Categorical data analysis using a skewed Weibull regression model

TL;DR

This paper introduces a skewed Weibull link model for categorical data analysis, unifying and extending traditional models like logit and probit, with Bayesian and frequentist estimation methods demonstrated on real datasets.

Contribution

The paper proposes a novel skewed Weibull regression model for categorical data, encompassing existing models as special cases and providing comprehensive estimation procedures.

Findings

The proposed model effectively captures asymmetrical data patterns.

It generalizes traditional link functions like logit and probit.

Empirical analysis shows improved fit on real datasets.

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 details. The analysis of two data sets to show the efficiency of the proposed model is performed.