Simple Incorporation of Interactions into Additive Models

By Brent A. Coull, David Ruppert, Matt P. Wand. 2001

91 citations recorded by the source corpus.

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.

Subfields: Genetics, Statistics and Probability

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Citations in the corpus

Partially Interpretable Estimators (PIE): Black-Box-Refined Interpretable Machine Learning (2021, background): “For example, Coull et al. (2001) incorporates factor-by-curve interactions which consider the interactions between numeric features and categorical features.”
Nonparametric small area estimation using penalized spline regression (2005, unknown): “Parise et al. (2001), Coull, Ruppert, and Wand (2001), Coull, Schwartz, and Wand (2001) and Liang (2003) all provide examples of using penalized splines in the construction of mixed effect regression models for the analysis of data containing random effects.”
Flexible smoothing with P-splines: a unified approach (2002, methodology): “Brumback et al. (1999) introduced the best linear unbiased predictor (BLUP) representation of penalized splines, Coull et al. (2001a) used penalized splines in the context of additive models and Coull et al. (2001b) extended this model to allow for correlated errors.”
Smoothing and mixed models (2003, background): “Coull, Ruppert and Wand (2001) describe how to treat (13) as a mixed model.”
Spatially Adaptive Bayesian Penalized Regression Splines (P-splines) (2005, methodology): “…14, Number 2, Pages 378–394 DOI: 10.1198/106186005X47345 378 parameter and the fit using P-splines are easy to compute using mixed model technology (see Robinson 1991; Coull, Ruppert, and Wand 2001; Rice and Wu 2001, among others), and are not sensitive to knot parameter selection (Ruppert 2002).”
Smoothing and forecasting mortality rates (2004, background): “Articles which emphasize applications include Marx and Eilers (1999), Parise et al. (2001), Coull et al. (2001a, 2001b) and Currie and Durban (2002).”