Article Categorical Data Analysis Using a Skewed Weibull Regression Model Renault Caron 1, Debajyoti Sinha 2, Dipak K. Dey 3 and Adriano Polpo 1,* 1 Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, Brazil;
[email protected] 2 Department of Statistics, Florida State University, Tallahassee, FL 32306, USA;
[email protected] 3 Department of Statistics, University of Connecticut, Storrs, CT 06269, USA;
[email protected] * Correspondence:
[email protected] Received: 24 November 2017; Accepted: 27 February 2018; Published: 7 March 2018 Abstract: In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log–log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as frequentist estimation procedures for binomial and multinomial data responses are presented in detail. The analysis of two datasets to show the efficiency of the proposed model is performed. Keywords: asymmetric model; binomial response; multinomial response; skewed link; Weibull distribution 1. Introduction The statistical problem of estimating binary response variables is very important in many areas including social science, biology and economics [1]. The vast bibliography of categorical data presents the big evolution of the methods that handle appropriately binary and polychotomous data. More details can be found in Agresti [2]. Generalized linear model (GLM) has a wide range of tools in regression for count data [3]. Two important and commonly used symmetric link functions in GLM are the logit and probit links [4].