B1354
Title: Generalized additive models with flexible link function
Authors: Elmar Spiegel - University of Goettingen (Germany) [presenting]
Fabian Sobotka - University Oldenburg (Germany)
Thomas Kneib - University of Goettingen (Germany)
Abstract: Ordinary generalized linear models (GLM) depend on several assumptions: (i) the specified linear predictor and (ii) the pre-specified likelihood/link function. In order to avoid the restriction of linear predictors, generalized additive models (GAM) with semiparametric predictors have been considered. The covariates may be included as flexible nonlinear or spatial functions to avoid biased estimates. The influence of misspecified link functions has been shown before and single index models are a common solution which results in a GLM with a flexibly estimated link function. However these single index models are usually restricted to a linear predictor and aim to compensate for the non-linear structure with the estimated link. We show that this is insufficient and present a solution by combining a flexible link estimation with GAM. The link functions are estimated with (strictly) monotone $p$-splines. Due to the monotonicity constraint, the estimations are identifiable and the results interpretable.
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