Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (viz. longitudinal viral load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew-normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, the skew-t, skew-slash and the skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses which are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a MCMC algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as a HIV case study involving analysis of longitudinal viral loads.

No abstract

We introduce a class of shape mixtures of skewed distributions and study some of its main properties. We discuss a Bayesian interpretation and some invariance results of the proposed class. We develop a Bayesian analysis of the skew-normal, skew-generalized-normal, skew-normal-t and skew-t-normal linear regression models under some special prior specifications for the model parameters.In particular, we show that the full posterior of the skew-normal regression model parameters is proper under an arbitrary proper prior for the shape parameter and noninformative prior for the other parameters. We implement a convenient hierarchical representation in order to obtain the corresponding posterior analysis. We illustrate our approach with an application to a real dataset on characteristics of Australian male athletes.

In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution G generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution G is not identified. It is finally shown that, after introducing two identification restrictions, either on the distribution G or on the item parameters, the distribution G and the item parameters are identified provided an infinite quantity of items is available.

Despite technological advances in efficiency enhancement of quantification assays, biomedical studies on HIV RNA collect viral load responses that are often subject to detection limits. Moreover, some related covariates such as CD4 cell count may be often measured with errors. Censored non-linear mixed-effects models are routinely used to analyze this type of data and are based on normality assumptions for the betweensubject and within-subject random terms. However, derived inference may not be robust when the underlying normality assumptions are questionable, especially in presence of skewness and heavy tails. In this article, we address these issues simultaneously under a Bayesian paradigm through joint modeling of the response and covariate processes using an attractive class of skew-normal independent densities. The methodology is illustrated using a case study on longitudinal HIV viral loads. Diagnostics for outlier detection is immediate from the MCMC output. Both simulation and real data analysis reveal the advantage of the proposed models in providing robust inference under non-normality situations commonly encountered in HIV/AIDS or other clinical studies.Supplementary materials accompanying this paper appear on-line.