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Author: search.filters.author.Víctor H. LachosHas files: No

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    Regression Modeling of Censored Data Based on Compound Scale Mixtures of Normal Distributions
    (Brazilian Statistical Association, 2023-06-01)
    In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibil-ity, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analyt-ically tractable and efficient EM-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodol-ogy addressed in this paper is implemented in the R package CensMixReg.
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    A New Class of Binary Regression Models for Unbalanced Data with Applications in Medical Data
    (Springer Science+Business Media, 2025-08-01)
    Imbalanced binary data may be more common than expected in medical trials. In this paper, we propose a new class of link function for binary response based on the cumulative distribution function of the scale mixture of skew-normal distributions, which can be useful for fitting imbalanced binary data. The proposed link class has as special cases several link functions proposed in the literature, such as the probit and Student’s-t link, and we present a Bayesian approach for model fitting. Further, we develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with one example as well as a simulation, which illustrates the potential of the proposed class of links as an alternative for binary regression models when imbalanced binary data is presented.
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