Hypothesis test of arbitrary parametric structure in a generalized additive model

Before applying flexible nonparametric models such as a generalized additive model (GAM), it is natural to ask whether a simpler parametric form suffices. To address this question, we develop TAPS (Test for Arbitrary Parametric Structure), a framework that integrates estimation and hypothesis testing to evaluate whether a prespecified parametric form adequately captures a covariate effect in a GAM. TAPS accommodates diverse structures, including linearity, piecewise linearity with changepoints, discontinuities with jumps, among many others. It is implemented in the R package mgcv.taps built directly on mgcv, enabling seamless adoption, broad outcome support, and scalability to biobank-scale data. Using UK Biobank data, we analyze 38 continuous and 8 binary traits to investigate two scientific questions: does the effect of a polygenic risk score (PRS) vary with age beyond a linear interaction, and does retirement at age 65 modify this age-varying effect? We find that age-varying PRS effects are common and often strongly non-linear, and that retirement at 65 significantly modifies these effects for five traits after multiple-testing correction.