Flexible Bayesian modelling in dichotomous item response theory using mixtures of skewed item curves.

Most item response theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals taking a test. This assumption restricts the use of those models to the case in which all items behave symmetrically. On the other hand, asymmetric models proposed in the literature impose that all the items in a test behave asymmetrically. This assumption is inappropriate for great majority of tests which are, in general, composed of both symmetric and asymmetric items. Furthermore, a straightforward extension of the existing models in the literature would require a prior selection of the items' symmetry/asymmetry status. This paper proposes a Bayesian IRT model that accounts for symmetric and asymmetric items in a flexible but parsimonious way. That is achieved by assigning a finite mixture prior to the skewness parameter, with one of the mixture components being a point mass at zero. This allows for analyses under both model selection and model averaging approaches. Asymmetric item curves are designed through the centred skew normal distribution, which has a particularly appealing parametrization in terms of parameter interpretation and computational efficiency. An efficient Markov chain Monte Carlo algorithm is proposed to perform Bayesian inference and its performance is investigated in some simulated examples. Finally, the proposed methodology is applied to a data set from a large-scale educational exam in Brazil.

A misclassification model for the non-disjunction fraction in meiosis I.

In this paper we introduce a misclassification model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies named trisomies. We obtain posteriors, and their moments, for the probability that a non-disjunction occurs in the first division of meiosis and for the misclassification errors. We also extend previous works by providing the exact posterior, and its moments, for the probability that a non-disjunction occurs in the first division of meiosis assuming the model proposed in the literature which does not consider that data are subject to misclassification. We perform Monte Carlo studies in order to compare Bayes estimates obtained by using both models. An application to Down Syndrome data is also presented.

Estimating the grid of time-points for the piecewise exponential model.

One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.

Identificação das características associadas com a aprovação de candidatos de escolas públicas e privadas, Vestibular-2004, UFMG / Identification of the factors associated with the approval of candidates from public and private schools, Vestibular-2004, UFMG

Este trabalho visa a conhecer melhor o perfil dos candidatos oriundos de escolas das redes públicas e privadas de ensino que tentaram ingressar na UFMG em 2004. Busca-se identificar quais das características definidas no questionário socioeconômico e cultural aplicado no ato da inscrição do candidato podem estar mais associadas com a aprovação no vestibular. Conclui-se que o local de moradia e o conhecimento de língua estrangeira são as variáveis mais fortemente associadas com a aprovação do candidato de escolas particulares e escolas públicas, respectivamente. Verificou-se que, entre os candidatos que concluíram o ensino médio em escolas públicas, os que estudaram em escolas públicas federais tendem a se concentrar nos grupos com maiores chances de aprovação.

This paper aims to better understand the profile of the candidates for the UFMG entrance examination in 2004, coming from public and private schools. The objective is to identify which of the characteristics defined through a socioeconomic and cultural questionnaire answered by the candidates upon their application for the entrance examination may be associated with their approval at the University exams. It was found that the place where the candidates live and their knowledge of a foreign language are the variants more strongly related to the approval of the candidates of private schools and public schools, respectively. It was also found that, among the candidates who concluded high school at public schools that attained the highest chances of approval, there was a large percentage of candidates that attended high school in federal establishments.

Testing and estimating the non-disjunction fraction in Meiosis I using reference priors.

In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-informative) priors. We consider Jeffreys's approach to built a non-informative prior (Jeffreys's prior) for the fraction of non-disjunction in Meiosis I. We prove that Jeffreys's prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys's and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of non-disjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.