Sums of smooth exponentials to decompose complex series of counts. (August 2016)

• Record Type: Journal Article
• Authors: Camarda, Carlo G; Eilers, Paul HC; Gampe, Jutta
• Is Part Of: Statistical modelling. Volume 16:Number 4(2016)
• Page Start: 279
• Page End: 296
• Publication Date: 2016-08
• Subjects: additive components -- Composite link model -- decomposition -- penalty -- shape constraints; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X16641796
• Languages: English
• ISSNs: 1471-082X

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.