Abstract:
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Smoothing spline ANOVA models are a nonparametric regression methology. The useful property of these models is that the contribution of the covariates to the outcome can be decomposed into main effects, two-way interactions, and all other higher-level interactions in a typical ANOVA fashion. A Goodness-of-fit test is proposed for the smoothing spline ANOVA models with continuous predictor. The test can check two types of lack-of-fit: first, if specific covariates that are not currently in the model need to be included, and secondly, if the current model is sufficient. The ANOVA decomposition is particularly useful since, after rejecting the null hypothesis that the model fits well to the data, higher-level interactions can be added sequentially until the test becomes unsignificant. Hence, the test can be used for model building. Multiplicity of testing can be easily incorporated to preserve a prespecified familywise error rate. The procedure uses the bootstrap approach to obtain critical values. Simulation studies verify the procedure preserves type-I error and has good power performance.
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