Statistical Modelling 16 (4) (2016), 279–296

Sums of smooth exponentials to decompose complex series of counts

Carlo G Camarda
Institut National d'Etudes Démographiques,
Paris,
France br> Center for Data Analysis,
Washington, DC,
United States
e-mail: carlo-giovanni.camarda@ined.fr

Paul HC Eilers
Department of Biostatistics,
Erasmus University Rotterdam,
Rotterdam,
the Netherlands


Jutta Gampe
Max Planck Institute for Demographic Research,
Rostock,
Germany


Abstract:

Representing the conditional mean in Poisson regression directly as a sum of smooth components can provide a realistic model of the data generating process. Here, we present an approach that allows such an additive decomposition of the expected values of counts. The model can be formulated as a penalized composite link model and can, therefore, be estimated by a modified iteratively weighted least-squares algorithm. Further shape constraints on the smooth additive components can be enforced by additional penalties, and the model is extended to two dimensions. We present two applications that motivate the model and demonstrate the versatility of the approach.

Keywords:

additive components; Composite link model; decomposition; penalty shape constraints.

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