Important omitted spatial variables in safety models: Understanding contributing crash causes at intersections

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causation—rests upon the pursuit of numerous lines of inquiry. The research community has focused on analytical methods development (negative binomial specifications, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might think of different lines of inquiry in terms of ‘low lying fruit’—areas of inquiry that might provide significant improvements in understanding crash causation. It is the contention of this research that omitted variable bias caused by the exclusion of important variables is an important line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant ability to better understand contributing factors to crashes. This study—believed to represent a unique contribution to the safety literature—develops and examines the role of a sizeable set of spatial variables in intersection crash occurrence. In addition to commonly considered traffic and geometric variables, examined spatial factors include local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools. The results indicate that inclusion of these factors results in significant improvement in model explanatory power, and the results also generally agree with expectation. The research illuminates the importance of spatial variables in safety research and also the negative consequences of their omissions.

The use of ZIP and CART to model cryptosporidiosis in relation to climatic variables

This research assesses the potential impact of weekly weather variability on the incidence of cryptosporidiosis disease using time series zero-inflated Poisson (ZIP) and classification and regression tree (CART) models. Data on weather variables, notified cryptosporidiosis cases and population size in Brisbane were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics, respectively. Both time series ZIP and CART models show a clear association between weather variables (maximum temperature, relative humidity, rainfall and wind speed) and cryptosporidiosis disease. The time series CART models indicated that, when weekly maximum temperature exceeded 31°C and relative humidity was less than 63%, the relative risk of cryptosporidiosis rose by 13.64 (expected morbidity: 39.4; 95% confidence interval: 30.9–47.9). These findings may have applications as a decision support tool in planning disease control and risk management programs for cryptosporidiosis disease.

Model-order selection in Zernike polynomial expansion of corneal surfaces using the efficient detection criterion

Corneal-height data are typically measured with videokeratoscopes and modeled using a set of orthogonal Zernike polynomials. We address the estimation of the number of Zernike polynomials, which is formalized as a model-order selection problem in linear regression. Classical information-theoretic criteria tend to overestimate the corneal surface due to the weakness of their penalty functions, while bootstrap-based techniques tend to underestimate the surface or require extensive processing. In this paper, we propose to use the efficient detection criterion (EDC), which has the same general form of information-theoretic-based criteria, as an alternative to estimating the optimal number of Zernike polynomials. We first show, via simulations, that the EDC outperforms a large number of information-theoretic criteria and resampling-based techniques. We then illustrate that using the EDC for real corneas results in models that are in closer agreement with clinical expectations and provides means for distinguishing normal corneal surfaces from astigmatic and keratoconic surfaces.

Heat effects of promoters and determination of burn criterion in promoted combustion testing

Promoted ignition testing (NASA) Test 17) [1] is used to determine the relative flammability of metal rods in oxygen-enriched atmospheres. A promotor is used to ignite a metal sample rod, initiating sample burning. If a predetermined length of the sample burns, beyond the promotor, the material is considered flammable at the condition tested. Historically, this burn length has been somewhat arbitrary. Experiments were performed to better understand this test by obtaining insight into the effect a burning promotor has on the preheating of a test sample. Test samples of several metallic materials were prepared and coupled to fast-responding thermocouples along their length. Thermocouple measurements and test video were synchronized to determine temperature increase with respect to time and length along each test sample. A recommended flammability burn length, based on a sample preheat of 500 degrees fahrenheit, was determined based on the preheated zone measured from these tests. This length was determined to be 30 mm (1.18 in.). Validation of this length and its rationale are presented.

An assessment system for evaluation of driving competencies

Automobiles have deeply impacted the way in which we travel but they have also contributed to many deaths and injury due to crashes. A number of reasons for these crashes have been pointed out by researchers. Inexperience has been identified as a contributing factor to road crashes. Driver’s driving abilities also play a vital role in judging the road environment and reacting in-time to avoid any possible collision. Therefore driver’s perceptual and motor skills remain the key factors impacting on road safety. Our failure to understand what is really important for learners, in terms of competent driving, is one of the many challenges for building better training programs. Driver training is one of the interventions aimed at decreasing the number of crashes that involve young drivers. Currently, there is a need to develop comprehensive driver evaluation system that benefits from the advances in Driver Assistance Systems. A multidisciplinary approach is necessary to explain how driving abilities evolves with on-road driving experience. To our knowledge, driver assistance systems have never been comprehensively used in a driver training context to assess the safety aspect of driving. The aim and novelty of this thesis is to develop and evaluate an Intelligent Driver Training System (IDTS) as an automated assessment tool that will help drivers and their trainers to comprehensively view complex driving manoeuvres and potentially provide effective feedback by post processing the data recorded during driving. This system is designed to help driver trainers to accurately evaluate driver performance and has the potential to provide valuable feedback to the drivers. Since driving is dependent on fuzzy inputs from the driver (i.e. approximate distance calculation from the other vehicles, approximate assumption of the other vehicle speed), it is necessary that the evaluation system is based on criteria and rules that handles uncertain and fuzzy characteristics of the driving tasks. Therefore, the proposed IDTS utilizes fuzzy set theory for the assessment of driver performance. The proposed research program focuses on integrating the multi-sensory information acquired from the vehicle, driver and environment to assess driving competencies. After information acquisition, the current research focuses on automated segmentation of the selected manoeuvres from the driving scenario. This leads to the creation of a model that determines a “competency” criterion through the driving performance protocol used by driver trainers (i.e. expert knowledge) to assess drivers. This is achieved by comprehensively evaluating and assessing the data stream acquired from multiple in-vehicle sensors using fuzzy rules and classifying the driving manoeuvres (i.e. overtake, lane change, T-crossing and turn) between low and high competency. The fuzzy rules use parameters such as following distance, gaze depth and scan area, distance with respect to lanes and excessive acceleration or braking during the manoeuvres to assess competency. These rules that identify driving competency were initially designed with the help of expert’s knowledge (i.e. driver trainers). In-order to fine tune these rules and the parameters that define these rules, a driving experiment was conducted to identify the empirical differences between novice and experienced drivers. The results from the driving experiment indicated that significant differences existed between novice and experienced driver, in terms of their gaze pattern and duration, speed, stop time at the T-crossing, lane keeping and the time spent in lanes while performing the selected manoeuvres. These differences were used to refine the fuzzy membership functions and rules that govern the assessments of the driving tasks. Next, this research focused on providing an integrated visual assessment interface to both driver trainers and their trainees. By providing a rich set of interactive graphical interfaces, displaying information about the driving tasks, Intelligent Driver Training System (IDTS) visualisation module has the potential to give empirical feedback to its users. Lastly, the validation of the IDTS system’s assessment was conducted by comparing IDTS objective assessments, for the driving experiment, with the subjective assessments of the driver trainers for particular manoeuvres. Results show that not only IDTS was able to match the subjective assessments made by driver trainers during the driving experiment but also identified some additional driving manoeuvres performed in low competency that were not identified by the driver trainers due to increased mental workload of trainers when assessing multiple variables that constitute driving. The validation of IDTS emphasized the need for an automated assessment tool that can segment the manoeuvres from the driving scenario, further investigate the variables within that manoeuvre to determine the manoeuvre’s competency and provide integrated visualisation regarding the manoeuvre to its users (i.e. trainers and trainees). Through analysis and validation it was shown that IDTS is a useful assistance tool for driver trainers to empirically assess and potentially provide feedback regarding the manoeuvres undertaken by the drivers.

Towards a classification of criterion referenced assessment models in mathematics courses : student and academic perspectives

We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

Evaluation of financial incentives as a quality improvement strategy in the public hospital context : clinician attitudes, design variables, and economic costs

In 2008, a three-year pilot ‘pay for performance’ (P4P) program, known as ‘Clinical Practice Improvement Payment’ (CPIP) was introduced into Queensland Health (QHealth). QHealth is a large public health sector provider of acute, community, and public health services in Queensland, Australia. The organisation has recently embarked on a significant reform agenda including a review of existing funding arrangements (Duckett et al., 2008). Partly in response to this reform agenda, a casemix funding model has been implemented to reconnect health care funding with outcomes. CPIP was conceptualised as a performance-based scheme that rewarded quality with financial incentives. This is the first time such a scheme has been implemented into the public health sector in Australia with a focus on rewarding quality, and it is unique in that it has a large state-wide focus and includes 15 Districts. CPIP initially targeted five acute and community clinical areas including Mental Health, Discharge Medication, Emergency Department, Chronic Obstructive Pulmonary Disease, and Stroke. The CPIP scheme was designed around key concepts including the identification of clinical indicators that met the set criteria of: high disease burden, a well defined single diagnostic group or intervention, significant variations in clinical outcomes and/or practices, a good evidence, and clinician control and support (Ward, Daniels, Walker & Duckett, 2007). This evaluative research targeted Phase One of implementation of the CPIP scheme from January 2008 to March 2009. A formative evaluation utilising a mixed methodology and complementarity analysis was undertaken. The research involved three research questions and aimed to determine the knowledge, understanding, and attitudes of clinicians; identify improvements to the design, administration, and monitoring of CPIP; and determine the financial and economic costs of the scheme. Three key studies were undertaken to ascertain responses to the key research questions. Firstly, a survey of clinicians was undertaken to examine levels of knowledge and understanding and their attitudes to the scheme. Secondly, the study sought to apply Statistical Process Control (SPC) to the process indicators to assess if this enhanced the scheme and a third study examined a simple economic cost analysis. The CPIP Survey of clinicians elicited 192 clinician respondents. Over 70% of these respondents were supportive of the continuation of the CPIP scheme. This finding was also supported by the results of a quantitative altitude survey that identified positive attitudes in 6 of the 7 domains-including impact, awareness and understanding and clinical relevance, all being scored positive across the combined respondent group. SPC as a trending tool may play an important role in the early identification of indicator weakness for the CPIP scheme. This evaluative research study supports a previously identified need in the literature for a phased introduction of Pay for Performance (P4P) type programs. It further highlights the value of undertaking a formal risk assessment of clinician, management, and systemic levels of literacy and competency with measurement and monitoring of quality prior to a phased implementation. This phasing can then be guided by a P4P Design Variable Matrix which provides a selection of program design options such as indicator target and payment mechanisms. It became evident that a clear process is required to standardise how clinical indicators evolve over time and direct movement towards more rigorous ‘pay for performance’ targets and the development of an optimal funding model. Use of this matrix will enable the scheme to mature and build the literacy and competency of clinicians and the organisation as implementation progresses. Furthermore, the research identified that CPIP created a spotlight on clinical indicators and incentive payments of over five million from a potential ten million was secured across the five clinical areas in the first 15 months of the scheme. This indicates that quality was rewarded in the new QHealth funding model, and despite issues being identified with the payment mechanism, funding was distributed. The economic model used identified a relative low cost of reporting (under $8,000) as opposed to funds secured of over $300,000 for mental health as an example. Movement to a full cost effectiveness study of CPIP is supported. Overall the introduction of the CPIP scheme into QHealth has been a positive and effective strategy for engaging clinicians in quality and has been the catalyst for the identification and monitoring of valuable clinical process indicators. This research has highlighted that clinicians are supportive of the scheme in general; however, there are some significant risks that include the functioning of the CPIP payment mechanism. Given clinician support for the use of a pay–for-performance methodology in QHealth, the CPIP scheme has the potential to be a powerful addition to a multi-faceted suite of quality improvement initiatives within QHealth.

Variables governing the dynamics of attacker-defender systems in team sport

This project was a step forward in the examination and identification of key variables on the perception, decision making and action of team sport athletes through theoretical insights provided by the ecological dynamics perspective. The methodology drew on experiential knowledge of elite coaches to drive further empirical investigation into the specific task, environmental and personal constraints that shape the behaviour of athletes in specific performance contexts. The thesis has provided an effective rationale for further investigation into the emergent perception, decision making and action demanded of athletes in these unpredictable, fluent, fast-paced environments.

Bounded parameter Markov Decision Processes with average reward criterion

Bounded parameter Markov Decision Processes (BMDPs) address the issue of dealing with uncertainty in the parameters of a Markov Decision Process (MDP). Unlike the case of an MDP, the notion of an optimal policy for a BMDP is not entirely straightforward. We consider two notions of optimality based on optimistic and pessimistic criteria. These have been analyzed for discounted BMDPs. Here we provide results for average reward BMDPs. We establish a fundamental relationship between the discounted and the average reward problems, prove the existence of Blackwell optimal policies and, for both notions of optimality, derive algorithms that converge to the optimal value function.

An economic evaluation of the Safe Motherhood programme in Guangxi, China

Maternal and infant mortality is a global health issue with a significant social and economic impact. Each year, over half a million women worldwide die due to complications related to pregnancy or childbirth, four million infants die in the first 28 days of life, and eight million infants die in the first year. Ninety-nine percent of maternal and infant deaths are in developing countries. Reducing maternal and infant mortality is among the key international development goals. In China, the national maternal mortality ratio and infant mortality rate were reduced greatly in the past two decades, yet a large discrepancy remains between urban and rural areas. To address this problem, a large-scale Safe Motherhood Programme was initiated in 2000. The programme was implemented in Guangxi in 2003. Interventions in the programme included both demand-side and supply side-interventions focusing on increasing health service use and improving birth outcomes. Little is known about the effects and economic outcomes of the Safe Motherhood Programme in Guangxi, although it has been implemented for seven years. The aim of this research is to estimate the effectiveness and cost-effectiveness of the interventions in the Safe Motherhood Programme in Guangxi, China. The objectives of this research include: 1. To evaluate whether the changes of health service use and birth outcomes are associated with the interventions in the Safe Motherhood Programme. 2. To estimate the cost-effectiveness of the interventions in the Safe Motherhood Programme and quantify the uncertainty surrounding the decision. 3. To assess the expected value of perfect information associated with both the whole decision and individual parameters, and interpret the findings to inform priority setting in further research and policy making in this area. A quasi-experimental study design was used in this research to assess the effectiveness of the programme in increasing health service use and improving birth outcomes. The study subjects were 51 intervention counties and 30 control counties. Data on the health service use, birth outcomes and socio-economic factors from 2001 to 2007 were collected from the programme database and statistical yearbooks. Based on the profile plots of the data, general linear mixed models were used to evaluate the effectiveness of the programme while controlling for the effects of baseline levels of the response variables, change of socio-economic factors over time and correlations among repeated measurements from the same county. Redundant multicollinear variables were deleted from the mixed model using the results of the multicollinearity diagnoses. For each response variable, the best covariance structure was selected from 15 alternatives according to the fit statistics including Akaike information criterion, Finite-population corrected Akaike information criterion, and Schwarz.s Bayesian information criterion. Residual diagnostics were used to validate the model assumptions. Statistical inferences were made to show the effect of the programme on health service use and birth outcomes. A decision analytic model was developed to evaluate the cost-effectiveness of the programme, quantify the decision uncertainty, and estimate the expected value of perfect information associated with the decision. The model was used to describe the transitions between health states for women and infants and reflect the change of both costs and health benefits associated with implementing the programme. Result gained from the mixed models and other relevant evidence identified were synthesised appropriately to inform the input parameters of the model. Incremental cost-effectiveness ratios of the programme were calculated for the two groups of intervention counties over time. Uncertainty surrounding the parameters was dealt with using probabilistic sensitivity analysis, and uncertainty relating to model assumptions was handled using scenario analysis. Finally the expected value of perfect information for both the whole model and individual parameters in the model were estimated to inform priority setting in further research in this area.The annual change rates of the antenatal care rate and the institutionalised delivery rate were improved significantly in the intervention counties after the programme was implemented. Significant improvements were also found in the annual change rates of the maternal mortality ratio, the infant mortality rate, the incidence rate of neonatal tetanus and the mortality rate of neonatal tetanus in the intervention counties after the implementation of the programme. The annual change rate of the neonatal mortality rate was also improved, although the improvement was only close to statistical significance. The influences of the socio-economic factors on the health service use indicators and birth outcomes were identified. The rural income per capita had a significant positive impact on the health service use indicators, and a significant negative impact on the birth outcomes. The number of beds in healthcare institutions per 1,000 population and the number of rural telephone subscribers per 1,000 were found to be positively significantly related to the institutionalised delivery rate. The length of highway per square kilometre negatively influenced the maternal mortality ratio. The percentage of employed persons in the primary industry had a significant negative impact on the institutionalised delivery rate, and a significant positive impact on the infant mortality rate and neonatal mortality rate. The incremental costs of implementing the programme over the existing practice were US $11.1 million from the societal perspective, and US $13.8 million from the perspective of the Ministry of Health. Overall, 28,711 life years were generated by the programme, producing an overall incremental cost-effectiveness ratio of US $386 from the societal perspective, and US $480 from the perspective of the Ministry of Health, both of which were below the threshold willingness-to-pay ratio of US $675. The expected net monetary benefit generated by the programme was US $8.3 million from the societal perspective, and US $5.5 million from the perspective of the Ministry of Health. The overall probability that the programme was cost-effective was 0.93 and 0.89 from the two perspectives, respectively. The incremental cost-effectiveness ratio of the programme was insensitive to the different estimates of the three parameters relating to the model assumptions. Further research could be conducted to reduce the uncertainty surrounding the decision, in which the upper limit of investment was US $0.6 million from the societal perspective, and US $1.3 million from the perspective of the Ministry of Health. It is also worthwhile to get a more precise estimate of the improvement of infant mortality rate. The population expected value of perfect information for individual parameters associated with this parameter was US $0.99 million from the societal perspective, and US $1.14 million from the perspective of the Ministry of Health. The findings from this study have shown that the interventions in the Safe Motherhood Programme were both effective and cost-effective in increasing health service use and improving birth outcomes in rural areas of Guangxi, China. Therefore, the programme represents a good public health investment and should be adopted and further expanded to an even broader area if possible. This research provides economic evidence to inform efficient decision making in improving maternal and infant health in developing countries.

Validating the is-impact model in the Malaysian public sector

This research is one of several ongoing studies conducted within the IT Professional Services (ITPS) research programme at Queensland University of Technology (QUT). In 2003, ITPS introduced the IS-Impact model, a measurement model for measuring information systems success from the viewpoint of multiple stakeholders. The model, along with its instrument, is robust, simple, yet generalisable, and yields results that are comparable across time, stakeholders, different systems and system contexts. The IS-Impact model is defined as “a measure at a point in time, of the stream of net benefits from the Information System (IS), to date and anticipated, as perceived by all key-user-groups”. The model represents four dimensions, which are ‘Individual Impact’, ‘Organizational Impact’, ‘Information Quality’ and ‘System Quality’. The two Impact dimensions measure the up-to-date impact of the evaluated system, while the remaining two Quality dimensions act as proxies for probable future impacts (Gable, Sedera & Chan, 2008). To fulfil the goal of ITPS, “to develop the most widely employed model” this research re-validates and extends the IS-Impact model in a new context. This method/context-extension research aims to test the generalisability of the model by addressing known limitations of the model. One of the limitations of the model relates to the extent of external validity of the model. In order to gain wide acceptance, a model should be consistent and work well in different contexts. The IS-Impact model, however, was only validated in the Australian context, and packaged software was chosen as the IS understudy. Thus, this study is concerned with whether the model can be applied in another different context. Aiming for a robust and standardised measurement model that can be used across different contexts, this research re-validates and extends the IS-Impact model and its instrument to public sector organisations in Malaysia. The overarching research question (managerial question) of this research is “How can public sector organisations in Malaysia measure the impact of information systems systematically and effectively?” With two main objectives, the managerial question is broken down into two specific research questions. The first research question addresses the applicability (relevance) of the dimensions and measures of the IS-Impact model in the Malaysian context. Moreover, this research question addresses the completeness of the model in the new context. Initially, this research assumes that the dimensions and measures of the IS-Impact model are sufficient for the new context. However, some IS researchers suggest that the selection of measures needs to be done purposely for different contextual settings (DeLone & McLean, 1992, Rai, Lang & Welker, 2002). Thus, the first research question is as follows, “Is the IS-Impact model complete for measuring the impact of IS in Malaysian public sector organisations?” [RQ1]. The IS-Impact model is a multidimensional model that consists of four dimensions or constructs. Each dimension is represented by formative measures or indicators. Formative measures are known as composite variables because these measures make up or form the construct, or, in this case, the dimension in the IS-Impact model. These formative measures define different aspects of the dimension, thus, a measurement model of this kind needs to be tested not just on the structural relationship between the constructs but also the validity of each measure. In a previous study, the IS-Impact model was validated using formative validation techniques, as proposed in the literature (i.e., Diamantopoulos and Winklhofer, 2001, Diamantopoulos and Siguaw, 2006, Petter, Straub and Rai, 2007). However, there is potential for improving the validation testing of the model by adding more criterion or dependent variables. This includes identifying a consequence of the IS-Impact construct for the purpose of validation. Moreover, a different approach is employed in this research, whereby the validity of the model is tested using the Partial Least Squares (PLS) method, a component-based structural equation modelling (SEM) technique. Thus, the second research question addresses the construct validation of the IS-Impact model; “Is the IS-Impact model valid as a multidimensional formative construct?” [RQ2]. This study employs two rounds of surveys, each having a different and specific aim. The first is qualitative and exploratory, aiming to investigate the applicability and sufficiency of the IS-Impact dimensions and measures in the new context. This survey was conducted in a state government in Malaysia. A total of 77 valid responses were received, yielding 278 impact statements. The results from the qualitative analysis demonstrate the applicability of most of the IS-Impact measures. The analysis also shows a significant new measure having emerged from the context. This new measure was added as one of the System Quality measures. The second survey is a quantitative survey that aims to operationalise the measures identified from the qualitative analysis and rigorously validate the model. This survey was conducted in four state governments (including the state government that was involved in the first survey). A total of 254 valid responses were used in the data analysis. Data was analysed using structural equation modelling techniques, following the guidelines for formative construct validation, to test the validity and reliability of the constructs in the model. This study is the first research that extends the complete IS-Impact model in a new context that is different in terms of nationality, language and the type of information system (IS). The main contribution of this research is to present a comprehensive, up-to-date IS-Impact model, which has been validated in the new context. The study has accomplished its purpose of testing the generalisability of the IS-Impact model and continuing the IS evaluation research by extending it in the Malaysian context. A further contribution is a validated Malaysian language IS-Impact measurement instrument. It is hoped that the validated Malaysian IS-Impact instrument will encourage related IS research in Malaysia, and that the demonstrated model validity and generalisability will encourage a cumulative tradition of research previously not possible. The study entailed several methodological improvements on prior work, including: (1) new criterion measures for the overall IS-Impact construct employed in ‘identification through measurement relations’; (2) a stronger, multi-item ‘Satisfaction’ construct, employed in ‘identification through structural relations’; (3) an alternative version of the main survey instrument in which items are randomized (rather than blocked) for comparison with the main survey data, in attention to possible common method variance (no significant differences between these two survey instruments were observed); (4) demonstrates a validation process of formative indexes of a multidimensional, second-order construct (existing examples mostly involved unidimensional constructs); (5) testing the presence of suppressor effects that influence the significance of some measures and dimensions in the model; and (6) demonstrates the effect of an imbalanced number of measures within a construct to the contribution power of each dimension in a multidimensional model.

Profiling and characterisation of key weather variables and their implication on building design

Local climate is a critical element in the design of buildings. In this paper, ten years of historical weather data in Australia's all eight capital cities are analyzed to characterize the variation profiles of climatic variables. The method of descriptive statistics is employed. Either the pattern of cumulative distribution and/or the profile of percentage distribution are used to graphically illustrate the similarity and difference between different study locations. It is found that although the weather variables vary with different locations, except for the extreme parts, there is often a good, nearly linear relation between weather variable and its cumulative percentage for the majority of middle part. The implication of these extreme parts and the slopes of the middle parts on building design is also discussed.

On the significance of omitted variables in intersection crash modeling

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causes and contributing factors—rest upon the pursuit of numerous lines of research inquiry. The research community has focused considerable attention on analytical methods development (negative binomial models, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might logically seek to know which lines of inquiry might provide the most significant improvements in understanding crash causation and/or prediction. It is the contention of this paper that the exclusion of important variables (causal or surrogate measures of causal variables) cause omitted variable bias in model estimation and is an important and neglected line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant opportunities to better understand contributing factors and/or causes of crashes. This study examines the role of important variables (other than Average Annual Daily Traffic (AADT)) that are generally omitted from intersection crash prediction models. In addition to the geometric and traffic regulatory information of intersection, the proposed model includes many spatial factors such as local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools—representing a mix of potential environmental and human factors that are theoretically important, but rarely used. Results suggest that these variables in addition to AADT have significant explanatory power, and their exclusion leads to omitted variable bias. Provided is evidence that variable exclusion overstates the effect of minor road AADT by as much as 40% and major road AADT by 14%.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.