An Outlier-Robust Fit for Generalized Additive Models with Applications to Outbreak Detection

• Activity Number: 308
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Matias Salibián-Barrera*+ and Azadeh Alimadad
• Companies: The University of British Columbia and Simon Fraser University
• Keywords: Generalized Additive Models ; robustness ; outliers ; robust quasi-likelihood

Abstract

We are interested in detecting disease outbreaks using Generalized Additive Models to model case counts. Unfortunately, GAMs can be very sensitive to a small proportion of outliers in the data. In other words, the outliers may cause the predicted values to not appear atypical, and hence mask the outbreak. In this paper we discuss an outlier-robust fit for GAMs based on the backfitting algorithm. The basic idea is to replace the MLE-based weights in the Generalized Local Scoring Algorithm with those derived from robust quasi-likelihood equations. We show that the resulting estimated mean function is resistant to outliers in the response variable. It also remains close to the GAM estimator when no outliers are present in the data. We illustrate our approach on the recent outbreak of H1N1 flu by looking at the weekly counts of influenza-like-illness doctor visits.