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Nonlinear regression models based on the normal mean-variance mixture of Birnbaum-Saunders distribution

JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2017年第3期46卷 476-485页

作者： Naderi, Mehrdad Arabpour, Alireza Lin, Tsung-I Jamalizadeh, Ahad Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran Shahid Bahonar Univ Kerman Young Researchers Soc Kerman Iran Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan

This paper presents a new extension of nonlinear regression models constructed by assuming the normal mean-variance mixture of Birnbaum-Saunders distribution for the unobserved error terms. A computationally analytical EM-type algorithm is developed for computing maximum likelihood estimates. The observed information matrix is derived for obtaining the asymptotic standard errors of parameter estimates. The practical utility of the methodology is illustrated through both simulated and real data sets. (C) 2017 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Birnbaum-Saunders distribution ecme algorithm GIG distribution Nonlinear regression

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Multivariate-t nonlinear mixed models with application to censored multi-outcome AIDS studies

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BIOSTATISTICS 2017年第4期18卷 666-681页

作者： Lin, Tsung-I Wang, Wan-Lun Natl Chung Hsing Univ Inst Stat Taichung 40201 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan Feng Chia Univ Grad Inst Stat & Actuarial Sci Dept Stat Taichung 40724 Taiwan

In multivariate longitudinal HIV/AIDS studies, multi-outcome repeated measures on each patient over time may contain outliers, and the viral loads are often subject to a upper or lower limit of detection depending on the quantification assays. In this article, we consider an extension of the multivariate nonlinear mixed-effects model by adopting a joint multivariate-t distribution for random effects and within-subject errors and taking the censoring information of multiple responses into account. The proposed model is called the multivariate-t nonlinear mixed-effects model with censored responses (MtNLMMC), allowing for analyzing multi-outcome longitudinal data exhibiting nonlinear growth patterns with censorship and fat-tailed behavior. Utilizing the Taylor-series linearization method, a pseudo-data version of expectation conditional maximization either (ecme) algorithm is developed for iteratively carrying out maximum likelihood estimation. We illustrate our techniques with two data examples from HIV/AIDS studies. Experimental results signify that the MtNLMMC performs favorably compared to its Gaussian analogue and some existing approaches.

关键词： CD4 CD8 ratio ecme algorithm HIV viral load Multiple nonlinear profiles Truncated multivariate-t distribution

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Autoregressive Models with Mixture of Scale Mixtures of Gaussian Innovations

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2017年第A4期41卷 1099-1107页

作者： Maleki, Mohsen Nematollahi, A. R. Shiraz Univ Dept Stat Shiraz Iran

This paper presents a theoretical and empirical study of likelihood inference for the autoregressive models with finite (m-component) mixture of scale mixtures of normal (Gaussian) (SMN) innovations. This model involves autoregressive models with single and mixture component of innovations, which are frequently used in time series data analysis. An EM-type algorithm for the maximum likelihood estimation is developed and the observed information matrix is obtained. The performance of the proposed model through a simulation study is also evaluated. The model is then applied on a real time series data set.

关键词： AR model ecme algorithm Scale-mixtures of normal family Mixture distributions

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Maximum a-posteriori estimation of autoregressive processes based on finite mixtures of scale-mixtures of skew-normal distributions

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2017年第6期87卷 1061-1083页

作者： Maleki, Mohsen Arellano-Valle, Reinaldo B. Shiraz Univ Dept Stat Shiraz Iran Pontificia Univ Catolica Chile Dept Estadist Santiago Chile

This article investigates maximum a-posteriori (MAP) estimation of autoregressive model parameters when the innovations (errors) follow a finite mixture of distributions that, in turn, are scale-mixtures of skew-normal distributions (SMSN), an attractive and extremely flexible family of probabilistic distributions. The proposed model allows to fit different types of data which can be associated with different noise levels, and provides a robust modelling with great flexibility to accommodate skewness, heavy tails, multimodality and stationarity simultaneously. Also, the existence of convenient hierarchical representations of the SMSN random variables allows us to develop an EM-type algorithm to perform the MAP estimates. A comprehensive simulation study is then conducted to illustrate the superior performance of the proposed method. The new methodology is also applied to annual barley yields data.

关键词： Autoregressive models ecme algorithm finite mixture distributed innovations maximum a-posteriori probabilities non-Gaussian me series SMSN family

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Likelihood-based inference for multivariate skew scale mixtures of normal distributions

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ASTA-ADVANCES IN STATISTICAL ANALYSIS 2016年第4期100卷 421-441页

作者： Ferreira, Clecio S. Lachos, Victor H. Bolfarine, Heleno Univ Fed Juiz de Fora Dept Stat Juiz De Fora MG Brazil Univ Estadual Campinas Dept Estat Cidade Univ Zeferino Vaz Sao Paulo Brazil Univ Sao Paulo Dept Estat Sao Paulo Brazil

Scale mixtures of normal distributions are often used as a challenging class for statistical analysis of symmetrical data. Recently, Ferreira et al. (Stat Methodol 8:154-171, 2011) defined the univariate skew scale mixtures of normal distributions that offer much needed flexibility by combining both skewness with heavy tails. In this paper, we develop a multivariate version of the skew scale mixtures of normal distributions, with emphasis on the multivariate skew-Student-t, skew-slash and skew-contaminated normal distributions. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine expectation/conditional maximisation either algorithms for maximum likelihood estimation. The observed information matrix is derived analytically to account for standard errors. Results obtained from real and simulated datasets are reported to illustrate the usefulness of the proposed method.

关键词： EM algorithm ecme algorithm Multivariate scale mixtures of normal distributions Skew distributions

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Estimation of adjusted rate differences using additive negative binomial regression

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STATISTICS IN MEDICINE 2016年第18期35卷 3166-3178页

作者： Donoghoe, Mark W. Marschner, Ian C. Macquarie Univ Dept Stat Sydney NSW 2109 Australia Univ Sydney NHMRC Clin Trials Ctr Sydney NSW 2006 Australia

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this;however, standard model-fitting methods are often unable to cope with the constrained parameter space arising from the non-negativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the expectation-conditional maximisation-either algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi-parametric regression functions. We illustrate the method using a placebo-controlled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： ecme algorithm negative binomial regression overdispersion rate difference semi-parametric regression

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Mixtures of common t-factor analyzers for modeling high-dimensional data with missing values

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2015年 83卷 223-235页

作者： Wang, Wan-Lun Feng Chia Univ Dept Stat Grad Inst Stat & Actuarial Sci Taichung 40724 Taiwan

Mixtures of common t-factor analyzers (MCtFA) have emerged as a sound parsimonious model-based tool for robust modeling of high-dimensional data in the presence of fattailed noises and atypical observations. This paper presents a generalization of MCtFA to accommodate missing values as they frequently occur in many scientific researches. Under a missing at random mechanism, a computationally efficient Expectation Conditional Maximization Either (ecme) algorithm is developed for parameter estimation. The techniques for visualization of the data, classification of new individuals, and imputation of missing values under an incomplete-data structure of MCtFA are also investigated. Illustrative examples concerning the analysis of real and simulated data sets are presented to describe the usefulness of the proposed methodology and compare the finite sample performance with its normal counterparts.

关键词： Clustering Common factor loadings Dimension reduction ecme algorithm Missing data Visualization

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Linear Mixed Function-on-Function Regression Models (vol 70, pg 794, 2014)

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BIOMETRICS 2014年第4期70卷 1062-1062页

作者： Wang, Wei Center for Outcomes Research Children's Hospital of Philadelphia Civic Center Blvd Philadelphia Pennsylvania 19104 U.S.A.

We develop a linear mixed regression model where both the response and the predictor are functions. Model parameters are estimated by maximizing the log likelihood via the ecme algorithm. The estimated variance parameters or covariance matrices are shown to be positive or positive definite at each iteration. In simulation studies, the approach outperforms in terms of the fitting error and the MSE of estimating the “regression coefficients.”

关键词： ecme algorithm Functional data analysis Linear mixed effects models Principal component analysis

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Likelihood-Based Inference in Autoregressive Models with Scaled t-Distributed Innovations by Means of EM-Based algorithms

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2013年第10期42卷 2239-2252页

作者： Haghbin, H. Nematollahi, A. R. Shiraz Univ Dept Stat Shiraz Iran

This article applies the EM-based (ECM and ecme) algorithms to find the maximum likelihood estimates of model parameters in general AR models with independent scaled t-distributed innovations whenever the degrees of freedom are unknown. The ecme, sharing advantages with both EM and NewtonRaphson algorithms, is an extension of ECM, which itself is an extension of the EM algorithm. The ECM and ecme algorithms, which are analytically quite simple to use, are then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ecme is efficient and usable in practice. We also show how our method can be applied to the Wolfer's sunspot data.

关键词： Autoregressive process ECM algorithm ecme algorithm EM algorithm t-distribution

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Maximum likelihood inference for mixtures of skew Student-t-normal distributions through practical EM-type algorithms

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STATISTICS AND COMPUTING 2012年第1期22卷 287-299页

作者： Ho, Hsiu J. Pyne, Saumyadipta Lin, Tsung I. Natl Chung Hsing Univ Dept Appl Math Taichung 404 Taiwan Natl Chung Hsing Univ Inst Stat Taichung 404 Taiwan Tunghai Univ Dept Stat Taichung 407 Taiwan Harvard Univ Sch Med Dana Farber Canc Inst Dept Med Oncol Boston MA 02115 USA China Med Univ Dept Publ Hlth Taichung 404 Taiwan

This paper deals with the problem of maximum likelihood estimation for a mixture of skew Student-t-normal distributions, which is a novel model-based tool for clustering heterogeneous (multiple groups) data in the presence of skewed and heavy-tailed outcomes. We present two analytically simple EM-type algorithms for iteratively computing the maximum likelihood estimates. The observed information matrix is derived for obtaining the asymptotic standard errors of parameter estimates. A small simulation study is conducted to demonstrate the superiority of the skew Student-t-normal distribution compared to the skew t distribution. The proposed methodology is particularly useful for analyzing multimodal asymmetric data as produced by major biotechnological platforms like flow cytometry. We provide such an application with the help of an illustrative example.

关键词： ECM algorithm ecme algorithm Flow cytometry Outliers ST mixtures STN mixtures

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