Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

The mechanism of maturation of insulin-like growth factor-1

This study, to elucidate the role of des(1-3)IGF-I in the maturation of IGF-I,used two strategies. The first was to detect the presence of enzymes in tissues, which would act on IGF-I to produce des(1-3)IGF-I, and the second was to detect the potential products of such enzymic activity, namely Gly-Pro-Glu(GPE), Gly-Pro(GP) and des(l- 3)IGF-I. No neutral tripeptidyl peptidase (TPP II), which would release the tripeptide GPE from IGF-I, was detected in brain, urine nor in red or white blood cells. The TPPlike activity which was detected, was attributed to a combined action of a dipeptidyl peptidase (DPP N) and an aminopeptidase (AP A). A true TPP II was, however, detected in platelets. Two purified TPP II enzymes were investigated but they did not release GPE from IGF-I under a variety of conditions. Consequently, TPP II seemed unlikely to participate in the formation of des(1-3)IGF-I. In contrast, an acidic tripeptidyl peptidase activity (TPP I) was detected in brain and colostrum, the former with a pH optimum of 4.5 and the latter 3.8. It seems likely that such an enzyme would participate in the formation of des( 1-3 )IGF-I in these tissues in vitro, ie. that des(1-3)IGF-I may have been produced as an artifact in the isolation of IGF-I from brain and colostrum in acidic conditions. This contrasts with suggestions of an in vivo role for des(1-3)IGF-I, as reported by others. The activity of a dipeptidyl peptidase N (DPP N) from urine, which should release the dipeptide GP from IGF-I, was assessed under a variety of conditions and with a variety of additives and potential enzyme stimulants, but there was no release of GP. The DPP N also exhibited a transferase activity with synthetic substrates in the presence of dipeptides, at lower concentrations than previously reported for other acceptors or other proteolytic enzymes. In addition, a low concentration of a product,possibly the tetrapeptide Gly-Pro-Gly-Leu, was detected with the action of the enzyme on IGF-I in the presence of the dipeptide Gly-Leu. As part of attempts to detect tissue production of des(1-3)IGF-I, a monoclonal antibody (MAb ), directed towards the GPE- end ofiGF-I was produced by immunisation with a 10-mer covalently attached to a carrier protein. By the use of indirect ELISA and inhibitor studies, the MAb was shown to selectively recognise peptides with anNterminal GPE- sequence, and applied to the indirect detection of des(1-3)IGF-I. The concentration of GPE in brain, measured by mass spectrometry ( MS), was low, and the concentration of total IGF-I (measured by ELISA with a commercial polyclonal antibody [P Ab]) was 40 times higher at 50 nmol/kg. This also, was not consistent with the action of a tripeptidyl peptidase in brain that converted all IGF-I to des(1-3)IGF-I plus GPE. Contrasting ELISA results, using the MAb prepared in this study, suggest an even higher concentration of intact IGF-I of 150 nmollkg. This would argue against the presence of any des( 1-3 )IGF-I in brain, but in turn, this indicates either the presence of other substances containing a GPE amino-terminus or other cross reacting epitope. Although the results of the specificity studies reported in Chapter 5 would make this latter possibility seem unlikely, it cannot be completely excluded. No GP was detected in brain by MS. No GPE was detected in colostrum by capillary electrophoresis (CE) but the interference from extraneous substances reduced the detectability of GPE by CE and this approach would require further, prior, purification and concentration steps. A molecule, with a migration time equal to that of the peptide GP, was detected in colostrum by CE, but the concentration (~ 10 11mo/L) was much higher than the IGF-I concentration measured by radio-immunoassay using a PAb (80 nmol/L) or using a Mab (300-400 nmolL). A DPP IV enzyme was detected in colostrum and this could account for the GP, derived from substrates other than IGF-1. Based on the differential results of the two antibody assays, there was no indication of the presence of des(1-3)IGF-I in brain or colostrum. In the absence of any enzyme activity directed towards the amino terminus of IGF-I and the absence any potential products, IGF-I, therefore, does not appear to "mature" via des(1-3)IGF-I in the brain, nor in the neutral colostrum. In spite of these results which indicate the absence of an enzymic attack on IGF-I and the absence of the expected products in tissues, the possibility that the conversion of IGF-I may occur in neutral conditions in limited amounts, cannot be ruled out. It remains possible that in the extracellular environment of the membrane, a complex interaction of IGF-I, binding protein, aminopeptidase(s) and receptor, produces des(1- 3)IGF-I as a transient product which is bound to the receptor and internalised.

Constructing the hallucinations of psychosis in Virtual Reality

Schizophrenia is a mental disorder affecting 1-2% of the population and it is estimated 12-16% of hospital beds in Australia are occupied by patients with psychosis. The suicide rate for patients with this diagnosis is higher than that of the general population. Any technique which enhances training and treatment of this disorder will have a significant societal and economic impact. A significant research project using Virtual Reality (VR), in which both visual and auditory hallucinations are simulated, is currently being undertaken at the University of Queensland. The virtual environments created by the new software are expected to enhance the experiential learning outcomes of medical students by enabling them to experience the inner world of a patient with psychosis. In addition the Virtual Environment has the potential to provide a technologically advanced therapeutic setting where behavioral, exposure therapies can be conducted with exactly controlled exposure stimuli with an expected reduction in risk of harm. This paper reports on the current work of the project, previous stages of software development and future educational and clinical applications of the Virtual Environments. (C) 2004 Elsevier Ltd. All rights reserved.

Evaluating the effect of a patient education brochure on patients’ expectations and satisfaction with emergency department service

Introduction: The purpose of this study was to assess the capacity of a written intervention, in this case a patient information brochure, to improve patient satisfaction during an Emergency Department (ED) visit. For the purpose of measuring the effect of the intervention the ED journey was conceptualised as a series of distinct areas of service comprising waiting time, service by the triage nurse, care from doctors and nurses and information giving Background of study: Research into patient satisfaction has become a widespread activity endorsed by both governments and hospital administrations. The literature on ED patient satisfaction has consistently indicated three primary areas of patient dissatisfaction: waiting time, nursing care and communication. Recent developments in the literature on patient satisfaction studies however have highlighted the relationship between patients. expectations of a service encounter and their consequent assessment of the experience as dissatisfying or satisfying. Disconfirmation theory posits that the degree to which expectations are confirmed will affect subsequent levels of satisfaction. The conceptual framework utilised in this study is Coye.s (2004) model of disconfirmation. Coye while reiterating satisfaction is a consequence of the degree expectations are either confirmed or disconfirmed also posits that expectations can be modified by interventions. Coye.s work conceptualises these interventions as intra encounter experiences (cues) which function to adjust expectations. Coye suggests some cues are unintended and may have a negative impact which also reinforces the value of planned cues intended to meet or exceed consumer expectations. Consequently the brochure can be characterized as a potentially positive cue, encouraging the patient to understand processes and to orient them in what can be a confronting environment. Only a limited number of studies have examined the effect of written interventions within an ED. No studies could be located which have tested the effect of ED interventions using a conceptual framework which relates the effect of the degree to which expectations are confirmed or disconfirmed in terms of satisfaction with services. Method: Two studies were conducted. Study One used qualitative methods to explore patients. expectations of the ED from the perspective of both patients and health care professionals. Study One was used in part to direct the development of the intervention (brochure) in Study Two. The brochure was an intervention designed to modify patients. expectations thus increasing their satisfaction with the provision of ED service. As there was no existing tools to measure ED patients. expectations and satisfaction a new tool was also developed based on the findings and the literature of Study One. Study Two used a non-randomised, quasi-experimental approach using a non-equivalent post-test only comparison group design used to investigate the effect of the patient education brochure (Stommel and Wills, 2004). The brochure was disseminated to one of two study groups (the intervention group). The effect of the brochure was assessed by comparing the data obtained from both the intervention and control group. These two groups consisted of 150 participants each. It was expected that any differences in the relevant domains selected for examination would indicate the effect of the brochure both on expectation and potentially satisfaction. Results: Study One revealed several areas of common ground between patients and nurses in terms of relevant content for the written intervention, including the need for information on the triage system and waiting times. Areas of difference were also found with patients emphasizing communication issues, whereas focus group members expressed concern that patients were often unable to assimilate verbal information. The findings suggested the potential utility of written material to reinforce verbal communication particularly in terms of the triage process and other ED protocols. This material was synthesized within the final version of the written intervention. Overall the results of Study Two indicated no significant differences between the two groups. The intervention group did indicate a significant number of participants who viewed the brochure of having changed their expectations. The effect of the brochure may have been obscured by a lack of parity between the two groups as the control group presented with statistically significantly higher levels of acuity and experienced significantly shorter waiting times. In terms of disconfirmation theory this would suggest expectations that had been met or exceeded. The results confirmed the correlation of expectations with satisfaction. Several domains also indicated age as a significant predictor with older patients tending to score higher satisfaction results. Other significant predictors of satisfaction established were waiting time and care from nurses, reinforcing the combination of efficient service and positive interpersonal experiences as being valued by patients. Conclusions: Information presented in written form appears to benefit a significant number of ED users in terms of orientation and explaining systems and procedures. The degree to which these effects may interact with other dimensions of satisfaction however is likely to be limited. Waiting time and interpersonal behaviours from staff also provide influential cues in determining satisfaction. Written material is likely to be one element in a series of coordinated strategies to improve patient satisfaction during periods of peak demand.

Daily disposable contact lens prescribing around the world

Daily disposable contact lenses were introduced into the market 16 years ago. Data that we have gathered from annual contact lens fitting surveys conducted in Australia, Canada, Japan, The Netherlands, Norway, the UK and the USA between 2000 and 2008 indicates an overall increase in daily disposable lens fitting during this period. Daily disposable lenses are especially popular in Japan, Norway and the UK. There is a trend for these lenses to be fitted on a part-time basis. Males are over-represented in daily disposable lens fitting—a trend that is especially evident in Canada. Daily disposable lens wearers are about two years younger than wearers of reusable lenses in Japan and The Netherlands. The convenience and health benefits of daily disposable lenses are expected to fuel continued growth in this sector.

Acid hydrolysis of easily dispersed and microaggregate-derived silt- and clay-sized fractions to isolate resistant soil organic matter

The current paradigm in soil organic matter (SOM) dynamics is that the proportion of biologically resistant SOM will increase when total SOM decreases. Recently, several studies have focused on identifying functional pools of resistant SOM consistent with expected behaviours. Our objective was to combine physical and chemical approaches to isolate and quantify biologically resistant SOM by applying acid hydrolysis treatments to physically isolated silt- and clay-sized soil fractions. Microaggegrate-derived and easily dispersed silt- and clay-sized fractions were isolated from surface soil samples collected from six long-term agricultural experiment sites across North America. These fractions were hydrolysed to quantify the non-hydrolysable fraction, which was hypothesized to represent a functional pool of resistant SOM. Organic C and total N concentrations in the four isolated fractions decreased in the order: native > no-till > conventional-till at all sites. Concentrations of non-hydrolysable C (NHC) and N (NHN) were strongly correlated with initial concentrations, and C hydrolysability was found to be invariant with management treatment. Organic C was less hydrolysable than N, and overall, resistance to acid hydrolysis was greater in the silt-sized fractions compared with the clay-sized fractions. The acid hydrolysis results are inconsistent with the current behaviour of increasing recalcitrance with decreasing SOM content: while %NHN was greater in cultivated soils compared with their native analogues, %NHC did not increase with decreasing total organic C concentrations. The analyses revealed an interaction between biochemical and physical protection mechanisms that acts to preserve SOM in fine mineral fractions, but the inconsistency of the pool size with expected behaviour remains to be fully explained.

Land use effects on soil carbon fractions in the southeastern United States. I. Management-intensive versus extensive grazing

Changes in grassland management intended to increase productivity can lead to sequestration of substantial amounts of atmospheric C in soils. Management-intensive grazing (MiG) can increase forage production in mesic pastures, but potential impacts on soil C have not been evaluated. We sampled four pastures (to 50 cm depth) in Virginia, USA, under MiG and neighboring pastures that were extensively grazed or bayed to evaluate impacts of grazing management on total soil organic C and N pools, and soil C fractions. Total organic soil C averaged 8.4 Mg C ha(-1) (22%) greater under MiG; differences were significant at three of the four sites examined while total soil N was greater for two sites. Surface (0-10 cm) particulate organic matter (POM) C increased at two sites; POM C for the entire depth increment (0-50 cm) did not differ significantly between grazing treatments at any of the sites. Mineral-associated C was related to silt plus clay content and tended to be greater under MiG. Neither soil C:N ratios, POM C, or POM C:total C ratios were accurate indicators of differences in total soil C between grazing treatments, though differences in total soil C between treatments attributable to changes in POM C (43%) were larger than expected based on POM C as a percentage of total C (24.5%). Soil C sequestration rates, estimated by calculating total organic soil C differences between treatments (assuming they arose from changing grazing management and can be achieved elsewhere) and dividing by duration of treatment, averaged 0.41 Mg C ha(-1) year(-1) across the four sites.

Role and purpose of standards in the context of national curriculum and assessment reform for accountability, improvement and equity in student learning

In this article our starting point is the current context of national curriculum change and intense speculation about the assessment, standards and reporting. It is written against a background of accountability measures and improvement imperatives, and focuses attention on standards as offering representations of quality. We understand standards to be constructs that aim to achieve public credibility and utility. Further, they can be examined for the purposes they seek to serve and also their expected functions. Fitness for purpose is therefore a useful notion in considering the nature of standards. Our interest in the discussion is the ‘fit’ between how standards are formulated and how they are used in practice, by whom and for what purposes. A related interest is in the matter of how standards can be harnessed to realise improvement.

Pandemic (H1N1) 2009 Influenza Outbreak in Australia: Impact on Emergency Departments.

Executive summary Objective: The aims of this study were to identify the impact of Pandemic (H1N1) 2009 Influenza on Australian Emergency Departments (EDs) and their staff, and to inform planning, preparedness, and response management arrangements for future pandemics, as well as managing infectious patients presenting to EDs in everyday practice. Methods This study involved three elements: 1. The first element of the study was an examination of published material including published statistics. Standard literature research methods were used to identify relevant published articles. In addition, data about ED demand was obtained from Australian Government Department of Health and Ageing (DoHA) publications, with several state health departments providing more detailed data. 2. The second element of the study was a survey of Directors of Emergency Medicine identified with the assistance of the Australasian College for Emergency Medicine (ACEM). This survey retrieved data about demand for ED services and elicited qualitative comments on the impact of the pandemic on ED management. 3. The third element of the study was a survey of ED staff. A questionnaire was emailed to members of three professional colleges—the ACEM; the Australian College of Emergency Nursing (ACEN); and the College of Emergency Nursing Australasia (CENA). The overall response rate for the survey was 18.4%, with 618 usable responses from 3355 distributed questionnaires. Topics covered by the survey included ED conditions during the (H1N1) 2009 influenza pandemic; information received about Pandemic (H1N1) 2009 Influenza; pandemic plans; the impact of the pandemic on ED staff with respect to stress; illness prevention measures; support received from others in work role; staff and others’ illness during the pandemic; other factors causing ED staff to miss work during the pandemic; and vaccination against Pandemic (H1N1) 2009 Influenza. Both qualitative and quantitative data were collected and analysed. Results: The results obtained from Directors of Emergency Medicine quantifying the impact of the pandemic were too limited for interpretation. Data sourced from health departments and published sources demonstrated an increase in influenza-like illness (ILI) presentations of between one and a half and three times the normal level of presentations of ILIs. Directors of Emergency Medicine reported a reasonable level of preparation for the pandemic, with most reporting the use of pandemic plans that translated into relatively effective operational infection control responses. Directors reported a highly significant impact on EDs and their staff from the pandemic. Growth in demand and related ED congestion were highly significant factors causing distress within the departments. Most (64%) respondents established a ‘flu clinic’ either as part of Pandemic (H1N1) 2009 Influenza Outbreak in Australia: Impact on Emergency Departments. the ED operations or external to it. They did not note a significantly higher rate of sick leave than usual. Responses relating to the impact on staff were proportional to the size of the colleges. Most respondents felt strongly that Pandemic (H1N1) 2009 Influenza had a significant impact on demand in their ED, with most patients having low levels of clinical urgency. Most respondents felt that the pandemic had a negative impact on the care of other patients, and 94% revealed some increase in stress due to lack of space for patients, increased demand, and filling staff deficits. Levels of concern about themselves or their family members contracting the illness were less significant than expected. Nurses displayed significantly higher levels of stress overall, particularly in relation to skill-mix requirements, lack of supplies and equipment, and patient and patients’ family aggression. More than one-third of respondents became ill with an ILI. Whilst respondents themselves reported taking low levels of sick leave, respondents cited difficulties with replacing absent staff. Ranked from highest to lowest, respondents gained useful support from ED colleagues, ED administration, their hospital occupational health department, hospital administration, professional colleges, state health department, and their unions. Respondents were generally positive about the information they received overall; however, the volume of information was considered excessive and sometimes inconsistent. The media was criticised as scaremongering and sensationalist and as being the cause of many unnecessary presentations to EDs. Of concern to the investigators was that a large proportion (43%) of respondents did not know whether a pandemic plan existed for their department or hospital. A small number of staff reported being redeployed from their usual workplace for personal risk factors or operational reasons. As at the time of survey (29 October –18 December 2009), 26% of ED staff reported being vaccinated against Pandemic (H1N1) 2009 Influenza. Of those not vaccinated, half indicated they would ‘definitely’ or ‘probably’ not get vaccinated, with the main reasons being the vaccine was ‘rushed into production’, ‘not properly tested’, ‘came out too late’, or not needed due to prior infection or exposure, or due to the mildness of the disease. Conclusion: Pandemic (H1N1) 2009 Influenza had a significant impact on Australian Emergency Departments. The pandemic exposed problems in existing plans, particularly a lack of guidelines, general information overload, and confusion due to the lack of a single authoritative information source. Of concern was the high proportion of respondents who did not know if their hospital or department had a pandemic plan. Nationally, the pandemic communication strategy needs a detailed review, with more engagement with media networks to encourage responsible and consistent reporting. Also of concern was the low level of immunisation, and the low level of intention to accept vaccination. This is a problem seen in many previous studies relating to seasonal influenza and health care workers. The design of EDs needs to be addressed to better manage infectious patients. Significant workforce issues were confronted in this pandemic, including maintaining appropriate staffing levels; staff exposure to illness; access to, and appropriate use of, personal protective equipment (PPE); and the difficulties associated with working in PPE for prolonged periods. An administrative issue of note was the reporting requirement, which created considerable additional stress for staff within EDs. Peer and local support strategies helped ensure staff felt their needs were provided for, creating resilience, dependability, and stability in the ED workforce. Policies regarding the establishment of flu clinics need to be reviewed. The ability to create surge capacity within EDs by considering staffing, equipment, physical space, and stores is of primary importance for future pandemics.

Vitrification as a prospect for cryopreservation of tissue-engineered constructs

Cryopreservation plays a significant function in tissue banking and will presume yet larger value when more and more tissue-engineered products will routinely enter the clinical arena. The most common concept underlying tissue engineering is to combine a scaffold (cellular solids) or matrix (hydrogels) with living cells to form a tissue-engineered construct (TEC) to promote the repair and regeneration of tissues. The scaffold and matrix are expected to support cell colonization, migration, growth and differentiation, and to guide the development of the required tissue. The promises of tissue engineering, however, depend on the ability to physically distribute the products to patients in need. For this reason, the ability to cryogenically preserve not only cells, but also TECs, and one day even whole laboratory-produced organs, may be indispensable. Cryopreservation can be achieved by conventional freezing and vitrification (ice-free cryopreservation). In this publication we try to define the needs versus the desires of vitrifying TECs, with particular emphasis on the cryoprotectant properties, suitable materials and morphology. It is concluded that the formation of ice, through both direct and indirect effects, is probably fundamental to these difficulties, and this is why vitrification seems to be the most promising modality of cryopreservation

Raman spectroscopic study of the uranyl titanate mineral betafite (Ca,U)2(Ti,Nb)2O6(OH) –Effect of Metamictization

Raman spectra of the uranyl titanate mineral betafite were obtained and related to the mineral structure. A comparison is made with the spectra of uranyl oxyhydroxide hydrates. Observed bands are attributed to the (UO2)2+ stretching and bending vibrations, U-OH bending vibrations, H2O and (OH)- stretching, bending and libration modes. U-O bond lengths in uranyls and O-H…O bond lengths are calculated from the wavenumbers assigned to the stretching vibrations. Raman bands of betafite are comparable with those of the uranyl oxyhydroxides. The mineral betafite is metamict as is evidenced by the intensity of the UO stretching and bending modes being of lower intensity than expected and with bands that are significantly broader.

Nonprofit organizational behaviour : sociological and psychological approaches

The study of organizations goes to the roots of social science. Abundant theory provides the basis for explanations of diverse aspects of organizational structure and process. As a subset of organizations, nonprofit organizations can be studied with many of the same theoretical approaches used for studying other organizations. Still, nonprofit organizations have some special characteristics, such as a multiplicity of stakeholders and the use of volunteers; some theories of organizations can therefore be expected to be especially useful for studying nonprofit organizations and some other theories not to be very useful. In general, our approach is to apply relevant organizational theory to nonprofit organizations. As such, this essay is not a typical review of literature about nonprofit organizations. Instead, the purpose is to equip the reader with conceptual and theoretical tools for understanding nonprofits as organizations.

The significance of endogeneity problems in crash models: An examination of left-turn lanes in intersection crash models

Crash prediction models are used for a variety of purposes including forecasting the expected future performance of various transportation system segments with similar traits. The influence of intersection features on safety have been examined extensively because intersections experience a relatively large proportion of motor vehicle conflicts and crashes compared to other segments in the transportation system. The effects of left-turn lanes at intersections in particular have seen mixed results in the literature. Some researchers have found that left-turn lanes are beneficial to safety while others have reported detrimental effects on safety. This inconsistency is not surprising given that the installation of left-turn lanes is often endogenous, that is, influenced by crash counts and/or traffic volumes. Endogeneity creates problems in econometric and statistical models and is likely to account for the inconsistencies reported in the literature. This paper reports on a limited-information maximum likelihood (LIML) estimation approach to compensate for endogeneity between left-turn lane presence and angle crashes. The effects of endogeneity are mitigated using the approach, revealing the unbiased effect of left-turn lanes on crash frequency for a dataset of Georgia intersections. The research shows that without accounting for endogeneity, left-turn lanes ‘appear’ to contribute to crashes; however, when endogeneity is accounted for in the model, left-turn lanes reduce angle crash frequencies as expected by engineering judgment. Other endogenous variables may lurk in crash models as well, suggesting that the method may be used to correct simultaneity problems with other variables and in other transportation modeling contexts.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites