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Simple Incorporation of Interactions into Additive Models
Author(s) -
Coull Brent A.,
Ruppert David,
Wand M. P.
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00539.x
Subject(s) - covariate , generalized additive model , categorical variable , additive model , smoothing spline , smoothing , model selection , simple (philosophy) , mathematics , mixed model , econometrics , computer science , spline (mechanical) , statistics , mathematical optimization , philosophy , structural engineering , epistemology , bilinear interpolation , engineering , spline interpolation
Summary. Often, the functional form of covariate effects in an additive model varies across groups defined by levels of a categorical variable. This structure represents a factor‐by‐curve interaction. This article presents penalized spline models that incorporate factor‐by‐curve interactions into additive models. A mixed model formulation for penalized splines allows for straightforward model fitting and smoothing parameter selection. We illustrate the proposed model by applying it to pollen ragweed data in which seasonal trends vary by year.