partially linear models sliced inverse regression ANOVA power R
Abstract:
In a partially linear model some covariates have a linear effect, while the effect of others may be nonlinear. We perform Monte Carlo simulations to compare two methods for testing the significance of covariates with (possibly) nonlinear effects. Both methods use the residuals from fitting only the covariates that have a linear effect. One of the methods is based on the sliced inverse regression (SIR) procedure of Li (1991) applied on the residuals. The other is an ANOVA-type procedure modeled after Wang, Akritas, and Van Keilegom (2008). We also use the two methods for testing two datasets, historical spirit consumption in the UK and a carbon dioxide study, both of which have been described in the literature with partially linear models. This study also serves as a preliminary investigation as to whether the asymptotic theory developed by Li (1991) for the SIR procedure is also relevant when residuals are used.