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

Photo-cross-linked poly(D,L-lactide)-based networks. Structural characterization by HR-MAS NMR spectroscopy and hydrolytic degradation behavior

To date, biodegradable networks and particularly their kinetic chain lengths have been characterized by analysis of their degradation products in solution. We characterize the network itself by NMR analysis in the solvent-swollen state under magic angle spinning conditions. The networks were prepared by photoinitiated cross-linking of poly(dl-lactide)−dimethacrylate macromers (5 kg/mol) in the presence of an unreactive diluent. Using diffusion filtering and 2D correlation spectroscopy techniques, all network components are identified. By quantification of network-bound photoinitiator fragments, an average kinetic chain length of 9 ± 2 methacrylate units is determined. The PDLLA macromer solution was also used with a dye to prepare computer-designed structures by stereolithography. For these networks structures, the average kinetic chain length is 24 ± 4 methacrylate units. In all cases the calculated molecular weights of the polymethacrylate chains after degradation are maximally 8.8 kg/mol, which is far below the threshold for renal clearance. Upon incubation in phosphate buffered saline at 37 °C, the networks show a similar mass loss profile in time as linear high-molecular-weight PDLLA (HMW PDLLA). The mechanical properties are preserved longer for the PDLLA networks than for HMW PDLLA. The initial tensile strength of 47 ± 2 MPa does not decrease significantly for the first 15 weeks, while HMW PDLLA lost 85 ± 5% of its strength within 5 weeks. The physical properties, kinetic chain length, and degradation profile of these photo-cross-linked PDLLA networks make them most suited materials for orthopedic applications and use in (bone) tissue engineering.

The effect of metamictization on the Raman spectroscopy of the uranyl titanate mineral davidite (La,Ce)(Y,U,Fe2+)(Ti,Fe3+)20(O,OH)38

Raman spectra of the uranyl titanate mineral davidite-(La) (La,Ce)(Y,U,Fe2+)(Ti,Fe3+)20(O,OH)38 were analysed and related to the mineral structure. Observed bands are attributed to the TiO and (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 davidite-(La) are in harmony with those of the uranyl oxyhydroxides. The mineral davidite-(La) 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.

Application of infrared emission spectroscopy to the thermal transition of indium hydroxide to indium oxide nanocubes

Cubic indium hydroxide nanomaterials were obtained by a low temperature soft-chemical method without any surfactants. The transition of nano-cubic indium hydroxide to cubic indium oxide during dehydroxylation has been studied by infrared emission spectroscopy. The spectra are related to the structure of the materials and the changes in the structure upon thermal treatment. The infrared absorption spectrum of In(OH)3 is characterised by an intense OH deformation band at 1150 cm-1 and two O-H stretching bands at 3107 and 3221 cm-1. In the infrared emission spectra, the hydroxyl-stretching and hydroxyl-bending bands diminish dramatically upon heating, and no intensity remains after 200 °C. However, new low intensity bands are found in the OH deformation region at 915 cm-1 and in OH stretching region at 3437 cm-1. These bands are attributed to the vibrations of newly formed InOH bonds because of the release and transfer of protons during calcination of the nanomaterial. The use of infrared emission spectroscopy enables the low-temperature phase transition brought about through dehydration of In(OH)3 nanocubes to be studied.

Structure of selected basic zinc/copper (II) phosphate minerals based upon near-infrared spectroscopy : implications for hydrogen bonding

The NIR spectra of reichenbachite, scholzite and parascholzite have been studied at 298 K. The spectra of the minerals are different, in line with composition and crystal structural variations. Cation substitution effects are significant in their electronic spectra and three distinctly different electronic transition bands are observed in the near-infrared spectra at high wavenumbers in the 12000-7600 cm-1 spectral region. Reichenbachite electronic spectrum is characterised by Cu(II) transition bands at 9755 and 7520 cm-1. A broad spectral feature observed for ferrous ion in the 12000-9000 cm-1 region both in scholzite and parascholzite. Some what similarities in the vibrational spectra of the three phosphate minerals are observed particularly in the OH stretching region. The observation of strong band at 5090 cm-1 indicates strong hydrogen bonding in the structure of the dimorphs, scholzite and parascholzite. The three phosphates exhibit overlapping bands in the 4800-4000 cm-1 region resulting from the combinations of vibrational modes of (PO4)3- units.

Raman spectroscopy of hydrogene-arsenate group (AsO3OH) in solid-state compounds: cobalt mineral phase burgessite Co2(H2O)4[AsO3OH]2•H2O

Raman spectrum of burgessite, Co2(H2O)4[AsO3OH]2.H2O was studied, interpreted and compared with its infrared spectrum. The stretching and bending vibrations of (AsO3) and As-OH units together with the stretching, bending and libration modes of water molecules and hydroxyl ions were assigned. The range of O-H...O hydrogen bond lengths was inferred from the Raman and infrared spectra of burgessite. The presence of (AsO3OH)2- units in the crystal structure of burgessite was proved in agreement with its recently solved crystal structure. Raman and infrared spectra of erythrite inferred from the RRUFF database are used for comparison.

Infrared and infrared emission spectroscopy of nesquehonite Mg(OH)(HCO3)•2H2O : implications for the formula of nesquehonite

The mineral nesquehonite Mg(OH)(HCO3)•2H2O has been analysed by a combination of infrared (IR) and infrared emission spectroscopy (IES). Both techniques show OH vibrations, both stretching and deformation modes. IES proves the OH units are stable up to 450°C. The strong IR band at 934 cm-1 is evidence for MgOH deformation modes supporting the concept of HCO3- units in the molecular structure. Infrared bands at 1027, 1052 and 1098 cm-1 are attributed to the symmetric stretching modes of HCO3- and CO32- units. Infrared bands at 1419, 1439, 1511, and 1528 cm-1 are assigned to the antisymmetric stretching modes of CO32- and HCO3- units. IES supported by thermoanalytical results defines the thermal stability of nesquehonite IES defines the changes in the molecular structure of nesquehonite with temperature. The results of IR and IES supports the concept that the formula of nesquehonite is better defined as Mg(OH)(HCO3)•2H2O.

Raman spectroscopy of selected borate minerals of the pinakiolite group

The Raman spectra of a series of related minerals of the pinakiolite group of minerals have been collected and the spectra related to the mineral structure. These minerals are based upon an isolated BO33- ion. The site symmetry is reduced from D3h to C1. Intense Raman bands are observed for the minerals takeuchiite, pinakiolite, fredrikssonite and azoproite at 1084, 1086, 1086 and 1086 cm-1. These bands are assigned to the ν1 BO33- symmetric stretching mode. Low intensity Raman bands are observed for the minerals at 1345, 1748; 1435, 1748; 1435, 1750; 1436, 1749 cm-1. One probable assignment is to ν3 BO33- antisymmetric stretching mode. Intense Raman bands of takeuchiite, pinakiolite, fredrikssonite and azoproite at 712 cm-1 attributed to the ν2 out-of-plane bending mode. Importantly, through the comparison of the Raman spectra, the molecular structure of borate minerals with ill-defined structures can be obtained.

Raman spectroscopy of hydrogen arsenate group (AsO3OH)2− in solid-state compounds: cobalt-containing zinc arsenate mineral, koritnigite (Zn,Co)(AsO3OH)·H2O

Raman spectra of two well-defined types of koritnigite crystals from the Jáchymov ore district, Czech Republic, were recorded and interpreted. No substantial differences were observed between both crystal types. Observed Raman bands were attributed to the (AsO3OH)2- stretching and bending vibrations, stretching and bending vibrations of water molecules and hydroxyl ions. Non-interpreted Raman spectra of koritnigite from the RRUFF database, and published infrared spectra of cobaltkoritnigite were used for comparison. The O-H...O hydrogen bond lengths in the crystal structure of koritnigite were inferred from the Raman spectra and compared with those derived from the X-ray single crystal refinement. The presence of (AsO3OH)2- units in the crystal structure of koritnigite was proved from the Raman spectra which supports the conclusions of the X-ray structure analysis.

Synthesis and vibrational spectroscopy of halotrichite and bilinite

Near infrared (NIR), infrared (IR) spectroscopy and X-ray diffraction (XRD) have been applied to halotrichites of the formula FeAl2(SO4)4∙22H2O and Fe2+Fe23+(SO4)4∙22H2O. Comparison of the halotrichites and their starting materials has been used to give a better understanding of the bonding involved in these types of minerals. The vibrational spectroscopy data has shown that Fe2+ oxidises during the formation of halotrichite, no preventative measures were implemented to prevent oxidation, and this has been clearly shown by the position and broadness of electronic bands of transition metals in the NIR spectra (12500 to 7500 cm-1). It is apparent from this region that Fe3+ substitutes for Al3+ in the synthesis of halotrichite. Due to the oxidation of Fe2+ to Fe3+ the halotrichite sample contains a small portion of bilinite. This has been confirmed by XRD, peaks at 9 and 14° 2θ were observed in the halotrichite sample and are identical to the XRD pattern obtained for bilinite. Substitution of aluminium for Fe3+ has resulted in significant changes in the overall infrared and NIR spectral profiles. However, the lower wavenumber regions of the NIR spectra have very similar spectral profiles, which indicate a similar structure to halotrichite has formed for bilinite. This work has shown that iron halotrichites can be synthesised and characterised by infrared and NIR spectroscopy.

Single crystal Raman spectroscopy of natural leiteite ZnAs2O4 and in comparison with the synthesised mineral

The oriented single crystal Raman spectrum of leiteite has been obtained and the spectra related to the structure of the mineral. The intensities of the observed bands vary according to orientation allowing them to be assigned to either Ag or Bg modes. Ag bands are generally the most intense in the CAAC spectrum, followed by ACCA, CBBC, and ABBA whereas Bg bands are generally the most intense in the CBAC followed by ABCA. The CAAC and ACCA spectra are identical, as are those obtained in the CBBC and ABBA orientations. Both cross-polarised spectra are identical. Band assignments were made with respect to bridging and non-bridging As-O bonds.

A forensic investigation of single human hair fibres using FTIR-ATR spectroscopy and chemometrics

Human hair fibres are ubiquitous in nature and are found frequently at crime scenes often as a result of exchange between the perpetrator, victim and/or the surroundings according to Locard's Principle. Therefore, hair fibre evidence can provide important information for crime investigation. For human hair evidence, the current forensic methods of analysis rely on comparisons of either hair morphology by microscopic examination or nuclear and mitochondrial DNA analyses. Unfortunately in some instances the utilisation of microscopy and DNA analyses are difficult and often not feasible. This dissertation is arguably the first comprehensive investigation aimed to compare, classify and identify the single human scalp hair fibres with the aid of FTIR-ATR spectroscopy in a forensic context. Spectra were collected from the hair of 66 subjects of Asian, Caucasian and African (i.e. African-type). The fibres ranged from untreated to variously mildly and heavily cosmetically treated hairs. The collected spectra reflected the physical and chemical nature of a hair from the near-surface particularly, the cuticle layer. In total, 550 spectra were acquired and processed to construct a relatively large database. To assist with the interpretation of the complex spectra from various types of human hair, Derivative Spectroscopy and Chemometric methods such as Principal Component Analysis (PCA), Fuzzy Clustering (FC) and Multi-Criteria Decision Making (MCDM) program; Preference Ranking Organisation Method for Enrichment Evaluation (PROMETHEE) and Geometrical Analysis for Interactive Aid (GAIA); were utilised. FTIR-ATR spectroscopy had two important advantages over to previous methods: (i) sample throughput and spectral collection were significantly improved (no physical flattening or microscope manipulations), and (ii) given the recent advances in FTIR-ATR instrument portability, there is real potential to transfer this work.s findings seamlessly to on-field applications. The "raw" spectra, spectral subtractions and second derivative spectra were compared to demonstrate the subtle differences in human hair. SEM images were used as corroborative evidence to demonstrate the surface topography of hair. It indicated that the condition of the cuticle surface could be of three types: untreated, mildly treated and treated hair. Extensive studies of potential spectral band regions responsible for matching and discrimination of various types of hair samples suggested the 1690-1500 cm^-1 IR spectral region was to be preferred in comparison with the commonly used 1750-800 cm^-1. The principal reason was the presence of the highly variable spectral profiles of cystine oxidation products (1200-1000 cm^-1), which contributed significantly to spectral scatter and hence, poor hair sample matching. In the preferred 1690-1500 cm^-1 region, conformational changes in the keratin protein attributed to the α-helical to β-sheet transitions in the Amide I and Amide II vibrations and played a significant role in matching and discrimination of the spectra and hence, the hair fibre samples. For gender comparison, the Amide II band is significant for differentiation. The results illustrated that the male hair spectra exhibit a more intense β-sheet vibration in the Amide II band at approximately 1511 cm^-1 whilst the female hair spectra displayed more intense α-helical vibration at 1520-1515cm^-1. In terms of chemical composition, female hair spectra exhibit greater intensity of the amino acid tryptophan (1554 cm^-1), aspartic and glutamic acid (1577 cm^-1). It was also observed that for the separation of samples based on racial differences, untreated Caucasian hair was discriminated from Asian hair as a result of having higher levels of the amino acid cystine and cysteic acid. However, when mildly or chemically treated, Asian and Caucasian hair fibres are similar, whereas African-type hair fibres are different. In terms of the investigation's novel contribution to the field of forensic science, it has allowed for the development of a novel, multifaceted, methodical protocol where previously none had existed. The protocol is a systematic method to rapidly investigate unknown or questioned single human hair FTIR-ATR spectra from different genders and racial origin, including fibres of different cosmetic treatments. Unknown or questioned spectra are first separated on the basis of chemical treatment i.e. untreated, mildly treated or chemically treated, genders, and racial origin i.e. Asian, Caucasian and African-type. The methodology has the potential to complement the current forensic analysis methods of fibre evidence (i.e. Microscopy and DNA), providing information on the morphological, genetic and structural levels.