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Inverse Prediction for Heteroscedastic Response Using Mixed Models Software

NCJ Number
Date Published
January 2017
9 pages
Lynn R. LaMotte, Jeffrey D. Wells
Distributions of a response y (height, for example) differ with values of a factor t (such as age). Given a response y* for a subject of unknown t*, the objective of inverse prediction is to infer the value of t* and to provide a defensible confidence set for it. This article describes how versatile models for this problem can be formulated in such a way that the computations can be accomplished with widely available software for mixed models, such as SAS PROC MIXED. Coverage probabilities of confidence sets on t* are illustrated in an example.
Training data provide values of y observed on subjects at known values of t. Models relating the mean and variance of y to t can be formulated as mixed (fixed and random) models in terms of sets of functions of t, such as polynomial spline functions. A confidence set on t* can then be had as those hypothetical values of t for which y* is not detected as an outlier when compared to the model fit to the training data. With nonconstant variance, the p-values for these tests are approximate. (Publisher abstract modified)
Date Created: March 18, 2019