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Likelihood-based quantile mixed effects models for longitudinal data with multiple features via mcem algorithm

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2020年第2期49卷 317-334页

作者： Tian, Yuzhu Wang, Liyong Tang, Manlai Tian, Maozai Henan Univ Sci & Technol Sch Math & Stat Luoyang 471023 Peoples R China Cent Univ Finance & Econ Sch Stat & Math Beijing Peoples R China Hang Seng Management Coll Dept Math & Stat Hong Kong Peoples R China Renmin Univ China Sch Stat Beijing Peoples R China

In longitudinal data analysis, many data features are frequently encountered in practice. For example, variates are usually measured with censoring, substantial errors and non-normal feature, etc. In such case, it is impossible to give a precise result by conducting statistical inference of separate analysis. The joint modeling may be a considerable alternative. The superiority of joint modeling is that it can implement a simultaneous analysis for longitudinal mixed models with random effects, censoring, nor-normal errors, errors in covariates and heavy-tailed feature by pooling all data information together. However, most of traditional modeling methods aim at depicting the average variation of outcome variable conditionally on covariates, which may result in non-robust estimation results when suffering outliers or non-normal errors. Quantile regression provides an attractive alternative to model longitudinal data with multiple data features, which can draw a complete picture of the conditional distributions of outcome variable and bring out robust estimation results. In this paper, we conduct the likelihood-based joint quantile regression for longitudinal mixed models by accounting for the above multiple data features simultaneously. Based on the asymmetric Laplace distribution (ALD), the Monte Carlo Expectation-Maximization (mcem) algorithm is employed to address the estimation problem. Finally, some Monte Carlo simulations are conducted and an AIDS data analysis is provided to illustrate the developed procedures.

关键词： Censoring covariates in error heavy-tailed distribution joint modeling mcem algorithm mixed effects models quantile regression analysis

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Parameter estimation for grouped data using EM and mcem algorithms

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第8期53卷 3616-3637页

作者： AghahosseinaliShirazi, Zahra da Silva, Joao Pedro A. R. de Souza, Camila P. E. Univ Western Ontario London ON Canada Univ Sao Paulo Sao Paulo SP Brazil

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For example, rather than providing the exact measurements of their clients, they may only provide researchers with grouped data, that is, the number of clients falling in each of a set of non-overlapping measurement intervals. The challenge is to estimate the mean and variance structure of the hidden ungrouped data based on the observed grouped data. To tackle this problem, this work considers the exact observed data likelihood and applies the Expectation-Maximization (EM) and Monte Carlo EM (mcem) algorithms for cases where the hidden data follow a univariate, bivariate, or multivariate normal distribution. Simulation studies are conducted to evaluate the performance of the proposed EM and mcem algorithms. The well-known Galton data set is considered as an application example.

关键词： EM algorithm Grouped data Maximum likelihood estimation mcem algorithm Normal distribution

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Joint mean-covariance random effect model for longitudinal data

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BIOMETRICAL JOURNAL 2020年第1期62卷 7-23页

作者： Bai, Yongxin Qian, Manling Tian, Maozai Renmin Univ China Ctr Appl Stat Sch Stat Beijing 100872 Peoples R China Xinjiang Univ Finance & Econ Sch Stat & Informat Urumqi Peoples R China Lanzhou Univ Finance & Econ Sch Stat Lanzhou Gansu Peoples R China

In this paper, we consider the inherent association between mean and covariance in the joint mean-covariance modeling and propose a joint mean-covariance random effect model based on the modified Cholesky decomposition for longitudinal data. Meanwhile, we apply M-H algorithm to simulate the posterior distributions of model parameters. Besides, a computationally efficient Monte Carlo expectation maximization (mcem) algorithm is developed for carrying out maximum likelihood estimation. Simulation studies show that the model taking into account the inherent association between mean and covariance has smaller standard deviations of the estimators of parameters, which makes the statistical inferences much more reliable. In the real data analysis, the estimation of parameters in the mean and covariance structure is highly efficient.

关键词： joint mean-covariance model longitudinal data mcem algorithm random effect

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Model Selection of Zero-Inflated Generalized Power Series Distribution with Missing Responses

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2012年第6期41卷 1013-1028页

作者： Fu, Ying-Zi Kunming Sci & Technol Univ Sch Sci Kunming 313000 Yunnan Province Peoples R China

Count data with extra zeros are common in many biomedical applications and the zero-inflated generalized power series (ZIGPS) distribution may be appropriate, in which the baseline discrete distribution is a generalized power series distribution, which is a natural extension of power series distribution. In this article, a Monte Carlo EM (mcem) algorithm is proposed to obtain maximum likelihood estimates and standard errors for ZIGPS distribution with missing responses. A Monte Carlo approximation method combining the Gibbs sampler and M-H algorithm is used to implement E-step, whereas the M-step is completed via the method of conditional maximization. As classical model selection procedure such as Akaike's information criterion (AIC) becomes problematic for our considered ZIGPS distribution with incomplete data, some variations on AIC are presented under two different missingness mechanisms, namely, missing at random (MAR) and missing not at random (MNAR), respectively. The most attractive point is that our methods cannot only be used to select distributions and variables, but also can be used to find out whether there exists zero-inflation or not, which is conducted via score test or Bayesian test in previous literature. Finally, a simulation study and a real example are used to illustrate the proposed methodology.

关键词： AIC mcem algorithm Missing data Model selection Zero-inflation

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Mixed Deep Gaussian Mixture Model: a clustering model for mixed datasets

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2022年第1期16卷 31-53页

作者： Fuchs, Robin Pommeret, Denys Viroli, Cinzia Aix Marseille Univ CNRS Cent Marseille I2MMIO Marseille France Univ Lyon UCBL ISFA LSAF EA2429 Lyon France Univ Bologna Dept Stat Sci Bologna Italy

Clustering mixed data presents numerous challenges inherent to the very heterogeneous nature of the variables. A clustering algorithm should be able, despite of this heterogeneity, to extract discriminant pieces of information from the variables in order to design groups. In this work we introduce a multilayer architecture model-based clustering method called Mixed Deep Gaussian Mixture Model that can be viewed as an automatic way to merge the clustering performed separately on continuous and non-continuous data. This architecture is flexible and can be adapted to mixed as well as to continuous or non-continuous data. In this sense we generalize Generalized Linear Latent Variable Models and Deep Gaussian Mixture Models. We also design a new initialisation strategy and a data driven method that selects the best specification of the model and the optimal number of clusters for a given dataset. Besides, our model provides continuous low-dimensional representations of the data which can be a useful tool to visualize mixed datasets. Finally, we validate the performance of our approach comparing its results with state-of-the-art mixed data clustering models over several commonly used datasets.

关键词： Binary and count data Deep Gaussian Mixture Model Generalized Linear Latent Variable Model mcem algorithm Ordinal and categorical data Two-heads architecture

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Modelling the aggregate loss for insurance claims with dependence

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第9期50卷 2080-2095页

作者： Wang, Ning Qian, Linyi Zhang, Nan Liu, Zehui East China Normal Univ Sch Stat Shanghai Peoples R China Macquarie Univ Macquarie Business Sch Dept Actuarial Studies & Business Analyt Macquarie Pk Australia East China Normal Univ Key Lab Adv Theory & Applicat Stat & Data Sci Sch Stat MOE 3663 North Zhongshan Rd Shanghai 200062 Peoples R China Ind Bank Co Ltd Ctr Credit Card Shanghai Peoples R China

In this paper, we propose a new model to relax the impractical independence assumption between the counts and the amounts of insurance claims, which is commonly made in the existing literature for mathematical convenience. When considering the dependence between the claim counts and the claim amounts, we treat the number of claims as an explanatory variable in the model for claim sizes. Besides, generalized linear models (GLMs) are employed to fit the claim counts in a given time period. To describe the claim amounts which are repeatedly measured on a group of subjects over time, we adopt generalized linear mixed models (GLMMs) to incorporate the dependence among the related observations on the same subject. In addition, a Monte Carlo Expectation-Maximization (mcem) algorithm is proposed by using a Metropolis-Hastings algorithm sampling scheme to obtain the maximum likelihood estimates of the parameters for the linear predictor and variance component. Finally, we conduct a simulation to illustrate the feasibility of our proposed model.

关键词： Claim counts claim amounts dependence generalized linear models generalized linear mixed models mcem algorithm Metropolis-Hastings algorithm

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Maximum likelihood analysis of a general latent variable model with hierarchically mixed data

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BIOMETRICS 2004年第3期60卷 624-636页

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

A general two-level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels. Nonlinear relationships among the latent variables in the structural equations at both levels, as well as the effects of fixed covariates in the measurement and structural equations at both levels, can be analyzed within the framework. Moreover, the methodology can be applied to hierarchically mixed continuous, dichotomous, and polytomous data. A Monte Carlo EM algorithm is implemented to produce the maximum likelihood estimate. The E-step is completed by approximating the conditional expectations through observations that are simulated by Markov chain Monte Carlo methods, while the M-step is completed by conditional maximization. A procedure is proposed for computing the complicated observed-data log likelihood and the BIC for model comparison. The methods are illustrated by using a real data set.

关键词： covariates dichotomous and polytomous data mcem algorithm model comparison nonlinear structural equations path sampling two-level latent variable model.

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Weighted composite quantile regression for longitudinal mixed effects models with application to AIDS studies

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第6期50卷 1837-1853页

作者： Tian, Yuzhu Wang, Liyong Tang, Manlai Tian, Maozai Northwest Normal Univ Sch Math & Stat Lanzhou Gansu Peoples R China Cent Univ Finance & Econ Sch Stat & Math Beijing Peoples R China HangSeng Univ Hong Kong Dept Math & Stat Hong Kong Hong Kong Peoples R China Renmin Univ China Sch Stat Beijing Peoples R China

In longitudinal data studies, a conjunct feature of the multitudinous statistical methods is to depict the conditional mean of outcome variable. However, the conditional mean is not the best measure of centrality which may be affected by outliers. As an available alterative, composite quantile regression (CQR) can result in robust estimation results even for non-normal error distributions in regression analysis instead of the least square estimation (LSE). In this paper, we develop a weighted CQR of longitudinal mixed model from a likelihood framework based on the composite asymmetric Laplace distribution (CALD). Using the mixture representation of the CALD, we establish the joint hierarchical likelihood of the model and achieve the iterative weighted least square estimators of unknown parameters via the mcem (Monte Carlo Expectation Maximization) algorithm. Finally, the developed procedures are illustrated by Monte Carlo simulations and an AIDS (Acquired Immune Deficiency Syndrome) data analysis.

关键词： Longitudinal data analysis AIDS data Quantile regression (QR) mcem algorithm Heavy-tailed random effects

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Spatio-Temporal Analysis and Prediction of Mass Telecommunication Base Station Failure Events

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TECHNOMETRICS 2024年第1期66卷 77-89页

作者： Wu, Tong Wang, Yudong Ye, Zhi-Sheng Chen, Nan Natl Univ Singapore Dept Ind Syst Engn & Management Singapore Singapore Natl Univ Singapore Dept Ind Syst Engn & Management Singapore 117576 Singapore

Large-scale telecommunication systems are lifeline infrastructure in modern society. A telecommunication system typically consists of a huge number of base stations with diverse geographical locations across a country, which highly complicates maintenance operations. To allocate maintenance resource properly, it is important to have a good understanding on the failure pattern of these base stations. Statistical inference of recurrent failures of these base stations is challenging because of the large number of base stations and the spatial correlation of their failure processes. Based on eight-month failure data of telecommunication base stations in Harbin, China, we propose a customized nonhomogeneous Poisson process (NHPP) model for recurrent failure data from telecommunication systems. The model consists of two layers, where the temporal layer applies an NHPP with station-specific frailty for failures of each base station, and the spatial layer uses a multivariate lognormal distribution to characterize the correlation among the frailties. The Monte Carlo EM (mcem) algorithm is applied to estimate parameters included in the proposed model. We demonstrate the proposed model using the Harbin telecommunication system example with 7725 base stations and 4615 failure records.

关键词： Failure prediction mcem algorithm NHPP Spatial frailty Telecommunication system

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Maximum likelihood estimation and model comparison of nonlinear structural equation models with continuous and polytomous variables

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2003年第1-2期44卷 125-142页

作者： Lee, SY Song, XY Chinese Univ Hong Kong Inst Stat Dept Stat Hong Kong Hong Kong Peoples R China Zhongshan Univ Guangzhou Peoples R China

Recently, it is recognized that nonlinear relationships among latent variables in a structural equation model are important. In this article, maximum likelihood (ML) analysis of a general nonlinear structural equation model that contains fixed covariates in the measurement equation and the nonlinear structural equation is investigated. A mcem algorithm is implemented to obtain the ML estimates, in which the E-step is completed with the help of a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm whilst the M-step is completed by conditional maximization. The importance sampling is employed to compute the observed-data likelihood in the Bayesian Information Criterion for model comparison. The methodology is illustrated with a simulation study and a real example. (C) 2002 Elsevier B.V. All rights reserved.

关键词： latent variables mcem algorithm Gibbs sampler Metropolis-Hastings algorithm importance sampling Bayesian information criterion

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