Edilberto Cepeda-Cuervo

Beta Regression Models: Joint Mean and Variance Modeling

In this article, joint mean and variance beta regression models are proposed. The proposed models are fitted by applying the Bayesian method and assuming normal prior distribution for the regression parameters. An analysis of synthetic and real data is included, assuming the proposed model, together with a comparison of the result obtained assuming joint modeling of the mean and precision parameters.

Violencia Intrafamiliar que afecta a Estudiantes de Educación Básica y Media en Bogotá

Objetivo Determinar el nivel de violencia intrafamiliar correspondiente a estudiantes de colegios de Ciudad Bolivar, Bogota, Colombia. Material y metodos La muestra esta conformada por 3 226 alumnos de educacion basica y media, de grados sexto a once, de colegios oficiales de la localidad Ciudad Bolivar de Bogota. Los datos obtenidos a traves de la aplicacion de una encuesta, en la que se establecio su percepcion de la violencia en sus hogares, fueron analizados estadisticamente utilizando SPSS 14.0. Resultados un alto porcentaje de estudiantes tiene dificultades en los procesos de comunicacion con sus padres y siente rechazo y falta de amor de algunos de los miembros de su hogar. Un 28,4 % de los encuestados, 915 alumnos, son victimas de mas de 20 de las situaciones de violencia y un 35 % de los estudiantes encuestados tienen ambientes familiares caracterizados por altos niveles de violencia. El porcentaje de alumnos que afirman ser maltratados fisicamente depende del grado escolar, presentandose los mas altos porcentajes en grados 7 y 8. Conclusiones La comunidad estudiantil de la localidad de Ciudad Bolivar, en Bogota, Colombia esta afectada por un alto numero de situaciones de violencia intrafamiliar.

Estimating infant mortality in Colombia: some overdispersion modelling approaches

It is common to fit generalized linear models with binomial and Poisson responses, where the data show a variability that is greater than the theoretical variability assumed by the model. This phenomenon, known as overdispersion, may spoil inferences about the model by considering significant parameters associated with variables that have no significant effect on the dependent variable. This paper explains some methods to detect overdispersion and presents and evaluates three well-known methodologies that have shown their usefulness in correcting this problem, using random mean models, quasi-likelihood methods and a double exponential family. In addition, it proposes some new Bayesian model extensions that have proved their usefulness in correcting the overdispersion problem. Finally, using the information provided by the National Demographic and Health Survey 2005, the departmental factors that have an influence on the mortality of children under 5 years and female postnatal period screening are determined. Based on the results, extensions that generalize some of the aforementioned models are also proposed, and their use is motivated by the data set under study. The results conclude that the proposed overdispersion models provide a better statistical fit of the data.

Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters

In this paper a bivariate beta regression model with joint modeling of the mean and dispersion parameters is proposed, defining the bivariate beta distribution from Farlie–Gumbel–Morgenstern (FGM) copulas. This model, that can be generalized using other copulas, is a good alternative to analyze non-independent pairs of proportions and can be fitted applying standard Markov chain Monte Carlo methods. Results of two applications of the proposed model in the analysis of structural and real data set are included.

Spatial Double Generalized Beta Regression Models: Extensions and Application to Study Quality of Education in Colombia.

In this article, a proposed Bayesian extension of the generalized beta spatial regression models is applied to the analysis of the quality of education in Colombia. We briefly revise the beta distribution and describe the joint modeling approach for the mean and dispersion parameters in the spatial regression models’ setting. Finally, we motivate the need for the innovative use of the generalized beta spatial regression model to the study of the performance of school children in Mathematics and Language, as well as in the analysis of illiteracy data, and present its results in the context of evaluating the quality of education in Colombia.

Bayesian modelling of the mean and covariance matrix in normal nonlinear models

An important problem in statistics is the study of longitudinal data taking into account the effect of other explanatory variables such as treatments and time. In this paper, a new Bayesian approach for analysing longitudinal data is proposed. This innovative approach takes into account the possibility of having nonlinear regression structures on the mean and linear regression structures on the variance–covariance matrix of normal observations, and it is based on the modelling strategy suggested by Pourahmadi [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterizations, Biometrika, 87 (1999), pp. 667–690.]. We initially extend the classical methodology to accommodate the fitting of nonlinear mean models then we propose our Bayesian approach based on a generalization of the Metropolis–Hastings algorithm of Cepeda [E.C. Cepeda, Variability modeling in generalized linear models, Unpublished Ph.D. Thesis, Mathematics Institute, Universidade Federal do Rio de Janeiro, 2001]. Finally, we illustrate the proposed methodology by analysing one example, the cattle data set, that is used to study cattle growth.

Generalized linear models with random effects in the two-parameter exponential family

In this paper, we develop a new class of double generalized linear models, introducing a random-effect component in the link function describing the linear predictor related to the precision parameter. This is a useful procedure to take into account extra variability and also to make the model more robust. The Bayesian paradigm is adopted to make inference in this class of models. Samples of the joint posterior distribution are drawn using standard Monte Carlo Markov Chain procedures. Finally, we illustrate this algorithm by considering simulated and real data sets.

Some Dependence Models for the Time Between Ozone Exceedances in Mexico City

In this paper, we consider several modelling approaches for the mean time between exceedances of a given environmental threshold. The interest here resides in the time between ozone exceedances (also called ozone inter-exceedances times). The proposed models assume two basic density functions for the time between surpassings: the Weibull and the generalised exponential functions. Considering those distributions, a random effect with autoregressive structure is taken into account to determine unexpected changes in the mean of the inter-exceedances density functions. Those unexpected changes could be captured either by their scale parameter or by both their scale and shape parameters. The models are applied to ozone data from the monitoring network of Mexico City. Selection of the model that best explains the data is performed using the deviance information criterion and also the sum of the absolute values of the differences between the estimated and observed means of the inter-exceedances times. An analysis to detect the possible presence of change-points is also presented.

Heteroscedastic normal–exponential mixture models: Bayesian and classical approaches

Abstract In this paper, we introduce a Bayesian analysis for mixture of distributions belonging to the exponential family. As a special case we consider a mixture of normal exponential distributions including joint modeling of the mean and variance. We also consider joint modeling of the mean and variance heterogeneity. Markov Chain Monte Carlo (MCMC) methods are used to obtain the posterior summaries of interest. We also introduce and apply an EM algorithm, where the maximization is obtained applying the Fisher scoring algorithm. Finally, we also include analysis of real data sets to illustrate the proposed methodology.