Hypothesis testing in semiparametric additive mixed models.
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.
Zhang
Daowen
D
Department of Statistics, North Carolina State University, USA. dzhang2@stat.ncsu.edu
Lin
Xihong
X
D000927:Anticonvulsants / Q000627:therapeutic use; D002648:Child; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004827:Epilepsy / Q000188:drug therapy; D005260:Female; D006801:Humans; D007214:Indonesia / Q000453:epidemiology; D016013:Likelihood Functions; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical; D010919:Placebos; D016032:Randomized Controlled Trials as Topic; D012141:Respiratory Tract Infections / Q000453:epidemiology; D018709:Statistics, Nonparametric; D014985:Xerophthalmia / Q000453:epidemiology; D005680:gamma-Aminobutyric Acid / Q000031:analogs & derivatives* / Q000627:therapeutic use
D000927:Anticonvulsants; D010919:Placebos; C017985:progabide; D005680:gamma-Aminobutyric Acid