Bayesian Inference for Skew-normal Linear Mixed Models

Arellano–Valle, Reinaldo B.; Bolfarine, Heleno; Lachos, Víctor H.

doi:10.1080/02664760701236905

Cited by 146 publications

(178 citation statements)

References 16 publications

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“…The skew-elliptical distribution is an attractive class of asymmetric thick-tailed parametric structure, which includes the skew-normal (SN) distribution as a special case. Different versions of the multivariate SN distributions have been considered and used in the literature (Arellano-Valle et al, 2005Arellano-Valle and Azzalini, 2006;Azzalini and Capitanio, 1999;Jara et al, 2008;Sahu et al, 2003;and others). These studies demonstrated that the SN distribution has reasonable flexibility in real data fitting, while it maintains some convenient formal properties of the normal density.…”

Section: Multivariate Skew-normal Distributionsmentioning

confidence: 99%

Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate

Huang

Chen²,

Yan³

2012

The International Journal of Biostatistics

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Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models, which enable us to account for between-subject and within-subject variations. To partially explain the variations, time-dependent covariates are usually introduced to these models. Some covariates, however, may be often measured with substantial errors and missing observations. It is often the case that model random error is assumed to be distributed normally, but the normality assumption may not always give robust and reliable results, particularly if the data exhibit skewness. In the literature, there has been considerable interest in accommodating either skewed response or covariate measured with error and missing data in such models, but there has been relatively little study concerning all these features simultaneously. This article is to address simultaneous impact of skewness in response and measurement error and missing data in covariate by jointly modeling the response and covariate processes under a framework of Bayesian semiparametric nonlinear mixed-effects models. In particular, we aim at exploring how mixed-effects joint models based on one-compartment model with one phase time-varying decay rate and two-compartment model with two phase time-varying decay rates contribute to modeling results and inference. The method is illustrated by an AIDS data example to compare potential models with different distributional specifications and various scenarios. The findings from this study suggest that the one-compartment model with a skewnormal distribution may provide more reasonable results if the data exhibit skewness in response and/or have measurement error and missing observations in covariates.

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Section: Multivariate Skew-normal Distributionsmentioning

confidence: 99%

Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate

Huang

Chen²,

Yan³

2012

The International Journal of Biostatistics

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“…Studies on the multivariate skew-normal distributions are also presented by (Azzalini and Dalla Valle, 1996). The skew-normal linear mixed models are presented by Arellano-Valle et al (2005), Lachos et al (2010) and Lin (2008).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Augmented Mixed Beta Models with Skew-Normal Random Effects

Mohsenkhani¹,

Mohammadzadeh²,

Baghfalaki³

2017

JSRI

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Abstract. Many studies in different areas include data in the form of rates or proportions that should be analyzed. The data may also accept values zero and one. Augmented beta regression models are an appropriate choice for continuous response variables in the closed unit interval [0, 1]. The data in this model are based on a combination of three distributions, degenerate distribution at 0 and 1, and a beta density in (0, 1). The random effects are usually added to the model for accommodating the data structures as well as correlation impacts. In most of these models, the random effects are generally assumed to be normally distributed, while this assumption is frequently violated in applied studies. In this paper, the augmented mixed beta regression model with skew-normal distributed random effects is presented. A Bayesian approach is adopted for parameter estimation using Markov Chain Monte Carlo method. The proposed model is applied to analyze a real data set from Labor Force Survey.

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“…In this paper, we apply the following properties of skew-normal distribution during parameter estimation of skew-normal mixed model (See [15] for more about the properties of skew-normal distribution).…”

Section: Introductionmentioning

confidence: 99%

Study on the Influencing Factors of Carbon Intensity Using Skew-normal Mixed Model

Ye¹,

Xu²,

Luo³

et al. 2018

JFE

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This paper firstly applies the EM algorithm and gives the maximum likelihood estimates of unknown parameters in skew-normal mixed model. For empirical analysis, we verify the skew-normal distribution characteristics of provincial carbon intensity data in China from 2000 to 2014. A skew-normal mixed model is then constructed to study the main influencing factors of carbon intensity of China. It is found that energy intensity would have the most significant influence on carbon intensity, among a group of factors including GDP per capita, proportion of secondary industry, and dependence on foreign trade. Finally, the results are compared with those based on normal mixed model, so as to confirm the statistical excellent properties of skew-normal mixed model.

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Bayesian Inference for Skew-normal Linear Mixed Models

Cited by 146 publications

References 16 publications

Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate

Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate

Bayesian Analysis of Augmented Mixed Beta Models with Skew-Normal Random Effects

Study on the Influencing Factors of Carbon Intensity Using Skew-normal Mixed Model

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