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Biostatistics 4:57-74 (2003)
© 2003 Oxford University Press

Hypothesis testing in semiparametric additive mixed models

Daowen Zhang* and Xihong Lin

Department of Statistics, North Carolina State University, USA dzhang2{at}stat.ncsu.edu
Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109-2029, USA xlin{at}umich.edu

*To whom correspondence should be addressed

We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the variance component score test by treating the inverse of the smoothing parameter as an extra variance component. We also consider testing the equivalence of two nonparametric functions in semiparametric additive mixed models for two groups, such as treatment and placebo groups. The proposed tests are applied to data from an epidemiological study and a clinical trial and their performance is evaluated through simulations.

Keywords: Equivalence test; Goodness of fit; Longitudinal data; Mixed models; Nonparametric regression; Polynomial test; Score test; Variance components


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