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A Comparison of Four Methods of Inverse Prediction

NCJ Number
Date Published
April 2019
5 pages
Christine G. Watters; Lynn R. LaMotte
Publication Type
Research (Applied/Empirical), Report (Study/Research), Report (Grant Sponsored), Program/Project Description
Grant Number(s)
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.
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)
Date Created: July 20, 2021