Correlation Engine 2.0
Clear Search sequence regions


Sizes of these terms reflect their relevance to your search.

The literature about Prediction Interval (PI) and Tolerance Interval (TI) in linear mixed models is usually developed for specific designs, which is a main limitation to their use. This paper proposes to reformulate the two-sided PI to be generalizable under a wide variety of designs (one random factor, nested and crossed designs for multiple random factors, and balanced or unbalanced designs). This new methodology is based on the Hessian matrix, namely, the inverse of (observed) Fisher Information matrix, and is built with a cell mean model. The degrees of freedom for the total variance are calculated with the generalized Satterthwaite method and compared to the Kenward-Roger's degrees of freedom for fixed effects. Construction of two-sided TIs are also detailed with one random factor, and two nested and two crossed random variables. An extensive simulation study is carried out to compare the widths and coverage probabilities of Confidence Intervals (CI), PIs, and TIs to their nominal levels. It shows excellent coverage whatever the design and the sample size are. Finally, these CIs, PIs, and TIs are applied to two real data sets: one from orthopedic surgery study (intralesional resection risk) and the other from assay validation study during vaccine development. © 2019 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Citation

Bernard G Francq, Dan Lin, Walter Hoyer. Confidence, prediction, and tolerance in linear mixed models. Statistics in medicine. 2019 Dec 30;38(30):5603-5622

Expand section icon Mesh Tags

Expand section icon Substances


PMID: 31659784

View Full Text