|Title||Goodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.|
|Publication Type||Journal Article|
|Year of Publication||2018|
|Authors||Hidalgo, Sebastian J. Teran, Michael C. Wu, Stephanie M. Engel, and Michael R. Kosorok|
|Journal||Comput Stat Data Anal|
|Date Published||2018 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 Journal||Comput Stat Data Anal|
|Original Publication||Goodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example.|
|PubMed Central ID||PMC5983390|
|Grant List||P01 CA142538 / CA / NCI NIH HHS / United States |
P01 ES009584 / ES / NIEHS NIH HHS / United States
U10 CA180819 / CA / NCI NIH HHS / United States
Goodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.