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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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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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Multiple-response logistic regression modeling with application to an analysis of cirrhosis liver disease data

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COMPUTATIONAL STATISTICS 2024年 1-24页

作者： Yang, Jing-Nan Tian, Yu-Zhu Wang, Yue Wu, Chun-Ho Northwest Normal Univ Sch Math & Stat Lanzhou Peoples R China Gansu Prov Res Ctr Basic Disciplines Math & Stat Lanzhou Peoples R China Educ Univ Hong Kong Dept Math & Informat Technol Hong Kong Peoples R China Hang Seng Univ Hong Kong Sch Decis Sci Hong Kong Peoples R China

In practical data analysis, individual measurements usually include two or more responses, and some statistical correlations often exist between the responses. Especially in medical data analysis, observations are often binary responses. A class of multi-response logistic regression model based on a joint modeling approach is investigated in this paper, and an application to a group data of primary biliary cirrhosis diseases is considered. Firstly, we propose a new class of multi-response logistic distribution and investigate its statistical properties. Secondly, a multi-response logistic regression model is constructed using a latent variable model and multi-variate logistic error distribution. Furthermore, the parameter estimation method of the model is provided by applying the monte carlo expectation maximization (mcem) algorithm and the multiple imputation method. Finally, numerical simulations and comparative predictions on a test set are performed to validate the finite sample performance of the proposed model, and the model is applied to a cirrhosis disease dataset for analysis.

关键词： Multi-response logistic regression Latent variable model mcem algorithm Multiple imputation Primary biliary cirrhosis (PBC)

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Quantile regression in random effects meta-analysis model

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STATISTICAL METHODS AND APPLICATIONS 2023年第2期32卷 469-492页

作者： Dai, Xiaowen Jin, Libin Shi, Lei Shanghai Lixin Univ Accounting & Finance Sch Stat & Math Shanghai 201209 Peoples R China Shanghai Lixin Univ Accounting & Finance Interdisciplinary Res Inst Data Sci Shanghai 201209 Peoples R China Yunnan Univ Finance & Econ Sch Stat & Math Kunming 650221 Yunnan Peoples R China

In meta-analysis model, due to the appearance of publication bias or outliers, as well as the small sample size, the normal assumption is usually unreliable. Therefore, the exploration of more robust estimation, such quantile regression (QR) method, is extremely important in meta-analysis area. This paper studies the QR estimation method in random-effects meta-analysis model based on the reformulation by asymmetric Laplace distribution (ALD). The maximum likelihood estimation using Monte Carlo Expectation Maximization algorithm and the Bayesian estimation using Markov chain Monte Carlo (MCMC) algorithm are proposed for computation of the QR estimates. The significance tests of regression coefficients are suggested using likelihood ratio statistics. For MCMC algorithm, a simple and efficient Gibbs sampling algorithm is employed based on a location-scale mixture representation of the ALD, and information criterions are considered for choosing the hyper-parameters. Monte Carlo simulations are conducted to study the finite sample performance of the proposed methodology and analysis of two real data sets are presented for illustrations. Our results show that QR estimation methods perform very well, especially in case of non-normal assumption in meta-regression models. The detailed algorithms and software code are available for easy use in applications.

关键词： Random-effects meta-analysis model Quantile regression Asymmetric Laplace distribution mcem algorithm MCMC algorithm

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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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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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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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An Improved Monte Carlo EM Acceleration algorithm

International Core Journal of Engineering

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International Core Journal of Engineering 2024年第5期10卷 493-499页

作者： Yugui Lu Qunlan Li

In this paper, an improved Monte Carlo EM (mcem) acceleration algorithm is proposed, aiming at solving the problems of slow convergence and difficult integral calculation of the traditional mcem algorithm when dealing with complex models. The article first reviews the basic concepts and application background of EM algorithms and mcem algorithms, and then points out the limitations of mcem algorithms with high-dimensional data and complex models. To overcome these challenges, the authors introduce a new algorithm that approximates the solution of N-R step integrals by means of a Monte Carlo simulation method, which improves the convergence speed of the algorithm and maintains the quadratic convergence property. Specifically, the improved mcem acceleration algorithm consists of the following key steps: random sampling in the E1 step, computation of the expectation in the E2 step, maximization of the objective function in the M step, and approximation of the integral using the Monte Carlo method in the improved N-R step. Through numerical examples, the authors demonstrate the advantages of the improved algorithm over the original mcem algorithm and the mcem accelerated algorithm in terms of accuracy of parameter estimation and speed of convergence. In addition, the article discusses the effect of random number selection on the performance of the algorithm and provides a method for choosing the appropriate number of random numbers. In conclusion, the improved mcem acceleration algorithm effectively improves the computational efficiency and accuracy of the results when dealing with complex data models, which has important practical application value for statistical analysis in the era of big data.

关键词： mcem algorithm Newton-Raphson algorithm Monte Carlo Simulation

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