Flávio B. Gonçalves

An Integrated Bayesian Model for DIF Analysis

In this article, an integrated bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item parameters, including differential functioning behavior, may be conveniently expressed in terms of prior distributions. Values of indicator variables are estimated in the model, indicating which items have DIF and which do not; as a result, the data analyst may not be required to specify an “anchor set” of items that do not exhibit DIF a priori to identify the model. It reduces the iterative procedures that are commonly used for proficiency purification and DIF detection and explanation. Examples demonstrate the efficiency of this method in simulated and real situations.

Simultaneous multifactor DIF analysis and detection in Item Response Theory

Item Response Theory (IRT) is a psychometric theory widely used in educational assessment and cognitive psychology to analyse data emerged from answers given to items contained in exams, questionnaires, etc. Standard IRT, however, is based on models which assume that items behave equally to all individuals. This may not be a reasonable assumption, especially when the individuals taking the test have different social and/or cultural backgrounds. Differential Item Functioning (DIF) is an area of IRT which allows an item to be perceived differently by distinct groups, respecting its usual characteristics. DIF hypothesis avoids neglecting items that may behave differently among groups and may also be used to provide important information about differences in the populations involved in the study. In this paper, two integrated Bayesian models for DIF analysis in IRT are proposed and compared. Both models are based on a two component mixture with one component describing DIF and the other accounting for the absence of DIF. Another contribution of this paper is the approach of the simultaneous presence of multiple factors causing DIF. Ideas from ANOVA models are used to characterize different possibilities associated with these factors. The models are also extended to account for explanation and detection in each factor. A simulation study was conducted to assess the models capabilities and to compare it against existing alternatives. Special attention has been directed to the conditions required to ensure model identification. An analysis of a Mathematics exam applied nationally to Brazilian elementary school students is made considering two DIF factors: geographical region and type of school. The results highlight the relevance of the proposed methodology to address important issues in educational studying and testing.

Análise bayesiana do funcionamento diferencial do item

This paper uses a Bayesian approach for parameter estimation in Item Response Theory Models for DIF - Differential Item Functioning - analysis. The models proposed are integrated, and incorporate regression structures that can be used to explain the DIF related to items associated covariates. The models are proposed for multiple groups and the approach used, naturally, consider the estimation error of the latent trace and the estimation error of the structural parameters. Examples with simulated data and real data are also presented.

Avaliação de uma medida de evidência de um ponto de mudança e sua utilização na identificação de mudanças na taxa de criminalidade em Belo Horizonte

A probabilidade a posteriori de um instante ser um ponto de mudanca foi proposta por Loschi & Cruz (2005) como uma medida de evidencia de que o comportamento de uma sequencia de dados mude em tal instante. A proposta deste trabalho e avaliar a eficiencia desta medida na identificacao de mudancas na taxa da distribuicao Poisson, em dados sequencialmente observados e compara-la com a medida proposta por Hartigan (1990), isto e, com a probabilidade a posteriori da particao aleatoria formada pelos pontos de mudanca. Cenarios ou sequencias de dados com e sem pontos de mudancas sao considerados. Em cenarios sem pontos de mudancas, assumem-se taxas pequenas e grandes para avaliar a eficiencia da medida proposta na presenca de pouca e muita variabilidade. Em cenarios com pontos de mudancas, consideram-se tanto mudancas estruturais quanto observacoes atipicas. Conclui-se que, em geral, a medida proposta teve melhor desempenho para identificar pontos de mudanca. Uma analise para dados de criminalidade da cidade de Belo Horizonte tambem e feita utilizando-se o modelo proposto e observou-se que esta taxa muda frequentemente ao longo do tempo.

Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.

Bayesian item response model: a generalized approach for the abilities' distribution using mixtures

ABSTRACT Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models. This paper presents a generalized approach for the distribution of the abilities in dichotomous 3-parameter Item Response models. A mixture of normal distributions is considered, allowing for features like skewness, multimodality and heavy tails. A solution is proposed to deal with model identifiability issues without compromising the flexibility and practical interpretation of the model. Inference is carried out under the Bayesian Paradigm through a novel MCMC algorithm. The algorithm is designed in a way to favour good mixing and convergence properties and is also suitable for inference in traditional IRT models. The efficiency and applicability of our methodology is illustrated in simulated and real examples.Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models. This paper presents a generalised approach for the distribution of the abilities in dichotomous 3-parameter Item Response models. A mixture of normal distributions is considered, allowing for features like skewness, multimodality and heavy tails. A solution is proposed to deal with model identifiability issues without compromising the flexibility and practical interpretation of the model. Inference is carried out under the Bayesian Paradigm through a novel MCMC algorithm. The algorithm is designed in a way to favour good mixing and convergence properties and is also suitable for inference in traditional IRT models. The efficiency and applicability of our methodology is illustrated in simulated and real examples.