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.
Highlights
The statistical problem of estimating binary response variables is very important in many areas including social science, biology and economics [1]
We show that the benefits of this model are as follows: (1) flexibility of the Weibull distribution; (2) logit, probit and complementary log–log links as limiting cases; (3) case of implementation of both frequentist and Bayesian inferences; and (4) a general extension to handle multinomial response
This study is used to illustrate the analysis of multinomial response data under Weibull link model, and comparing the results with those obtained by Grazeffe et al [25]
Summary
The statistical problem of estimating binary response variables is very important in many areas including social science, biology and economics [1]. We show that the benefits of this model are as follows: (1) flexibility of the Weibull distribution; (2) logit, probit and complementary log–log links as limiting cases; (3) case of implementation of both frequentist and Bayesian inferences; and (4) a general extension to handle multinomial response. (1) For the experiment to study the potencies of three poisons [24], the main binary response is whether the insect is alive after being treated with assigned dose level For this example, we compare our Weibull link model with other asymmetric and symmetric link models. This study is used to illustrate the analysis of multinomial response data under Weibull link model, and comparing the results with those obtained by Grazeffe et al [25].
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