Jorge L. Bazán

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.

A New Robust Regression Model for Proportions

A new regression model for proportions is presented by considering the Beta rectangular distribution proposed by Hahn (2008). This new model includes the Beta regression model introduced by Ferrari and Cribari-Neto (2004) and the variable dispersion Beta regression model introduced by Smithson and Verkuilen (2006) as particular cases. Like Branscum, Johnson, and Thurmond (2007), a Bayesian inference approach is adopted using Markov Chain Monte Carlo (MCMC) algorithms. Simulation studies on the in∞uence of outliers by considering contam- inated data under four perturbation patterns to generate outliers were carried out and conflrm that the Beta rectangular regression model seems to be a new robust alternative for modeling proportion data and that the Beta regression model shows sensitivity to the estimation of regression coe-cients, to the posterior distribution of all parameters and to the model comparison criteria considered. Furthermore, two applications are presented to illustrate the robustness of the Beta rectangular model.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

A Framework for Skew-Probit Links in Binary Regression

We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.

New class of Johnson SB distributions and its associated regression model for rates and proportions

By starting from the Johnson SB distribution pioneered by Johnson (), we propose a broad class of distributions with bounded support on the basis of the symmetric family of distributions. The new class of distributions provides a rich source of alternative distributions for analyzing univariate bounded data. A comprehensive account of the mathematical properties of the new family is provided. We briefly discuss estimation of the model parameters of the new class of distributions based on two estimation methods. Additionally, a new regression model is introduced by considering the distribution proposed in this article, which is useful for situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. The regression model allows to model both location and dispersion effects. We define two residuals for the proposed regression model to assess departures from model assumptions as well as to detect outlying observations, and discuss some influence methods such as the local influence and generalized leverage. Finally, an application to real data is presented to show the usefulness of the new regression model.

A Weibull Mixture Model for the Votes of a Brazilian Political Party

Statistical modeling in political analysis is used recently to describe electoral behaviour of political party. In this chapter we propose a Weibull mixture model that describes the votes obtained by a political party in Brazilian presidential elections. We considered the votes obtained by the Workers’ Party in five presidential elections from 1994 to 2010. A Bayesian approach was considered and a random walk Metropolis algorithm within Gibbs sampling was implemented. Next, Bayes factor was considered to the choice of the number of components in the mixture. In addition the probability of obtain 50 % of the votes in the first round was estimated. The results show that only few components are needed to describe the votes obtained in this election. Finally, we found that the probability of obtaining 50 % of the votes in the first ballot is increasing along time. Future developments are discussed.

Validação do Body Image Relationship Scale para mulheres com câncer de mama

PURPOSE To validate the instrument Body Image Relationship Scale (BIRS) for Brazilian women with breast cancer. METHODS The instrument was administered by trained interviewers to 139 women who used the Brazilian Unified Health System (SUS). All of them had been submitted to cancer treatments between 2006 and 2010. The instrument was validated considering internal consistency and reliability. In order to compare the techniques, the same factorial analysis as used in the original paper was carried out. RESULTS The Spearman-Brown correlation value was 0.8, indicating high internal reliability. The Cronbachs alpha found was 0.9, indicating a high level of internal consistency. Factorial analysis showed that four items had low factorial load and no discriminatory power, and another five items were relocated to other factors. When the instrument was applied, it showed variability to that of the original instrument. CONCLUSION The Brazilian version of the Body Image Relationship Scale (BIRS), named Escala de Relacionamento e Imagem Corporal (ERIC), showed evidence of adequate reliability and internal consistency, making this instrument suitable to be recommended for application to Brazilian women with breast cancer, despite some limitations.

Bayesian estimation for a mixture of simplex distributions with an unknown number of components: HDI analysis in Brazil

ABSTRACTVariables taking value in (0,1), such as rates or proportions, are frequently analyzed by researchers, for instance, political and social data, as well as the Human Development Index (HDI). However, sometimes this type of data cannot be modeled adequately using a unique distribution. In this case, we can use a mixture of distributions, which is a powerful and flexible probabilistic tool. This manuscript deals with a mixture of simplex distributions to model proportional data. A fully Bayesian approach is proposed for inference which includes a reversible-jump Markov Chain Monte Carlo procedure. The usefulness of the proposed approach is confirmed by using of the simulated mixture data from several different scenarios and by using the methodology to analyze municipal HDI data of cities (or towns) in the Northeast region and Sao Paulo state in Brazil. The analysis shows that among the cities in the Northeast, some appear to have a similar HDI to other cities in Sao Paulo state.ABSTRACT Variables taking value in , such as rates or proportions, are frequently analyzed by researchers, for instance, political and social data, as well as the Human Development Index (HDI). However, sometimes this type of data cannot be modeled adequately using a unique distribution. In this case, we can use a mixture of distributions, which is a powerful and flexible probabilistic tool. This manuscript deals with a mixture of simplex distributions to model proportional data. A fully Bayesian approach is proposed for inference which includes a reversible-jump Markov Chain Monte Carlo procedure. The usefulness of the proposed approach is confirmed by using of the simulated mixture data from several different scenarios and by using the methodology to analyze municipal HDI data of cities (or towns) in the Northeast region and São Paulo state in Brazil. The analysis shows that among the cities in the Northeast, some appear to have a similar HDI to other cities in São Paulo state.

Sensitivity analysis and choosing between alternative polytomous IRT models using Bayesian model comparison criteria

ABSTRACT Polytomous Item Response Theory (IRT) models are used by specialists to score assessments and questionnaires that have items with multiple response categories. In this article, we study the performance of five model comparison criteria for comparing fit of the graded response and generalized partial credit models using the same dataset when the choice between the two is unclear. Simulation study is conducted to analyze the sensitivity of priors and compare the performance of the criteria using the No-U-Turn Sampler algorithm, under a Bayesian approach. The results were used to select a model for an application in mental health data.

An extended exponentiated-G-negative binomial family with threshold effect

In this paper, we formulate a very flexible family of models which unifies most recent lifetime distributions. The main idea is to obtain a cumulative distribution function to transform the baseline distribution with an activation mechanism characterized by a latent threshold variable. The new family has a strong biological interpretation from the competitive risks point of view and the Box–Cox transformation provides an elegant manner to interpret the effect on the baseline distribution to obtain this alternative model. Several structural properties of the new model are investigated. A Bayesian analysis using Markov Chain Monte Carlo procedure is developed to illustrate with a real data the usefulness of the proposed family.