Partly Parametric Generalized Additive Model

• Activity Number: 527
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kung-Sik Chan* and Tianyang Zhang
• Companies: The University of Iowa and Travelers
• Keywords: Consistency ; Asymptotic normality ; GAM ; Generalized nonlinear regression ; Penalized likelihood

Abstract

In many scientific studies, the response variable bears a generalized nonlinear regression relationship with a certain covariate of interest, which may, however, be confounded by other covariates with unknown functional form. We propose a new class of models, the partly parametric generalized additive model (PPGAM) for doing generalized nonlinear regression with the confounding covariate effects adjusted nonparametrically. The response distribution is assumed to belong to the exponential family with the mean linked to an additive predictor comprising a nonlinear parametric function that is of main interest, plus additive, smooth functions of other covariates. The PPGAM extends both the generalized additive model (GAM) and the generalized nonlinear regression model. We propose to estimate a PPGAM by the method of penalized likelihood. We derive some asymptotic properties of the penalized likelihood estimator, including consistency and asymptotic normality of the parametric estimator of the nonlinear regression component. We propose a model selection criterion for the PPGAM, which resembles the BIC. We illustrate the new methodologies by simulations and real applications.