Monte Carlo Test for Polynomial Covariates

Abstract

In this paper, we review the score test procedure used for testing polynomial covariate effects in a semi parametric additive mixed model. This test is based on the mixed model representation of the smoothing spline estimator of the nonparametric function and treating the inverse of the smoothing parameter as an extra variance component. Zhang and Lin (2003) found that the score test of polynomial test for non Gaussian responses follows a scaled chi-squared distribution. Simulation studies showed that their approximation is less satisfactory for binary data. To overcome this deficiency, we apply the technique of Monte Carlo in order to obtain provably exact procedures. Derivation and performance of each testing procedure are discussed throughout the simulations that we conducted.