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Quantile regression in random effects meta-analysis model

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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Maximum likelihood estimation and model comparison for mixtures of structural equation models with ignorable missing data

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JOURNAL OF CLASSIFICATION 2003年第2期20卷 221-255页

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

The objective of this paper is to develop the maximum likelihood approach for analyzing a finite mixture of structural equation models with missing data that are missing at random. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates. A well-known statistic in model comparison, namely the Bayesian Information Criterion (BIC), is used for model comparison. With the presence of missing data, the computation of the observed-data likelihood function value involved in the BIC is not straightforward. A procedure based on path sampling is developed to compute this function value. It is shown by means of simulation studies that ignoring the incomplete data with missing entries gives less accurate ML estimates. An illustrative real example is also presented.

关键词： BIC Gibbs sampler MAR missing data mcem algorithm Mixture Path sampling

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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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Maximum likelihood inference for multivariate frailty models using an automated Monte Carlo EM algorithm

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LIFETIME DATA ANALYSIS 2002年第4期8卷 349-360页

作者： Ripatti, S Larsen, K Palmgren, J Univ Helsinki Rolf Nevanlinna Inst FIN-00014 Helsinki Finland Stockholm Univ Dept Matemat Stat Stockholm Sweden Univ Copenhagen Dept Biostat DK-1168 Copenhagen Denmark Karolinska Inst S-10401 Stockholm Sweden

We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples drawn from the posterior distribution of the frailties using rejection sampling. The maximization step reduces to a standard partial likelihood maximization. We also propose a simple rule based on the relative change in the parameter estimates to decide on sample size in each iteration and a stopping time for the algorithm. An important new concept is acquiring absolute convergence of the algorithm through sample size determination and an efficient sampling technique. The method is illustrated using a rat carcinogenesis dataset and data on vase lifetimes of cut roses. The estimation results are compared with approximate inference based on penalized partial likelihood using these two examples. Unlike the penalized partial likelihood estimation, the proposed full maximum likelihood estimation method accounts for all the uncertainty while estimating standard errors for the parameters.

关键词： mcem algorithm multivariate survival model random effects variance components

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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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Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution

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COMPUTATIONAL STATISTICS 2013年第4期28卷 1485-1500页

作者： Jiang, Jie Liu, Xinsheng Yu, Keming Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Inst Nano Sci Nanjing 210016 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Sci Nanjing 210016 Peoples R China Brunel Univ Dept Math Sci Uxbridge UB8 3PH Middx England Shihezi Univ Sch Business Shihezi 832003 Peoples R China

We propose a model for multinomial probit factor analysis by assuming t-distribution error in probit factor analysis. To obtain maximum likelihood estimation, we use the Monte Carlo expectation maximization algorithm with its M-step greatly simplified under conditional maximization and its E-step made feasible by Monte Carlo simulation. Standard errors are calculated by using Louis's method. The methodology is illustrated with numerical simulations.

关键词： Multinomial probit model Factor analysis mcem algorithm t-distribution

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Extended mixture factor analysis model with covariates for mixed binary and continuous responses

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STATISTICS IN MEDICINE 2011年第21期30卷 2634-2647页

作者： An, Xinming Bentler, Peter M. Univ Calif Los Angeles Dept Psychol Los Angeles CA 90024 USA

Finite mixture factor analysis provides a parsimonious model to explore latent group structures of high-dimensional data. In this modeling framework, we can explore latent structures for continuous responses. However, dichotomous items are often used to define latent domains in practice. This paper proposes an extended finite mixture factor analysis model with covariates to model mixed continuous and binary responses. We use a Monte Carlo expectation-maximization (mcem) algorithm to estimate the model. In the E step, closed-form solutions are not available for the conditional expectation of complete data log likelihood, so it is approximated by sample means, which are in turn generated by the Gibbs sampler from the joint conditional distribution of latent variables. To monitor the convergence of the mcem algorithm, we use bridge sampling to calculate the log likelihood ratio of two successive iterations. We adopt a diagnostic plot of the log likelihood ratio against iterations for monitoring the convergence of the mcem algorithm. We compare different models based on BIC, in which we approximate the observed data log likelihood by using a Monte Carlo method. We investigate the computational properties of the mcem algorithm by simulation studies. We use a real data example to illustrate the practical usefulness of the model. Finally, we discuss limitations and possible extensions. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： finite mixture model factor analysis model mcem algorithm Gibbs sampler

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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 crossed random effects modeling approach for estimating diagnostic accuracy from ordinal ratings without a gold standard

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STATISTICS IN MEDICINE 2013年第20期32卷 3472-3485页

作者： Xie, Yunlong Chen, Zhen Albert, Paul S. Eunice Kennedy Shriver Natl Inst Child Hlth & Hum Biostat & Bioinformat Branch Div Epidemiol Stat & Prevent Res NIH Bethesda MD 20892 USA

In diagnostic studies without a gold standard, the assumption on the dependence structure of the multiple tests or raters plays an important role in model performance. In case of binary disease status, both conditional independence and crossed random effects structure have been proposed and their performance investigated. Less attention has been paid to the situation where the true disease status is ordinal. In this paper, we propose crossed subject-specific and rater-specific random effects to account for the dependence structure and assess the robustness of the proposed model to misspecification in the random effects distributions. We applied the models to data from the Physician Reliability Study, which focuses on assessing the diagnostic accuracy in a population of raters for the staging of endometriosis, a gynecological disorder in women. Using this new methodology, we estimate the probability of a correct classification and show that regional experts can more easily classify the intermediate stage than resident physicians. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： random effects models endometriosis mcem algorithm

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Improved Estimation and Uncertainty Quantification Using Monte Carlo-Based Optimization algorithms

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2015年第3期24卷 771-791页

作者： Xu, Cong Baines, Paul Wang, Jane-Ling Univ Calif Davis Davis CA 95616 USA

In this article, we present a novel method to obtain both improved estimates and reliable stopping rules for stochastic optimization algorithms such as the Monte Carlo EM (mcem) algorithm. By characterizing a stationary point, theta*, of the algorithm as the solution to a fixed point equation, we provide a parameter estimation procedure by solving for the fixed point of the update mapping. We investigate various ways to model the update mapping, including the use of a local linear (regression) smoother. This simple approach allows increased stability in estimating the value of theta* as well as providing a natural quantification of the estimation uncertainty. These uncertainty measures can then also be used to construct convergence criteria that reflect the inherent randomness in the algorithm. We establish convergence properties of our modified estimator. In contrast to existing literature, our convergence results do not require the Monte Carlo sample size to go to infinity. Simulation studies are provided to illustrate the improved stability and reliability of our estimator.

关键词： Stochastic optimization Stopping rules mcem algorithm Local linear smoothing

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