Goodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.

TitleGoodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.
Publication TypeJournal Article
Year of Publication2018
AuthorsHidalgo, Sebastian J. Teran, Michael C. Wu, Stephanie M. Engel, and Michael R. Kosorok
JournalComput Stat Data Anal
Date Published2018 Jun

Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counter-parts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing spline ANOVA models. The test can consider two sources of lack-of-fit: whether covariates that are not currently in the model need to be included, and whether the current model fits the data well. The proposed method derives estimated residuals from the model. Then, statistical dependence is assessed between the estimated residuals and the covariates using the HSIC. If dependence exists, the model does not capture all the variability in the outcome associated with the covariates, otherwise the model fits the data well. The bootstrap is used to obtain p-values. Application of the method is demonstrated with a neonatal mental development data analysis. We demonstrate correct type I error as well as power performance through simulations.

Alternate JournalComput Stat Data Anal
Original PublicationGoodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example.
PubMed ID29867285
PubMed Central IDPMC5983390
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
P01 ES009584 / ES / NIEHS NIH HHS / United States
U10 CA180819 / CA / NCI NIH HHS / United States