Coverage Properties of Confidence Intervals for Generalized Additive Model Components

Giampiero Marra*, Simon N. Wood

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the coverage properties of Bayesian confidence intervals for the smooth component functions of generalized additive models (GAMs) represented using any penalized regression spline approach. The intervals are the usual generalization of the intervals first proposed by Wahba and Silverman in 1983 and 1985, respectively, to the GAM component context. We present simulation evidence showing these intervals have close to nominal 'across-the-function' frequentist coverage probabilities, except when the truth is close to a straight line/plane function. We extend the argument introduced by Nychka in 1988 for univariate smoothing splines to explain these results. The theoretical argument suggests that close to nominal coverage probabilities can be achieved, provided that heavy oversmoothing is avoided, so that the bias is not too large a proportion of the sampling variability. The theoretical results allow us to derive alternative intervals from a purely frequentist point of view, and to explain the impact that the neglect of smoothing parameter variability has on confidence interval performance. They also suggest switching the target of inference for component-wise intervals away from smooth components in the space of the GAM identifiability constraints.

Original languageEnglish
Pages (from-to)53-74
Number of pages22
JournalScandinavian Journal of Statistics
Volume39
Issue number1
Early online date25 Jan 2012
DOIs
Publication statusPublished - 31 Mar 2012

Keywords

  • Bayesian confidence interval
  • Generalized additive model
  • Penalized regression spline

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