Seth D. Guikema

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

This paper documents the application of the Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM) for modeling motor vehicle crashes. The COM-Poisson distribution, originally developed in 1962, has recently been re-introduced by statisticians for analyzing count data subjected to over- and under-dispersion. This innovative distribution is an extension of the Poisson distribution. The objectives of this study were to evaluate the application of the COM-Poisson GLM for analyzing motor vehicle crashes and compare the results with the traditional negative binomial (NB) model. The comparison analysis was carried out using the most common functional forms employed by transportation safety analysts, which link crashes to the entering flows at intersections or on segments. To accomplish the objectives of the study, several NB and COM-Poisson GLMs were developed and compared using two datasets. The first dataset contained crash data collected at signalized four-legged intersections in Toronto, Ont. The second dataset included data collected for rural four-lane divided and undivided highways in Texas. Several methods were used to assess the statistical fit and predictive performance of the models. The results of this study show that COM-Poisson GLMs perform as well as NB models in terms of GOF statistics and predictive performance. Given the fact the COM-Poisson distribution can also handle under-dispersed data (while the NB distribution cannot or has difficulties converging), which have sometimes been observed in crash databases, the COM-Poisson GLM offers a better alternative over the NB model for modeling motor vehicle crashes, especially given the important limitations recently documented in the safety literature about the latter type of model.

A flexible count data regression model for risk analysis

In many cases, risk and reliability analyses involve estimating the probabilities of discrete events such as hardware failures and occurrences of disease or death. There is often additional information in the form of explanatory variables that can be used to help estimate the likelihood of different numbers of events in the future through the use of an appropriate regression model, such as a generalized linear model. However, existing generalized linear models (GLM) are limited in their ability to handle the types of variance structures often encountered in using count data in risk and reliability analysis. In particular, standard models cannot handle both underdispersed data (variance less than the mean) and overdispersed data (variance greater than the mean) in a single coherent modeling framework. This article presents a new GLM based on a reformulation of the Conway-Maxwell Poisson (COM) distribution that is useful for both underdispersed and overdispersed count data and demonstrates this model by applying it to the assessment of electric power system reliability. The results show that the proposed COM GLM can provide as good of fits to data as the commonly used existing models for overdispered data sets while outperforming these commonly used models for underdispersed data sets.

Estimating the spatial distribution of power outages during hurricanes in the Gulf coast region

Hurricanes have caused severe damage to the electric power system throughout the Gulf coast region of the US, and electric power is critical to post-hurricane disaster response as well as to long-term recovery for impacted areas. Managing power outage risk and preparing for post-storm recovery efforts requires accurate methods for estimating the number and location of power outages. This paper builds on past work on statistical power outage estimation models to develop, test, and demonstrate a statistical power outage risk estimation model for the Gulf Coast region of the US. Previous work used binary hurricane-indicator variables representing particular hurricanes in order to achieve a good fit to the past data. To use these models for predicting power outages during future hurricanes, one must implicitly assume that an approaching hurricane is similar to the average of the past hurricanes. The model developed in this paper replaces these indicator variables with physically measurable variables, enabling future predictions to be based on only well-understood characteristics of hurricanes. The models were developed using data about power outages during nine hurricanes in three states served by a large, investor-owned utility company in the Gulf Coast region.

Virtual Cities for Water Distribution and Infrastructure System Research

In a society concerned over the possibility of terrorism, secrecy , and security of infrastructure data is crucial. However, research on infrastructure security is difficult in this environment since experiments on real systems can not be publicized. “Virtual cities” are one potential answer to this problem, and a library of these virtual cities is now under development. “Micropolis” is a virtual city of 5000 resi dents fully described in both GIS and EPANet hydraulic model frameworks. To simulate realism of infrastructure, a developmental timeline spanning 130 years was included. This timeline is manifested in items such as pipe material, diameter, and topology. An example of using the virtual city for simulation of fire protection is presented. The data files describing Micropolis are avail able from the authors for other s’ use. A larger city, “Mesopolis,” is currently under development and will incorporate add itional critical infrastructure dependencies such as electrical power grids and communications. This will supplement the development of further models to account for risks and probability of electrical power failure due to hurricane events. It is hoped t hat Micropolis, Mesopolis , and additional virtual cities will serve as a “hub” for the development of further research models.

Post-Earthquake Restoration Planning for Los Angeles Electric Power

This paper describes the application of a new discrete-event-simulation model of the post-earthquake electric power restoration process in Los Angeles. The findings are that (1) Los Angeles residents may experience power outages lasting up to 10 days; (2) what we call the power rapidity risk (the joint probability distribution of restoration of a specified number of customers in a specified amount of time) varies throughout the area; (3) there is a relatively high likelihood that more repair materials than are currently available will be required if a large earthquake occurs; and (4) there are ways to reduce the expected duration of earthquake-initiated power outages and they should be subjected to cost-benefit analysis. These results should be useful to utilities and emergency planners in Los Angeles. The new simulation modeling approach could be used in other seismically active cities to gain insights into the restoration process that other modeling approaches cannot provide.

Comparison and Validation of Statistical Methods for Predicting Power Outage Durations in the Event of Hurricanes

This article compares statistical methods for modeling power outage durations during hurricanes and examines the predictive accuracy of these methods. Being able to make accurate predictions of power outage durations is valuable because the information can be used by utility companies to plan their restoration efforts more efficiently. This information can also help inform customers and public agencies of the expected outage times, enabling better collective response planning, and coordination of restoration efforts for other critical infrastructures that depend on electricity. In the long run, outage duration estimates for future storm scenarios may help utilities and public agencies better allocate risk management resources to balance the disruption from hurricanes with the cost of hardening power systems. We compare the out-of-sample predictive accuracy of five distinct statistical models for estimating power outage duration times caused by Hurricane Ivan in 2004. The methods compared include both regression models (accelerated failure time (AFT) and Cox proportional hazard models (Cox PH)) and data mining techniques (regression trees, Bayesian additive regression trees (BART), and multivariate additive regression splines). We then validate our models against two other hurricanes. Our results indicate that BART yields the best prediction accuracy and that it is possible to predict outage durations with reasonable accuracy.

Improving the predictive accuracy of hurricane power outage forecasts using generalized additive models.

Electric power is a critical infrastructure service after hurricanes, and rapid restoration of electric power is important in order to minimize losses in the impacted areas. However, rapid restoration of electric power after a hurricane depends on obtaining the necessary resources, primarily repair crews and materials, before the hurricane makes landfall and then appropriately deploying these resources as soon as possible after the hurricane. This, in turn, depends on having sound estimates of both the overall severity of the storm and the relative risk of power outages in different areas. Past studies have developed statistical, regression-based approaches for estimating the number of power outages in advance of an approaching hurricane. However, these approaches have either not been applicable for future events or have had lower predictive accuracy than desired. This article shows that a different type of regression model, a generalized additive model (GAM), can outperform the types of models used previously. This is done by developing and validating a GAM based on power outage data during past hurricanes in the Gulf Coast region and comparing the results from this model to the previously used generalized linear models.

Extension of the Application of Conway-Maxwell-Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion

The objective of this article is to evaluate the performance of the COM-Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM-Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over- or underdispersion. Over the last year, the COM-Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson-gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM-Poisson models were estimated using crash data collected at 162 railway-highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM-Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.

Statistical models for the analysis of water distribution system pipe break data

The deterioration of pipes leading to pipe breaks and leaks in urban water distribution systems is of concern to water utilities throughout the world. Pipe breaks and leaks may result in reduction in the water-carrying capacity of the pipes and contamination of water in the distribution systems. Water utilities incur large expenses in the replacement and rehabilitation of water mains, making it critical to evaluate the current and future condition of the system for maintenance decision-making. This paper compares different statistical regression models proposed in the literature for estimating the reliability of pipes in a water distribution system on the basis of short time histories. The goals of these models are to estimate the likelihood of pipe breaks in the future and determine the parameters that most affect the likelihood of pipe breaks. The data set used for the analysis comes from a major US city, and these data include approximately 85,000 pipe segments with nearly 2500 breaks from 2000 through 2005. The results show that the set of statistical models previously proposed for this problem do not provide good estimates with the test data set. However, logistic generalized linear models do provide good estimates of pipe reliability and can be useful for water utilities in planning pipe inspection and maintenance.

Multidecadal increase in North Atlantic coccolithophores and the potential role of rising CO2

Passing an acid test Calcifying marine organisms will generally find it harder to make and maintain their carbonate skeletons as increasing concentrations of atmospheric CO2 acidify the oceans. Nevertheless, some types of organisms will be damaged more than others, and some may even benefit from higher CO2 levels. Coccolithophores are a case in point, because their photosynthetic ability is strongly carbon-limited. Rivero-Calle et al. show that the abundance of coccolithophores in the North Atlantic has increased by up to 20% or more in the past 50 years (see the Perspective by Vogt). Thus, this major phytoplankton functional group may be able to adapt to a future with higher CO2 concentrations. Science, this issue p. 1533; see also p. 1466 Coccolithophores may be able to adapt to a world with higher levels of carbon dioxide. [Also see Perspective by Vogt] As anthropogenic carbon dioxide (CO2) emissions acidify the oceans, calcifiers generally are expected to be negatively affected. However, using data from the Continuous Plankton Recorder, we show that coccolithophore occurrence in the North Atlantic increased from ~2 to more than 20% from 1965 through 2010. We used random forest models to examine more than 20 possible environmental drivers of this change, finding that CO2 and the Atlantic Multidecadal Oscillation were the best predictors, leading us to hypothesize that higher CO2 levels might be encouraging growth. A compilation of 41 independent laboratory studies supports our hypothesis. Our study shows a long-term basin-scale increase in coccolithophores and suggests that increasing CO2 and temperature have accelerated the growth of a phytoplankton group that is important for carbon cycling.