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A Comparison of Four Methods of Inverse Prediction

NCJ Number
Christine G. Watters; Lynn R. LaMotte
Date Published
April 2019
5 pages
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 Published: April 1, 2019