Bounded count response data arise naturally in health applications. In general, the well-known beta-binomial regression model form the basis for analyzing this data, specially when we have overdispersed data. Little attention, however, has been given to the literature on the possibility of having extreme observations and overdispersed data.
View Article and Find Full Text PDFIn the current literature on latent variable models, much effort has been put on the development of dichotomous and polytomous cognitive diagnostic models (CDMs) for assessments. Recently, the possibility of using continuous responses in CDMs has been brought to discussion. But no Bayesian approach has been developed yet for the analysis of CDMs when responses are continuous.
View Article and Find Full Text PDFThe complementary log-log link was originally introduced in 1922 to R. A. Fisher, long before the logit and probit links.
View Article and Find Full Text PDFContinuous clustered proportion data often arise in various areas of the social and political sciences where the response variable of interest is a proportion (or percentage). An example is the behavior of the proportion of voters favorable to a political party in municipalities (or cities) of a country over time. This behavior can be different depending on the region of the country, giving rise to groups (or clusters) with similar profiles.
View Article and Find Full Text PDFMultidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits while other items may only measure one or two traits. In order to facilitate a clear expression of which items measure which traits and formulate such relationships as a math function in MIRT models, we applied the concept of the Q-matrix commonly used in diagnostic classification models to MIRT models.
View Article and Find Full Text PDFStudies of risk perceived using continuous scales of [0,100] were recently introduced in psychometrics, which can be transformed to the unit interval, but the presence of zeros or ones are commonly observed. Motivated by this, we introduce a full inferential set of tools that allows for augmented and limited data modeling. We considered parameter estimation, residual analysis, influence diagnostic and model selection for zero-and/or-one augmented beta rectangular (ZOABR) regression models and their particular nested models, which is based on a new parameterization of the beta rectangular distribution.
View Article and Find Full Text PDFResponse variables in medical sciences are often bounded, e.g. proportions, rates or fractions of incidence of some disease.
View Article and Find Full Text PDFThe deterministic inputs, noisy, "and" gate (DINA) model is a popular cognitive diagnosis model (CDM) in psychology and psychometrics used to identify test takers' profiles with respect to a set of latent attributes or skills. In this work, we propose an estimation method for the DINA model with the No-U-Turn Sampler (NUTS) algorithm, an extension to Hamiltonian Monte Carlo (HMC) method. We conduct a simulation study in order to evaluate the parameter recovery and efficiency of this new Markov chain Monte Carlo method and to compare it with two other Bayesian methods, the Metropolis Hastings and Gibbs sampling algorithms, and with a frequentist method, using the Expectation-Maximization (EM) algorithm.
View Article and Find Full Text PDFBy 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.
View Article and Find Full Text PDFPurpose: 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.