Using Count Data to Model Infrastructure Distress Initiation and Progression

Transportation infrastructure condition (or distress) can be modeled as continuous or discrete variables. As discrete variables, they are commonly recorded with nonnegative integers. In deterioration models, these variables can be treated as count data. For this purpose, Poisson and Negative Binomial models are commonly used. The Negative Binomial model was proved to perform better than the Poisson model resulting from its ability to address a critical statistical issue: over-dispersion. This study employs an extension to improve these existing models. A Hurdle-Negative Binomial model is applied, which accounts not only for over-dispersion but also for different deterioration mechanisms between distress initiation and progression. A case study is conducted based on the observations of real-world pavement cracking conditions. The advantages of this approach are demonstrated through integrating two joint deterioration models, which estimate the crack initiation probability with a choice model and the probabilities of numbers of progressed cracks with a truncated Negative Binomial model, respectively. The Hurdle-Negative Binomial model is shown to outperform the previous models from both statistical and engineering perspectives.