Confidence Bands for the Logistic and Probit Regression Models Over Intervals

TL;DR

This paper develops methods for constructing more accurate two-sided and new one-sided confidence bands for logistic and probit regression models over specific predictor intervals, improving upon existing conservative bands.

Contribution

It introduces novel methods for sharper two-sided and the first-ever one-sided confidence bands for logistic and probit models within restricted predictor ranges.

Findings

Sharpened confidence bands for logistic models

First methods for one-sided bands in logistic models

Extension of bands to probit models

Abstract

This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are constructed based on the asymptotic properties of the maximum likelihood estimators. Past articles have considered building two-sided asymptotic confidence bands for the logistic model, such as Piegorsch and Casella (1988). However, the confidence bands given by Piegorsch and Casella are conservative under a single interval restriction, and it is shown in this article that their bands can be sharpened using the methods proposed here. Furthermore, no method has yet appeared in the literature for constructing one-sided confidence bands for the logistic model, and no work has been done for building confidence bands for the probit model, over a limited range of the predictor variable. This article provides methods for computing critical points in these areas.