcem algorithm

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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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A resource selection model for analyzing pseudoreplicated data due to grouping behavior of animals

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2008年第3期13卷 294-312页

作者： Okamura, Hiroshi Kiyota, Masashi Kitakado, Toshihide Natl Res Inst Far Seas Fisheries Kanagawa 2368648 Japan Tokyo Univ Marine Sci & Technol Minato Ku Tokyo 1088477 Japan

Quantifying resource selection is of primary interest in animal ecology. Many analyses of resource selection assume spatial and temporal independence of the sampling unit. Autocorrelation between observations, which is a general property of ecological variables, causes difficulties for most standard statistical procedures of resource selection because autocorrelated data violate the assumption of independence. To overcome this problem, we develop a mixed-effects model to estimate resource selection functions from data that are autocorrelated because of unobserved grouping behavior by animals. In the application of the expectation-maximization (EM) algorithm, the computation of the conditional expectation of the complete-data log-likelihood function does not have a closed-form solution requiring numerical integration. A Monte Carlo EM algorithm with Gibbs sampling can be used effectively in such situations to find exact maximum likelihood estimates. We propose a simple automated Monte Carlo EM algorithm with multiple sequences in which the Monte Carlo sample size is increased when the FM step is swamped by Monte Carlo errors. We demonstrate that the model can detect inherent autocorrelation and provide reasonable variance estimates when applied 10 nocturnal bird migration data. This approach could also be applied to ecological processes with various types of spatially and temporally autocorrelated data, circumventing serious problems caused by dangerous pseudoreplication.

关键词： autocorrelation Gibbs sampling mcem algorithm nocturnal bird migration portable ceilometer

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A unified maximum likelihood approach for analyzing structural equation models with missing nonstandard data

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SOCIOLOGICAL METHODS & RESEARCH 2007年第3期35卷 352-381页

作者： Lee, Sik-Yum Song, Xin-Yuan Chinese Univ Hong Kong Dept Stat Hong Kong Hong Kong Peoples R China

In this article, the authors present a unified approach for maximum likelihood analysis of structural equation models that involve subtle model formulations and nonstandard data structures. Based on the idea of data augmentation, they describe a generic Monte Carlo expectation-maximization algorithm for estimation. They propose path sampling for computing the observed data likelihood functions that usually involve complicated integrals and show how to apply this method for computing the Bayesian information criterion for model comparison. An application of the proposed unified approach to a two-level nonlinear structural equation model with missing continuous and ordered categorical data is presented. An illustrative example with a real data set is given.

关键词： mcem algorithm Gibbs sampler Bayesian information criterion path sampling

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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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Estimation of wood fibre length distributions from censored data through an EM algorithm

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SCANDINAVIAN JOURNAL OF STATISTICS 2006年第3期33卷 503-522页

作者： Svensson, Ingrid Sjostedt-De Luna, Sara Bondesson, Lennart Umea Univ Dept Math & Math Sci SE-90187 Umea Sweden

An expectation maximization (EM) algorithm is proposed to find fibre length distributions in standing trees. The available data come from cylindric wood samples (increment cores). The sample contains uncut fibres as well as fibres cut once or twice. The sample contains not only fibres, but also other cells, the so-called 'fines'. The lengths are measured by an automatic fibre-analyser, which is not able to distinguish fines from fibres and cannot tell if a cell has been cut. The data thus come from a censored version of a mixture of the fine and fibre length distributions in the tree. The parameters of the length distributions are estimated by a stochastic version of the EM algorithm, and an estimate of the corresponding covariance matrix is derived. The method is applied to data from northern Sweden. A simulation study is also presented. The method works well for sample sizes commonly obtained from increment cores.

关键词： censoring EM algorithm fibre length distribution increment core length bias mcem algorithm mixture distribution

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Maximum likelihood methods in treating outliers and symmetrically heavy-tailed distributions for nonlinear structural equation models with missing data

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PSYCHOMETRIKA 2006年第3期71卷 565-585页

作者： Lee, Sik-Yum Xia, Ye-Mao Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China

By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the development of robust methods to reduce the influence of outliers and the distributional deviation in the analysis. In this paper we develop a maximum likelihood (ML) approach that is robust to outliers and symmetrically heavy-tailed distributions for analyzing nonlinear SEMs with ignorable missing data. The analytic strategy is to incorporate a general class of distributions into the latent variables and the error measurements in the measurement and structural equations. A Monte Carlo EM (mcem) algorithm is constructed to obtain the ML estimates, and a path sampling procedure is implemented to compute the observed-data log-likelihood and then the Bayesian information criterion for model comparison. The proposed methodologies are illustrated with simulation studies and an example.

关键词： outliers heavy-tailed distributions mcem algorithm Gibbs sampler path sampling Bayesian information criterion

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Linear unmixing of multivariate observations: A structural model

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2005年第472期100卷 1328-1342页

作者： Wolbers, M Stahel, W F Hoffmann La Roche & Co Ltd Dept Biostat CH-4070 Basel Switzerland ETH Stat Consulting Grp Seminar Stat CH-8092 Zurich Switzerland

In many fields of science there are multivariate observations that may be assumed to be generated by a (physical) linear mixing process of contributions from different sources. If the compositions of the sources are constant for different observations, then these observations are, up to a random error term, nonnegative linear combinations of a fixed set of so-called "source profiles" that characterize the sources. The goal of linear unmixing is to recover both the source profiles and the source activities (also called scores) from a multivariate dataset. We present a new parametric mixing model that assumes a multivariate lognormal distribution for the scores. This model is proved to be identifiable. Moreover, consistency and asymptotic normality of the maximum likelihood estimator (MLE) are established in special cases. To calculate the MLE, we propose the combination of two variants of the Monte Carlo EM algorithm. The proposed model is applied to simulated datasets and to a set of air pollution measurements. In addition to the basic model, several extensions are discussed.

关键词： identifiability latent variables linear mixing model mcem algorithm receptor modeling source apportionment

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