Prediction-interval procedures and (fixed-effects) confidence-interval procedures for mixed linear models

Abstract

A general approach is presented for devising an approximate 100(1-α)% prediction interval for an unobservable random variable w based on the value of an observable random vector y. It is assumed theat E(w) and E(y) are ;linear combinations of unknown parameters β₁,β₂,…,β_pand that the joint distribution of w-E(w) and yE(y) is symmetric and known up to the value of a vector θ of unknown parameters, as would be the case if y followed a mixed linear model (with normally distributed random effects and errors) and w were a linear combination of the model's fixed and random effects. Various implementations of the proposed approach are illustrated (and comparisons among them made) in the context of the Behrens-Fisher problem and the problem of making inferences about a group mean under a balanced one-way random-effects model.

Keywords:

• One-way random-effects model
• Behrens-Fisher problem
• best linear unbiased prediction
• variance components