Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros

Modeling crash outcome probabilities at rural intersections: Application of hierarchical binomial logistic models

It is important to examine the nature of the relationships between roadway, environmental, and traffic factors and motor vehicle crashes, with the aim to improve the collective understanding of causal mechanisms involved in crashes and to better predict their occurrence. Statistical models of motor vehicle crashes are one path of inquiry often used to gain these initial insights. Recent efforts have focused on the estimation of negative binomial and Poisson regression models (and related deviants) due to their relatively good fit to crash data. Of course analysts constantly seek methods that offer greater consistency with the data generating mechanism (motor vehicle crashes in this case), provide better statistical fit, and provide insight into data structure that was previously unavailable. One such opportunity exists with some types of crash data, in particular crash-level data that are collected across roadway segments, intersections, etc. It is argued in this paper that some crash data possess hierarchical structure that has not routinely been exploited. This paper describes the application of binomial multilevel models of crash types using 548 motor vehicle crashes collected from 91 two-lane rural intersections in the state of Georgia. Crash prediction models are estimated for angle, rear-end, and sideswipe (both same direction and opposite direction) crashes. The contributions of the paper are the realization of hierarchical data structure and the application of a theoretically appealing and suitable analysis approach for multilevel data, yielding insights into intersection-related crashes by crash type.

Development of accident prediction models for rural highway intersections

A study was done to develop macrolevel crash prediction models that can be used to understand and identify effective countermeasures for improving signalized highway intersections and multilane stop-controlled highway intersections in rural areas. Poisson and negative binomial regression models were fit to intersection crash data from Georgia, California, and Michigan. To assess the suitability of the models, several goodness-of-fit measures were computed. The statistical models were then used to shed light on the relationships between crash occurrence and traffic and geometric features of the rural signalized intersections. The results revealed that traffic flow variables significantly affected the overall safety performance of the intersections regardless of intersection type and that the geometric features of intersections varied across intersection type and also influenced crash type.

Further notes on the application of zero-inflated models in highway safety

The intent of this note is to succinctly articulate additional points that were not provided in the original paper (Lord et al., 2005) and to help clarify a collective reluctance to adopt zero-inflated (ZI) models for modeling highway safety data. A dialogue on this important issue, just one of many important safety modeling issues, is healthy discourse on the path towards improved safety modeling. This note first provides a summary of prior findings and conclusions of the original paper. It then presents two critical and relevant issues: the maximizing statistical fit fallacy and logic problems with the ZI model in highway safety modeling. Finally, we provide brief conclusions.

Limited information estimation and evaluation of DSGE models

We advance the proposition that dynamic stochastic general equilibrium (DSGE) models should not only be estimated and evaluated with full information methods. These require that the complete system of equations be specified properly. Some limited information analysis, which focuses upon specific equations, is therefore likely to be a useful complement to full system analysis. Two major problems occur when implementing limited information methods. These are the presence of forward-looking expectations in the system as well as unobservable non-stationary variables. We present methods for dealing with both of these difficulties, and illustrate the interaction between full and limited information methods using a well-known model.

Sustainability performance of construction : conceptual models of satisfaction levels in construction projects

In general, the performance of construction projects, including their sustainability performance, does not meet optimal expectations. One aspect of this is the performance of the participants who are independent and make a significance impact on overall project outcomes. Of these participants, the client is traditionally the owner of the project, the architect or engineer is engaged as the lead designer and a contractor is selected to construct the facilities. Generally, the performance of the participants is gauged by considering three main factors, namely, time, cost and quality. As the level of satisfaction is a subjective issue, it is rarely used in the performance evaluation of construction work. Recently, various approaches to the measurement of satisfaction have been made in an attempt to determine the performance of construction project outcomes - for instance, client satisfaction, customer satisfaction, contractor satisfaction, occupant satisfaction and home buyer satisfaction. These not only identify the performance of the construction project but are also used to improve and maintain relationships. In addition, these assessments are necessary for the continuous improvement and enhanced cooperation of participants. The measurement of satisfaction levels primarily involves expectations and perceptions. An expectation can be regarded as a comparative standard of different needs, motives and beliefs, while a perception is a subjective interpretation that is influenced by moods, experiences and values. This suggests that the disparity between perceptions and expectations may possibly be used to represent different levels of satisfaction. However, this concept is rather new and in need of further investigation. This chapter examines the methods commonly practised in measuring satisfaction levels today and the advantages of promoting these methods. The results provide a preliminary review of the advantages of satisfaction measurement in the construction industry and recommendations are made concerning the most appropriate methods to use in identifying the performance of project outcomes.

A review of simulation models for railway systems

With the advances in computer hardware and software development techniques in the past 25 years, digital computer simulation of train movement and traction systems has been widely adopted as a standard computer-aided engineering tool [1] during the design and development stages of existing and new railway systems. Simulators of different approaches and scales are used extensively to investigate various kinds of system studies. Simulation is now proven to be the cheapest means to carry out performance predication and system behaviour characterisation. When computers were first used to study railway systems, they were mainly employed to perform repetitive but time-consuming computational tasks, such as matrix manipulations for power network solution and exhaustive searches for optimal braking trajectories. With only simple high-level programming languages available at the time, full advantage of the computing hardware could not be taken. Hence, structured simulations of the whole railway system were not very common. Most applications focused on isolated parts of the railway system. It is more appropriate to regard those applications as primarily mechanised calculations rather than simulations. However, a railway system consists of a number of subsystems, such as train movement, power supply and traction drives, which inevitably contains many complexities and diversities. These subsystems interact frequently with each other while the trains are moving; and they have their special features in different railway systems. To further complicate the simulation requirements, constraints like track geometry, speed restrictions and friction have to be considered, not to mention possible non-linearities and uncertainties in the system. In order to provide a comprehensive and accurate account of system behaviour through simulation, a large amount of data has to be organised systematically to ensure easy access and efficient representation; the interactions and relationships among the subsystems should be defined explicitly. These requirements call for sophisticated and effective simulation models for each component of the system. The software development techniques available nowadays allow the evolution of such simulation models. Not only can the applicability of the simulators be largely enhanced by advanced software design, maintainability and modularity for easy understanding and further development, and portability for various hardware platforms are also encouraged. The objective of this paper is to review the development of a number of approaches to simulation models. Attention is, in particular, given to models for train movement, power supply systems and traction drives. These models have been successfully used to enable various ‘what-if’ issues to be resolved effectively in a wide range of applications, such as speed profiles, energy consumption, run times etc.

Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

GVS : A flexible, low-end, 3D visualisation framework for enhancing conceptual groundwater models for community, management and simulations

In this paper we discuss an advanced, 3D groundwater visualisation and animation system that allows scientists, government agencies and community groups to better understand the groundwater processes that effect community planning and decision-making. The system is unique in that it has been designed to optimise community engagement. Although it incorporates a powerful visualisation engine, this open-source system can be freely distributed and boasts a simple user interface allowing individuals to run and investigate the models on their own PCs and gain intimate knowledge of the groundwater systems. The initial version of the Groundwater Visualisation System (GVS v1.0), was developed from a coastal delta setting (Bundaberg, QLD), and then applied to a basalt catchment area (Obi Obi Creek, Maleny, QLD). Several major enhancements have been developed to produce higher quality visualisations, including display of more types of data, support for larger models and improved user interaction. The graphics and animation capabilities have also been enhanced, notably the display of boreholes, depth logs and time-series water level surfaces. The GVS software remains under continual development and improvement

Nonprofit organizational and work unit identification and the occupational stress process

Research investigating the transactional approach to the work stressor-employee adjustment relationship has described many negative main effects between perceived stressors in the workplace and employee outcomes. A considerable amount of literature, theoretical and empirical, also describes potential moderators of this relationship. Organizational identification has been established as a significant predictor of employee job-related attitudes. To date, research has neglected investigation of the potential moderating effect of organizational identification in the work stressor-employee adjustment relationship. On the basis of identity, subjective fit and sense of belonging literature it was predicted that higher perceptions of identification at multiple levels of the organization would mitigate the negative effect of work stressors on employee adjustment. It was expected, further, that more proximal, lower order identifications would be more prevalent and potent as buffers of stressors on strain. Predictions were tested with an employee sample from five organizations (N = 267). Hierarchical moderated multiple regression analyses revealed some support for the stress-buffering effects of identification in the prediction of job satisfaction and organizational commitment, particularly for more proximal (i.e., work unit) identification. These positive stress-buffering effects, however, were present for low identifiers in some situations. The present study represents an extension of the application of organizational identity theory by identifying the effects of organizational and workgroup identification on employee outcomes in the nonprofit context. Our findings will contribute to a better understanding of the dynamics in nonprofit organizations and therefore contribute to the development of strategy and interventions to deal with identity-based issues in nonprofits.

Clone Detection in Repositories of Business Process Models

Business process model repositories capture precious knowledge about an organization or a business domain. In many cases, these repositories contain hundreds or even thousands of models and they represent several man-years of effort. Over time, process model repositories tend to accumulate duplicate fragments, as new process models are created by copying and merging fragments from other models. This calls for methods to detect duplicate fragments in process models that can be refactored as separate subprocesses in order to increase readability and maintainability. This paper presents an indexing structure to support the fast detection of clones in large process model repositories. Experiments show that the algorithm scales to repositories with hundreds of models. The experimental results also show that a significant number of non-trivial clones can be found in process model repositories taken from industrial practice.

Online service delivery models : an international comparison in the public sector

Governments around the world are facing the challenge of responding to increased expectations by their customers with regard to public service delivery. Citizens, for example, expect governments to provide better and more efficient electronic services on the Web in an integrated way. Online portals have become the approach of choice in online service delivery to meet these requirements and become more customer-focussed. This study describes and analyses existing variants of online service delivery models based upon an empirical study and provides valuable insights for researchers and practitioners in government. For this study, we have conducted interviews with senior management representatives from five international governments. Based on our findings, we distinguish three different classes of service delivery models. We describe and characterise each of these models in detail and provide an in-depth discussion of the strengths and weaknesses of these approaches.

Fragment-based version management for repositories of business process models

As organizations reach higher levels of Business Process Management maturity, they tend to accumulate large collections of process models. These repositories may contain thousands of activities and be managed by different stakeholders with varying skills and responsibilities. However, while being of great value, these repositories induce high management costs. Thus, it becomes essential to keep track of the various model versions as they may mutually overlap, supersede one another and evolve over time. We propose an innovative versioning model and associated storage structure, specifically designed to maximize sharing across process model versions, and to automatically handle change propagation. The focal point of this technique is to version single process model fragments, rather than entire process models. Indeed empirical evidence shows that real-life process model repositories have numerous duplicate fragments. Experiments on two industrial datasets confirm the usefulness of our technique.

Adapting to the work-life interface : the influence of individual differences, work and family on well-being, mental health and work engagement

Bronfenbrenner.s Bioecological Model, expressed as the developmental equation, D f PPCT, is the theoretical framework for two studies that bring together diverse strands of psychology to study the work-life interface of working adults. Occupational and organizational psychology is focused on the demands and resources of work and family, without emphasising the individual in detail. Health and personality psychology examine the individual but without emphasis on the individual.s work and family roles. The current research used Bronfenbrenner.s theoretical framework to combine individual differences, work and family to understand how these factors influence the working adult.s psychological functioning. Competent development has been defined as high well-being (measured as life satisfaction and psychological well-being) and high work engagement (as work vigour, work dedication and absorption in work) and as the absence of mental illness (as depression, anxiety and stress) and the absence of burnout (as emotional exhaustion, cynicism and professional efficacy). Study 1 and 2 were linked, with Study 1 as a cross-sectional survey and Study 2, a prospective panel study that followed on from the data used in Study1. Participants were recruited from a university and from a large public hospital to take part in a 3-wave, online study where they completed identical surveys at 3-4 month intervals (N = 470 at Time 1 and N = 198 at Time 3). In Study 1, hierarchical multiple regressions were used to assess the effects of individual differences (Block 1, e.g. dispositional optimism, coping self-efficacy, perceived control of time, humour), work and family variables (Block 2, e.g. affective commitment, skill discretion, work hours, children, marital status, family demands) and the work-life interface (Block 3, e.g. direction and quality of spillover between roles, work-life balance) on the outcomes. There were a mosaic of predictors of the outcomes with a group of seven that were the most frequent significant predictors and which represented the individual (dispositional optimism and coping self-efficacy), the workplace (skill discretion, affective commitment and job autonomy) and the work-life interface (negative work-to-family spillover and negative family-to-work spillover). Interestingly, gender and working hours were not important predictors. The effects of job social support, generally and for work-life issues, perceived control of time and egalitarian gender roles on the outcomes were mediated by negative work-to-family spillover, particularly for emotional exhaustion. Further, the effect of negative spillover on depression, anxiety and work engagement was moderated by the individual.s personal and workplace resources. Study 2 modelled the longitudinal relationships between the group of the seven most frequent predictors and the outcomes. Using a set of non-nested models, the relative influences of concurrent functioning, stability and change over time were assessed. The modelling began with models at Time 1, which formed the basis for confirmatory factor analysis (CFA) to establish the underlying relationships between the variables and calculate the composite variables for the longitudinal models. The CFAs were well fitting with few modifications to ensure good fit. However, using burnout and work engagement together required additional analyses to resolve poor fit, with one factor (representing a continuum from burnout to work engagement) being the only acceptable solution. Five different longitudinal models were investigated as the Well-Being, Mental Distress, Well-Being-Mental Health, Work Engagement and Integrated models using differing combinations of the outcomes. The best fitting model for each was a reciprocal model that was trimmed of trivial paths. The strongest paths were the synchronous correlations and the paths within variables over time. The reciprocal paths were more variable with weak to mild effects. There was evidence of gain and loss spirals between the variables over time, with a slight net gain in resources that may provide the mechanism for the accumulation of psychological advantage over a lifetime. The longitudinal models also showed that there are leverage points at which personal, psychological and managerial interventions can be targeted to bolster the individual and provide supportive workplace conditions that also minimise negative spillover. Bronfenbrenner.s developmental equation has been a useful framework for the current research, showing the importance of the person as central to the individual.s experience of the work-life interface. By taking control of their own life, the individual can craft a life path that is most suited to their own needs. Competent developmental outcomes were most likely where the person was optimistic and had high self-efficacy, worked in a job that they were attached to and which allowed them to use their talents and without too much negative spillover between their work and family domains. In this way, individuals had greater well-being, better mental health and greater work engagement at any one time and across time.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.