TY - JOUR

T1 - On p-values for smooth components of an extended generalized additive model

AU - Wood, Simon N

PY - 2013/3

Y1 - 2013/3

N2 - 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 \hat f(i) ~ N{f(i),V_f(i,i)}, where f is the vector of evaluated values for the smooth component of interest and V_f is the covariance matrix for f according to the Bayesian view of the smoothing process. Based on this result, a Wald-type test of f=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 p-values are routine and efficient to compute from a fitted model, without requiring extra model fits or null distribution simulation.

AB - 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 \hat f(i) ~ N{f(i),V_f(i,i)}, where f is the vector of evaluated values for the smooth component of interest and V_f is the covariance matrix for f according to the Bayesian view of the smoothing process. Based on this result, a Wald-type test of f=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 p-values are routine and efficient to compute from a fitted model, without requiring extra model fits or null distribution simulation.

UR - http://www.scopus.com/inward/record.url?scp=84874762668&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1093/biomet/ass048

U2 - 10.1093/biomet/ass048

DO - 10.1093/biomet/ass048

M3 - Article

VL - 100

SP - 221

EP - 228

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 1

ER -