A Comparison of Four Methods of Inverse Prediction

• NCJ Number: 254094
• Journal: Communications in Statistics-Simulation and Computation Dated: 2019
• Author(s): Christine G. Watters; Lynn R. LaMotte
• Date Published: April 2019
• Length: 5 pages
• Grant Number(s): 2013-DN-BX-K042
• Agencies: NIJ-Sponsored
• Publication Type: Research (Applied/Empirical); Report (Study/Research); Report (Grant Sponsored); Program/Project Description

Annotation

This study compared the performances of four methods of inverse prediction in terms of the rates at which they reject potential values x0 of the true condition x*; i.e., in terms of powers of tests.

Abstract

The object of inverse prediction is to infer the value of a condition x* that caused an observed response y*, based on a linear model relating responses to conditions fit to training data. The four methods compared are (1) inverse regression(IR), based on a point estimate of x* from y*, along with a delta-method approximation to its variance to find an interval estimate; (2) reverse regression(RR), in which x is modeled by ordinary least squares in terms of y to get a prediction interval estimate of x* at y*; (3) inverse prediction(IP), which produces a confidence set on x* as the values of x0 for which y* is not rejected as an outlier; and (4) inverse prediction extended to models in which the variance of the response increases with the mean(IM). IR, RR, and IP are well-known in the voluminous literature on inverse prediction and calibration. In practice, it appears that RR is the consensus choice, because of its simplicity. (publisher abstract modified)