Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in-variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].Skew-normal distribution, Gibbs algorithm, skewness, multivariate null intercepts model, measurement error,

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.FAPESP Fundacao de Amparo a Pesquisa do Estado de Sao PauloFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

A robust multivariate measurement error model with skew-normal/independent distributions and Bayesian MCMC implementation

Skew-normal/independent distributions are a class of asymmetric thick-tailed distributions that include the skew-normal distribution as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in multivariate measurement errors models. We propose the use of skew-normal/independent distributions to model the unobserved value of the covariates (latent variable) and symmetric normal/independent distributions for the random errors term, providing an appealing robust alternative to the usual symmetric process in multivariate measurement errors models. Among the distributions that belong to this class of distributions, we examine univariate and multivariate versions of the skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set. © 2009 Elsevier B.V.Skew-normal/independent distributions are a class of asymmetric thick-tailed distributions that include the skew-normal distribution as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian anal65527541FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçãoArellano-Valle, R.B., Bolfarine, H., Elliptical structural models (1996) Communications in Statistics: Theory and Methods, 25, pp. 2319-2341Arellano-Valle, R.B., Bolfarine, H., Lachos, V.H., Skew-normal linear mixed models (2005) Journal of Data Science, 3, pp. 415-438Arellano-Valle, R.B., Branco, M.D., Genton, M.G., A unified view on skewed distributions arising from selections (2006) The Canadian Journal of Statistics, 34, pp. 581-601Arellano-Valle, R.B., Ozan, S., Bolfarine, H., Lachos, V.H., Skew normal measurement error models (2005) Journal of Multivariate Analysis, 98, pp. 265-281Azzalini, A., Capitanio, A., Statistical applications of the multivariate skew normal distribution (1999) Journal of the Royal Statistical Society, Series B, 61, pp. 579-602Azzalini, A., Capitanio, A., Distributions generated by perturbation of symmetry with emphasis on the multivariate skew t-distribution (2003) Journal of the Royal Statistical Society, Series B, 61, pp. 367-389Azzalini, A., Dalla-Valle, A., The multivariate skew-normal distribution (1996) Biometrika, 83, pp. 715-726Azzalini, A., Genton, M.G., Robust likelihood methods based on the skew-t and related distributions (2008) International Statistical Review, 76, pp. 106-129Barnett, V.D., Simultaneous pairwise linear structural relationships (1969) Biometrics, 25, pp. 129-142Bolfarine, H., Galea-Rojas, M., On structural comparative calibration under a t-model (1996) Computational Statistics, 11, pp. 63-85Bolfarine, H., Cabral, C.R.B., Paula, G.A., Distance tests under nonregular conditions: Applications to the comparative calibration model (2002) Journal of Statistics Computation and Simulation, 72 (2), pp. 125-140Branco, M., Dey, D., A general class of multivariate skew-elliptical distribution (2001) Journal of Multivariate Analysis, 79, pp. 93-113Brown, P.J., Fuller, W.A., Statistical analysis of measurement errors models and applications (1990) Contemporary Mathematics, 112Chen, M.H., Shao, Q.M., Ibrahim, J.Q., (2000) Monte Carlo Methods in Bayesian Computation, , Springer-Verlag, New YorkCheng, C.L., Van Ness, J.W., (1999) Statistical Regression with Measurement Error, , Arnold, LondonChipkevitch, E., Nishimura, R., Tu, D., Galea-Rojas, M., Clinical measurement of testicular volume in adolescents: Comparison of the reliability of 5 methods (1996) Journal of Urology, 156, pp. 2050-2053Dempster, A.P., Laird, N.M., Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm (1977) Journal of the Royal Statistical Society, Series B, 39, pp. 1-22Fuller, W.A., (1987) Measurement Error Models, , Wiley, New YorkGaribay, V.C., Aoki, R., Lachos, V.H., Bayesian analysis for a skew extension of the multivariate null intercept measurement error model (2008) Journal of Applied Statistics, 35, pp. 1239-1251Geisser, S., Eddy, W., A predictive approach to model selection (1979) Journal of the American Statistical Association, Alexandria, 79, pp. 153-160Geisser, S., (1993) Predictive Inference: An Introduction, , Chapman and Hall, LondonGelfand, A.E., Dey, D.K., Chang, H., Model determination using predictive distributions with implementation via sampling-based methods (with discussion) (1992) Bayesian Statistics, 4. , Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. 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Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178]

Stochastic volatility in mean models with scale mixtures of normal distributions and correlated errors: a Bayesian approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A stochastic volatility in mean model with correlated errors using the symmetrical class of scale mixtures of normal distributions is introduced in this article. The scale mixture of normal distributions is an attractive class of symmetric distributions that includes the normal, Student-t, slash and contaminated normal distributions as special cases, providing a robust alternative to estimation in stochastic volatility in mean models in the absence of normality. Using a Bayesian paradigm, an efficient method based on Markov chain Monte Carlo (MCMC) is developed for parameter estimation. The methods developed are applied to analyze daily stock return data from the Sao Paulo Stock, Mercantile & Futures Exchange index (IBOVESPA). The Bayesian predictive information criteria (BPIC) and the logarithm of the marginal likelihood are used as model selection criteria. The results reveal that the stochastic volatility in mean model with correlated errors and slash distribution provides a significant improvement in model fit for the IBOVESPA data over the usual normal model. (C) 2010 Elsevier B.V. All rights reserved.A stochastic volatility in mean model with correlated errors using the symmetrical class of scale mixtures of normal distributions is introduced in this article. The scale mixture of normal distributions is an attractive class of symmetric distributions t141518751887FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)sem informaçãosem informaçãosem informaçã

Stochastic volatility in mean models with scale mixtures of normal distributions and correlated errors: A Bayesian approach

Abstract The stochastic volatility in mean model with correlated errors using the symmetrical class of scale mixtures of normal distributions is introduced in this article. The scale mixture of normal distributions is an attractive class of symmetric distributions that includes the normal, Student-t, slash and contaminated normal distributions as special cases, providing a robust alternative to estimation in stochastic volatility in mean models in the absence of normality

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.Fundacao de Amparo Za Pesquisa do Estado de Sao Paulo (FAPESP)[04/14721-2]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundacao de Amparo Za Pesquisa do Estado de Sao Paulo (FAPESP)[2007/03140-7]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Local influence analysis for regression models with scale mixtures of skew-normal distributions

The robust estimation and the local influence analysis for linear regression models with scale mixtures of multivariate skew-normal distributions have been developed in this article. The main virtue of considering the linear regression model under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows an easy implementation of inference. Inspired by the expectation maximization algorithm, we have developed a local influence analysis based on the conditional expectation of the complete-data log-likelihood function, which is a measurement invariant under reparametrizations. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and with Cook's well-known approach it can be very difficult to obtain measures of the local influence. Some useful perturbation schemes are discussed. In order to examine the robust aspect of this flexible class against outlying and influential observations, some simulation studies have also been presented. Finally, a real data set has been analyzed, illustrating the usefulness of the proposed methodology.

Influence diagnostics in linear and nonlinear mixed-effects models with censored data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays, and consequently the responses are either left or right censored. Linear and nonlinear mixed-effects models, with modifications to accommodate censoring (LMEC and NLMEC), are routinely used to analyze this type of data. Recently, Vaida and Liu (2009) proposed an exact EM-type algorithm for LMEC/NLMEC, called the SAGE algorithm (Meng and Van Dyk, 1997), that uses closed-form expressions at the E-step, as opposed to Monte Carlo simulations. Motivated by this algorithm, we propose here an exact ECM algorithm (Meng and Rubin, 1993) for LMEC/NLMEC, which enables us to develop local influence analysis for mixed-effects models on the basis of conditional expectation of the complete-data log-likelihood function. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex which makes it difficult to directly apply the approach of Cook (1977, 1986). Some useful perturbation schemes are also discussed. Finally, the results obtained from the analyses of two HIV AIDS studies on viral loads are presented to illustrate the newly developed methodology. (C) 2012 Elsevier B.V. All rights reserved.HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays, and consequently the responses are either left or right censored. Linear and nonlinear mixed-effects models, with modification571450464FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)sem informaçãosem informaçã