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Biometrika· 2012Q1

On p-values for smooth components of an extended generalized additive model

Simon N. Wood

Short summary

A new Wald-type test is proposed for assessing the significance of smooth components in extended generalized additive models, offering routine and efficient p-value computation without extra model fits or simulations.

AI-generated from the title and abstract; the full text is not read.

Key points

  • Proposes a Wald-type test for smooth components in extended generalized additive models.
  • Confidence intervals based on the approximate result <f><inline-fig><link locator="ASS048IM1"></link></inline-fig></f> exhibit good across-the-function coverage.
  • The method extends applicability beyond Gaussian cases and tests for zero effect.
  • P-values are computed efficiently from fitted models without extra fits or simulations.

AI-generated from the title and abstract; the full text is not read.

Abstract

The problem of testing smooth components of an extended generalized additive model for equality to zero is considered. Confidence intervals for such components exhibit good across-the-function coverage probabilities if based on the approximate result &lt;f&gt;&lt;inline-fig&gt;&lt;link locator="ASS048IM1"&gt;&lt;/inline-fig&gt;&lt;/f&gt;, where &lt;it&gt;f&lt;/it&gt; is the vector of evaluated values for the smooth component of interest and &lt;it&gt;V&lt;/it&gt; &lt;inf&gt;&lt;it&gt;f&lt;/it&gt;&lt;/inf&gt; is the covariance matrix for &lt;it&gt;f&lt;/it&gt; according to the Bayesian view of the smoothing process. Based on this result, a Wald-type test of &lt;it&gt;f&lt;/it&gt;=0 is proposed. It is shown that care must be taken in selecting the rank used in the test statistic. The method complements previous work by extending applicability beyond the Gaussian case, while considering tests of zero effect rather than testing the parametric hypothesis given by the null space of the component’s smoothing penalty. The proposed &lt;it&gt;p&lt;/it&gt;-values are routine and efficient to compute from a fitted model, without requiring extra model fits or null distribution simulation.

The authors' abstract, as published at the source. Biometrika, 2012 · DOI ↗

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