A study of the calibration-inverse prediction problem in a mixed model setting

Abstract

The Calibration-Inverse Prediction Problem was investigated in a mixed model setting. Two methods were used to construct inverse prediction intervals. Method 1 ignores the random block effect in the mixed model and constructs the inverse prediction interval in the standard manner using quantiles from an F distribution. Method 2 uses a bootstrap to estimate quantiles of an approximate pivotal and then follows essentially the same procedure as in method 1.

A simulation study was carried out to compare how the intervals created by the two methods performed in terms of coverage rate and mean interval length. Results from our simulation study suggest that when the variance component of the block is large relative to the location variance component, the coverage rate of the intervals produced by the two methods differ significantly. Method 2 appears to yield intervals which have a slightly higher coverage rate and wider interval length then did method 1. Both methods yielded intervals with coverage rates below nominal for approximately 1/3 of the simulation settings.