Penalized Splines Fitting for a Poisson Response Including Outliers

Abstract

There have been various studies in the literature on investigating the relationship between a count response and several covariates. Most researchers study count variables and use traditional methods (i.e. generalized linear models-GLM). However, GLM is limited when dealing with outliers and nonlinear relationships. Generalized Additive Models (GAM) is an extension of GLM, where the assumptions on the link functions and components are additive and smooth, respectively. Our aim is to propose a flexible extension of GLM and demonstrate the usefulness and performance of GAMs for the analysis of Poisson data set including outliers in the response variable through extensive Monte Carlo Simulations and using three applications.

Ecological conditions predict the intensity of Hendra virus excretion over space and time from bat reservoir hosts

“…We therefore used spatial buffers of 50, 100, 200, 300, 400 and 500 km. We modelled counts of spillovers within each buffer through a set of GAMs that used Poisson distributions and penalised splines for AUC, again using REML and γ = 1.4 to limit overfitting (Kilinc & Asfha, 2019). To more specifically estimate the shape of the association between AUC and spillover, we also applied nonlinear least squares to fit linear, saturating, and quadratic relationships using the nls package for each spatial scale and compared models with AICc (Seber & Wild, 2005).…”

Ecological conditions experienced by bat reservoir hosts predict the intensity of Hendra virus excretion over space and time

“…We therefore used spatial buffers of 50, 100, 200, 300, 400, and 500 km. We modeled counts of spillovers within each buffer through a set of GAMs that used Poisson distributions and penalized splines for pathogen pressure [62]. As in our GAM analyses of AUC, we also included a bivariate smooth of longitude and latitude.…”