Practical Considerations in Statistical Modeling of Count Data for Infrastructure Systems

Count data arise in a number of infrastructure assessment problems such as modeling traffic accidents, pipe breaks in water distribution systems, and electric power outages. A common goal in these problems is to model the number of occurrences of an event of interest in the future based on past data. There is usually a great deal of variability in the past data, but there is a considerable amount of other information available that can help inform the models. A number of statistical models have been proposed and used for modeling count data in infrastructure assessment, including linear regression and generalized linear models. This paper summarizes these approaches and their past uses in infrastructure assessment. It then gives an overview of a class of models called generalized additive models that can incorporate nonlinear relationships between explanatory variables and counts of events in a flexible manner. Throughout the paper, the focus is on the practical usefulness of the different models, and an actual data set is used to demonstrate the different models.