On generalized multinomial models and joint percentile estimation

•We introduce a family of link function for multinomial regression models.•Conditions for the local orthogonality of the link and the regression parameters are given.•Confidence regions for jointly estimating the percentiles based on the parametric family of link functions are proposed.•The methodology is illustrated with data from a combination drug study.

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.