Statistica Sinica 9(1999), 679-698

CONFIDENCE BANDS FOR GROWTH AND

RESPONSE CURVES

Jiayang Sun, Jonathan Raz$^*$ and Julian J. Faraway$^*$

Case Western Reserve University and $^*$The University of Michigan

Abstract: Linear models with structured covariance matrices are applicable to a wide variety of longitudinal data sets. This paper presents a method for constructing simultaneous confidence bands for the growth or response curve. The bands can be defined on finite intervals and various other subsets of the real line. Previous results on simultaneous confidence bands in linear regression with independent errors are generalized to include correlated errors when the covariance matrix depends on a finite number of unknown parameters. A correction for the additional variability arising from estimation of unknown covariance parameters is presented. The method is evaluated using data simulated from several different linear models, and it is applied to the analysis of pig metabolite concentrations after brief myocardial ischemia.

Key words and phrases: Longitudinal data, mixed effects, nuclear magnetic resonance, repeated measurements, structured covariance, tube method.