Heleno Bolfarine

Skew-normal Linear Mixed Models

Normality (symmetric) of the random effects and the within-subject errors is a routine assumptions for the linear mixed model, but it may be unrealistic, obscuring important features of among- and within-subjects variation. We relax this assumption by considering that the random effects and model errors follow a skew-normal distributions, which includes normality as a special case and provides flexibility in capturing a broad range of non-normal behavior. The marginal distribution for the observed quantity is derived which is expressed in closed form, so inference may be carried out using existing statistical software and standard optimization techniques. We also implement an EM type algorithm which seem to provide some advantages over a direct maximization of the likelihood. Results of simulation studies and applications to real data sets are reported.

Prediction theory for finite populations

A large number of papers have appeared in the past 20 years on estimating and predicting characteristics of finite populations. This monograph is designed to present this modern theory in a systematic and consistent manner. The authors approach is that of superpopulation models in which values of the population elements are considered as random variables having joint distributions. Throughout, the emphasis is on the analysis of data rather than on the design of samples. Topics covered include: optimal predictors for various superpopulation models, Bayes, minimax, and maximum likelihood predictors, classical and Bayesian prediction internals, model robustness, and models with measurement errors. Each chapter contains numerous examples, and exercises which extend and illustrate the themes in the text. As a result, this book will be ideal for all those research workers seeking an up-to-date and well-referenced introduction to the subject.

Local influence in elliptical linear regression models

Influence diagnostic methods are extended in this paper to elliptical linear models. These include several symmetric multivariate distributions such as the normal, Student t-, Cauchy and logistic distributions, among others. For a particular perturbation scheme and for the likelihood displacement the diagnostics agree with those developed for the normal linear regression model by Cook when the coefficients and the scale parameter are treated separately. This result shows the invariance of the diagnostics with respect to the induced model in the elliptical linear family. However, if the coefficients and the scale parameter are treated jointly we have a different diagnostic for each induced model, which makes this approach helpful for selecting the less sensitive model in the elliptical linear family. An example on the salinity of water is given for illustration.

Bayesian Inference for Skew-normal Linear Mixed Models

Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units (or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.

Influence diagnostics in generalized log-gamma regression models

We discuss in this paper application of influence diagnostics in generalized log-gamma regression models considering the possibility of censored observations. We derive the appropriate matrices for assessing the local influence on the parameter estimates as well as the predictions from the fitted model under different perturbation schemes. The effect of censoring on local influence is also investigated. An example, for which we apply the diagnostic methods, is given as illustration.

On some characterizations of the t-distribution

In this paper we discuss three different characterizations of the generalized t-distribution within the class of the eliptical distributions. We show that this distribution can be characterized in terms of its unconditional and conditional marginals and in terms of quadratic forms. Similar results have been proved for the normal distribution. An additional characterization of the t distribution within the subclass of the compound normal distributions (or scale mixture of normal distributions) is also studied.

A skew item response model

We introduce a new skew-probit link for item response theory (IRT) by considering an accumulated skew-normal distribution. The model extends the symmetric probit-normal IRT model by considering a new item (or skewness) parameter for the item characteristic curve. A special interpretation is given for this parameter, and a latent linear structure is indicated for the model when an augmented likelihood is considered. Bayesian MCMC inference approach is developed and an efficiency study in the estimation of the model parameters is undertaken for a data set from Tanner (1996, p. 190) by using the notion of effective sample size (ESS) as defined in Kass et al. (1998) and the sample size per second (ESS/s) as considered in Sahu (2002). The methodology is illustrated using a data set corresponding to a Mathematical Test applied in Peruvian schools for which a sensitivity analysis of the chosen priors is conducted and also a comparison with seven parametric IRT models is conducted. The main conclusion is that the skew-probit item response model seems to provide the best fit.

Population variance prediction under normal dynamic superpopulation models

In this paper, the prediction of the population variance is considered under normal dynamic superpopulation models from a Bayesian viewpoint. Generalizations are proposed for the case where the variance of the superpopulation model is considered unknown.

Likelihood-Based Inference for Multivariate Skew-Normal Regression Models

In this article, we present EM algorithms for performing maximum likelihood estimation for three multivariate skew-normal regression models of considerable practical interest. We also consider the restricted estimation of the parameters of certain important special cases of two models. The methodology developed is applied in the analysis of longitudinal data on dental plaque and cholesterol levels.

The Log-exponentiated-Weibull Regression Models with Cure Rate: Local Influence and Residual Analysis

In this paper the log-exponentiated-Weibull regression model is modified to allow the possibility that long term survivors are present in the data. The modification leads to a log-exponentiated-Weibull regression model with cure rate, encompassing as special cases the log-exponencial regression and log-Weibull regression models with cure rate typically used to model such data. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. Assuming censored data, we consider a classic analysis and Bayesian analysis for the parameters of the proposed model. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-exponentiated-Weibull error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.