Construction of Simultaneous Confidence Bands for Multiple Logistic Regression Models over Restricted Regions

TL;DR

This paper develops methods for constructing more accurate simultaneous confidence bands for multiple logistic regression models over restricted predictor regions, improving upon existing conservative approaches.

Contribution

It introduces novel procedures for confidence band construction over general and rectangular regions, outperforming previous methods in accuracy and applicability.

Findings

Proposed methods produce narrower confidence bands.

The new approach outperforms Piegorsch and Casella (1988) in examples.

Applicable to common rectangular predictor regions.

Abstract

This article presents methods for constructing an asymptotic hyperbolic band under the multiple logistic regression model when the predictor variables are restricted to a specific region $\mathscr{X}$. Scheff\'{e}'s method yields unnecessarily wide, and hence conservative, bands if the predictor variables can be restricted to a certain region. Piegorsch and Casella (1988) developed a procedure to build an asymptotic confidence band for the multiple logistic regression model over particular regions. Those regions are shown to be special cases of the region $\mathscr{X}$, which was first investigated by Seppanen and Uusipaikka (1992) in the multiple linear regression context. This article also provides methods for constructing conservative confidence bands when the restricted region is not of the specified form. Particularly, rectangular restricted regions, which are commonly encountered in practice, are considered. Two examples are given to illustrate the proposed methodology, and one example shows that the proposed procedure outperforms the method given by Piegorsch and Casella (1988).