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

Derivation of motor vehicle tailpipe particle emission factors suitable for modelling urban fleet emissions and air quality assessments

Background, aim, and scope Urban motor vehicle fleets are a major source of particulate matter pollution, especially of ultrafine particles (diameters < 0.1 µm), and exposure to particulate matter has known serious health effects. A considerable body of literature is available on vehicle particle emission factors derived using a wide range of different measurement methods for different particle sizes, conducted in different parts of the world. Therefore the choice as to which are the most suitable particle emission factors to use in transport modelling and health impact assessments presented as a very difficult task. The aim of this study was to derive a comprehensive set of tailpipe particle emission factors for different vehicle and road type combinations, covering the full size range of particles emitted, which are suitable for modelling urban fleet emissions. Materials and methods A large body of data available in the international literature on particle emission factors for motor vehicles derived from measurement studies was compiled and subjected to advanced statistical analysis, to determine the most suitable emission factors to use in modelling urban fleet emissions. Results This analysis resulted in the development of five statistical models which explained 86%, 93%, 87%, 65% and 47% of the variation in published emission factors for particle number, particle volume, PM1, PM2.5 and PM10 respectively. A sixth model for total particle mass was proposed but no significant explanatory variables were identified in the analysis. From the outputs of these statistical models, the most suitable particle emission factors were selected. This selection was based on examination of the statistical robustness of the statistical model outputs, including consideration of conservative average particle emission factors with the lowest standard errors, narrowest 95% confidence intervals and largest sample sizes, and the explanatory model variables, which were Vehicle Type (all particle metrics), Instrumentation (particle number and PM2.5), Road Type (PM10) and Size Range Measured and Speed Limit on the Road (particle volume). Discussion A multiplicity of factors need to be considered in determining emission factors that are suitable for modelling motor vehicle emissions, and this study derived a set of average emission factors suitable for quantifying motor vehicle tailpipe particle emissions in developed countries. Conclusions The comprehensive set of tailpipe particle emission factors presented in this study for different vehicle and road type combinations enable the full size range of particles generated by fleets to be quantified, including ultrafine particles (measured in terms of particle number). These emission factors have particular application for regions which may have a lack of funding to undertake measurements, or insufficient measurement data upon which to derive emission factors for their region. Recommendations and perspectives In urban areas motor vehicles continue to be a major source of particulate matter pollution and of ultrafine particles. It is critical that in order to manage this major pollution source methods are available to quantify the full size range of particles emitted for traffic modelling and health impact assessments.

Ions in motor vehicle exhaust and their dispersion near busy roads

Measurements in the exhaust plume of a petrol-driven motor car showed that molecular cluster ions of both signs were present in approximately equal amounts. The emission rate increased sharply with engine speed while the charge symmetry remained unchanged. Measurements at the kerbside of nine motorways and five city roads showed that the mean total cluster ion concentration near city roads (603 cm-3) was about one-half of that near motorways (1211 cm-3) and about twice as high as that in the urban background (269 cm-3). Both positive and negative ion concentrations near a motorway showed a significant linear increase with traffic density (R2=0.3 at p<0.05) and correlated well with each other in real time (R2=0.87 at p<0.01). Heavy duty diesel vehicles comprised the main source of ions near busy roads. Measurements were conducted as a function of downwind distance from two motorways carrying around 120-150 vehicles per minute. Total traffic-related cluster ion concentrations decreased rapidly with distance, falling by one-half from the closest approach of 2m to 5m of the kerb. Measured concentrations decreased to background at about 15m from the kerb when the wind speed was 1.3 m s-1, this distance being greater at higher wind speed. The number and net charge concentrations of aerosol particles were also measured. Unlike particles that were carried downwind to distances of a few hundred metres, cluster ions emitted by motor vehicles were not present at more than a few tens of metres from the road.

Interaction of NPR1 with basic leucine zipper protein transcription factors that bind sequences required for salicylic acid induction of the PR–1 gene

The Arabidopsis thaliana NPR1 has been shown to be a key regulator of gene expression during the onset of a plant disease-resistance response known as systemic acquired resistance. The npr1 mutant plants fail to respond to systemic acquired resistance-inducing signals such as salicylic acid (SA), or express SA-induced pathogenesis-related (PR) genes. Using NPR1 as bait in a yeast two-hybrid screen, we identified a subclass of transcription factors in the basic leucine zipper protein family (AHBP-1b and TGA6) and showed that they interact specifically in yeast and in vitro with NPR1. Point mutations that abolish the NPR1 function in A. thaliana also impair the interactions between NPR1 and the transcription factors in the yeast two-hybrid assay. Furthermore, a gel mobility shift assay showed that the purified transcription factor protein, AHBP-1b, binds specifically to an SA-responsive promoter element of the A. thaliana PR-1 gene. These data suggest that NPR1 may regulate PR-1 gene expression by interacting with a subclass of basic leucine zipper protein transcription factors.

Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

Common mode voltage in a motor drive system with PFC

Common mode voltage generated by a power converter in combination with parasitic capacitive couplings is a potential source of shaft voltage in an AC motor drive system. In this paper, a three-phase motor drive system supplied with a single-phase AC-DC diode rectifier is investigated in order to reduce shaft voltage in a three-phase AC motor drive system. In this topology, the common mode voltage generated by the inverter is influenced by the AC-DC diode rectifier because the placement of the neutral point is changing in different rectifier circuit states. A pulse width modulation technique is presented by a proper placement of the zero vectors to reduce the common mode voltage level, which leads to a cost effective shaft voltage reduction technique without load current distortion, while keeping the switching frequency constant. Analysis and simulations have been presented to investigate the proposed method.

Property Agents and Motor Dealers Act : strike three

The Tourism, Racing and Fair Trading (Miscellaneous Provisions) Act 2002 (“the Act”) which was passed on 18 April 2002 contains a number of significant amendments relevant to the operation of the Property Agents and Motor Dealers Act 2000. The main changes relevant to property transactions are: (i) Changes to the process for appointment of a real estate agent and consolidation of the appointment forms; (ii) Additions to the disclosure obligation of agents and property developers; (iii) Simplification of the process for commencing the cooling off period; (iv) Alteration of the common law position concerning when the parties are bound by a contract; (v) Removal of the requirement for a seller’s signature on the warning statement to be witnessed; (vi) Retrospective amendment of s 170 of the Body Corporate and Community Management Act 1997; (vii) Inclusion of a new power to allow inspectors to enter the place of business of a licensee or a marketeer without consent and without a warrant; and (viii) Inclusion of a new power for inspectors to require documents to be produced by marketeers. The majority of the amendments are effective from the date of assent, 24 April 2002, however, some of the amendments do not commence until a date fixed by proclamation. No proclamation has been made at the time of writing (2 May 2002). Where the amendments have not commenced this will be noted in the article. Before providing clients with advice, practitioners should carefully check proclamation details.

Property Agents and Motor Dealers Act : take two

The Property Agents and Motor Dealers Act 2000 commenced on 1 July 2001. Significant changes have now been made to the Act by the Property Agents and Motor Dealers Amendment Act 2001 (“the amending Act”). The amending Act contains two distinct parts. First, ss 11-19 of the amending Act provide for increased disclosure obligations on real estate agents, property developers and lawyers together with an extension of the 5 business day cooling-off period imposed by the original Act to all residential property (other than contracts formed on a sale by auction). These provisions commenced on 29 October 2001. The remaining provisions of the amending Act provide for increased jurisdiction and powers to the Property Agents and Motor Dealers Tribunal (“the Tribunal”) enabling the Tribunal to deal with claims against marketeers. These provisions commenced on the date of assent, 21 September 2001.

Waiver of statutory requirements : Property Agents and Motor Dealers Act 2000 (Qld)

One of the many difficulties associated with the drafting of the Property Agents and Motor Dealers Act 2000 (Qld) (‘the Act’) is the operation of s 365. If the requirements imposed by this section concerning the return of the executed contract are not complied with, the buyer and the seller will not be bound by the relevant contract and the cooling-off period will not commence. In these circumstances, it is clear that a buyer’s offer may be withdrawn. However, the drafting of the Act creates a difficulty in that the ability of the seller to withdraw from the transaction prior to the parties being bound by the contract is not expressly provided by s 365. On one view, if the buyer is able to withdraw an offer at any time before receiving the prescribed contract documentation the seller also should not be bound by the contract until this time, notwithstanding that the seller may have been bound at common law. However, an alternative analysis is that the legislative omission to provide the seller with a right of withdrawal may be deliberate given the statutory focus on buyer protection. If this analysis were correct the seller would be denied the right to withdraw from the transaction after the contract was formed at common law (that is, after the seller had signed and the fact of signing had been communicated to the buyer).

Property Agents and Motor Dealers Act (Qld) : disclosure, cooling-off and marketeers

The Property Agents and Motor Dealers Act 2000 commenced on 1 July 2001. Significant changes have now been made to the Act by the Property Agents and Motor Dealers Amendment Act 2001 (“the amending Act”). The amending Act contains two distinct parts. First, ss 11-19 of the amending Act provide for increased disclosure obligations on real estate agents, property developers and lawyers together with an extension of the 5 business day cooling-off period imposed by the original Act to all residential property (other than contracts formed on a sale by auction). These provisions are expected to commence on 29 October 2001. The remaining provisions of the amending Act provide for increased jurisdiction and powers to the Property Agents and Motor Dealers Tribunal (“the Tribunal”) enabling the Tribunal to deal with claims against marketeers. These provisions commenced on the date of assent (21 September 2001).

The 'nurdle to leg' and other ways of winning cricket matches

The emergence of Twenty20 cricket at the elite level has been marketed on the excitement of the big hitter, where it seems that winning is a result of the muscular batter hitting boundaries at will. This version of the game has captured the imagination of many young players who all want to score runs with “big hits”. However, in junior cricket, boundary hitting is often more difficult due to size limitations of children and games played on outfields where the ball does not travel quickly. As a result, winning is often achieved via a less spectacular route – by scoring more singles than your opponents. However, most standard coaching texts only describe how to play boundary scoring shots (e.g. the drives, pulls, cuts and sweeps) and defensive shots to protect the wicket. Learning to bat appears to have been reduced to extremes of force production, i.e. maximal force production to hit boundaries or minimal force production to stop the ball from hitting the wicket. Initially, this is not a problem because the typical innings of a young player (<12 years) would be based on the concept of “block” or “bash” – they “block” the good balls and “bash” the short balls. This approach works because there are many opportunities to hit boundaries off the numerous inaccurate deliveries of novice bowlers. Most runs are scored behind the wicket by using the pace of the bowler’s delivery to re-direct the ball, because the intrinsic dynamics (i.e. lack of strength) of most children means that they can only create sufficient power by playing shots where the whole body can contribute to force production. This method works well until the novice player comes up against more accurate bowling when they find they have no way of scoring runs. Once batters begin to face “good” bowlers, batters have to learn to score runs via singles. In cricket coaching manuals (e.g. ECB, n.d), running between the wickets is treated as a separate task to batting, and the “basics” of running, such as how to “back- up”, carry the bat, calling and turning and sliding the bat into the crease are “drilled” into players. This task decomposition strategy focussing on techniques is a common approach to skill acquisition in many highly traditional sports, typified in cricket by activities where players hit balls off tees and receive “throw-downs” from coaches. However, the relative usefulness of these approaches in the acquisition of sporting skills is increasingly being questioned (Pinder, Renshaw & Davids, 2009). We will discuss why this is the case in the next section.