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Local influence analysis for mixture of structural equation models

JOURNAL OF CLASSIFICATION 2004年第1期21卷 111-137页

作者： Song, XY Lee, SY Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China Sun Yat Sen Univ Guangzhou Peoples R China

Finite mixture of structural equation models is very useful to analyze data from heterogeneous populations. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influential aspects on the maximum likelihood estimation of a finite mixture of structural equation models. A Monte Carlo EM algorithm which treats both latent variables and allocation variables as hypothetical missing data is implemented. The local influence measures are developed on the basis of a Q-displacement function at the E-step of the algorithm. The diagnostic measures are based on the conformal normal curvature that can be computed easily. Building blocks of the diagnostic measures are derived, and they are evaluated via observations simulated by the Gibbs sampler from the appropriate conditional distributions. A number of interesting and novel perturbations are considered. The methodology is illustrated with a real example.

关键词： mixture structural equation models mcem algorithm Q-displacement function Gibbs sampler perturbation

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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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Linear censored regression models with skew scale mixtures of normal distributions

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JOURNAL OF APPLIED STATISTICS 2021年第16期48卷 3060-3085页

作者： Guzman, Daniel C. F. Ferreira, Clecio S. Zeller, Camila B. Univ Fed Juiz de Fora Dept Stat Juiz De Fora Brazil

A special source of difficulty in the statistical analysis is the possibility that some subjects may not have a complete observation of the response variable. Such incomplete observation of the response variable is called censoring. Censorship can occur for a variety of reasons, including limitations of measurement equipment, design of the experiment, and non-occurrence of the event of interest until the end of the study. In the presence of censoring, the dependence of the response variable on the explanatory variables can be explored through regression analysis. In this paper, we propose to examine the censorship problem in context of the class of asymmetric, i.e., we have proposed a linear regression model with censored responses based on skew scale mixtures of normal distributions. We develop a Monte Carlo EM (mcem) algorithm to perform maximum likelihood inference of the parameters in the proposed linear censored regression models with skew scale mixtures of normal distributions. The mcem algorithm has been discussed with an emphasis on the skew-normal, skew Student-t-normal, skew-slash and skew-contaminated normal distributions. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset.

关键词： Censoring mcem algorithm linear regression models skew scale mixtures of normal distributions

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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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Analysis of bivariate zero inflated count data with missing responses

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JOURNAL OF MULTIVARIATE ANALYSIS 2016年 148卷 73-82页

作者： Yang, Miao Das, Kalyan Majumdar, Anandamayee Oregon State Univ Dept Stat Corvallis OR 97330 USA Univ Calcutta Dept Stat 35 Ballygunge Circular Rd Kolkata 700019 India Soochow Univ Ctr Adv Stat & Econometr Suzhou Peoples R China

Bivariate zero-inflated Poisson regression models have recently been used in various medical and biological settings to model excess zeros. However, there has not been any definite approach to deal with the same in the event of missing responses. The model itself is complex and as the responses are paired, missing values can occur in either or both coordinates. We propose a flexible Monte Carlo expectation maximization based approach to handle bivariate zero inflated count data with missing responses. We report the results of a simulation study designed to evaluate the performance of the proposed approach. To illustrate the application of our model and methodology, we consider a bivariate data concerning the demand for health care in Australia. (c) 2016 Elsevier Inc. All rights reserved.

关键词： Bivariate zero-inflated Poisson Generalized linear model mcem algorithm Missing data

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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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A Spatial Logistic Regression Model Based on a Valid Skew-Gaussian Latent Field

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2023年第1期28卷 59-73页

作者： Tadayon, Vahid Saber, Mohammad Mehdi Higher Educ Ctr Eghlid Dept Stat Eghlid Iran

Logistic regression is commonly used to estimate the association of one (or more) independent variable(s) with a binary- dependent outcome. In many applications latent sources are both spatially dependent and non-Gaussian;thus, it is desirable to exploit both properties jointly. Spatial logistic regression is a well-established technique of including spatial dependence in logistic regression models. In this paper, we develop a spatial logistic regression model based on a valid skew-Gaussian random field. For parameter estimation, we use a Monte Carlo extension of the EM algorithm along with an approximation based on the standard logistic function. A simulation study is applied in order to determine the performance of the proposed model and also to compare the results with a recently introduced model with established efficiency. The identifiability of the parameters is investigated as well. As an illustrative purpose, an application to the Meuse heavy metals dataset is presented. Supplementary materials accompanying this paper appear online.

关键词： Binary spatial data mcem algorithm Spatial modeling Non-Gaussian random field

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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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Nonlinear structural equation modeling with distribution-free method

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Model Assisted Statistics and Applications 2011年第1期6卷 39-46页

作者： Zhao, Yan D. Rahardja, Dewi Department of Clinical Sciences Simmons Cancer Center UT Southwestern Medical Center Dallas TX United States Department of Clinical Sciences UT Southwestern Medical Center Dallas TX United States Dallas TX 75390-8590 5323 Harry Hines Blvd United States

Structural equation models (SEM) are widely used in many fields including economics and social science. Typical nonlinear SEMs consist of two parts: a linear measurement model relating observed measurements to underlying latent variables, and a nonlinear structural model describing relationships among the latent variables. For such models, we propose a pseudo likelihood approach based on a hypothetical normal mixture assumption on the latent variables. To obtain pseudo likelihood parameter estimates, a Monte Carlo EM algorithm is developed. Standard errors for the structural parameter estimates are obtained by combining an empirical observed information matrix and a bootstrap estimated covariance matrix. For nonlinear SEMs with latent variables with various distributions, we conduct simulations to show our approach produced unbiased parameter estimates and confidence intervals with nominal coverage. © 2011 - IOS Press and the authors. All rights reserved.

关键词： Bootstrap deconvolution latent variable modeling mcem algorithm normal mixture standard error estimation

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Parameter estimate with only one complete failure observation using Monte Carlo EM algorithm

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International Journal of Reliability, Quality and Safety Engineering 2001年第2期8卷 109-122页

作者： Pang, Wan-Kai Leung, Ping-Kei Xiao-Long, P.U. Shi-Song, Mao Department of Applied Mathematics Hong Kong Polytechnic University Hong Kong Department of Statistics East China Normal University Shanghai China

In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likelihood estimation of parameters becomes a difficult problem. Mao and Chen published a real data set of the lifetime of a certain type of bearings which only contains one failure data. They used a Bayesian method to analyze the data and obtained some results for model parameter estimation. However, in their method the choice of prior distribution will affect heavily the final results. In this paper, we propose a Monte Carlo EM (mcem) algorithm to estimate reliability model parameters using the Weibull distribution. Based on the same data set of Mao and Chen, we obtain some results using the mcem algorithm. Our results do not depend on the choice of arbitrary prior distributions. © World Scientific Publishing Company.

关键词： EM algorithm Failure data Likelihood function mcem algorithm Weibull distribution

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