On generalized multinomial models and joint percentile estimation

TL;DR

This paper introduces a new family of link functions for multinomial models, enhancing joint percentile estimation with improved invariance and confidence region methods, demonstrated through a drug study example.

Contribution

It proposes a flexible parametric link family for multinomial models with conditions for orthogonality, invariance, and confidence region derivation, advancing joint percentile estimation techniques.

Findings

The link family includes the multicategorical logistic link.

Orthogonality conditions lead to invariance properties.

Confidence regions for joint percentiles are effectively constructed.

Abstract

This article proposes a family of link functions for the multinomial response model. The link family includes the multicategorical logistic link as one of its members. Conditions for the local orthogonality of the link and the regression parameters are given. It is shown that local orthogonality of the parameters in a neighbourhood makes the link family location and scale invariant. Confidence regions for jointly estimating the percentiles based on the parametric family of link functions are also determined. A numerical example based on a combination drug study is used to illustrate the proposed parametric link family and the confidence regions for joint percentile estimation.