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

Bis(4-carbamoylpiperidinium)biphenyl-4,4'-disulfonate

In the title isonipecotamide salt 2C6H13N2O+.C12H8O6S22-,the asymmetric unit comprises one biphenyl-4,4'-disulfonate dianion which lies across a crystallographic inversion centre and another in a general position [dihedral angle between the two phenyl rings is 37.1(1)deg], together with three isonipecotamide cations. Two of these cations give a cyclic homomeric amide-amide dimer interaction [graph set R2/2(8)],the other giving a similar dimeric interaction but across an inversion centre, both dimers then forming lateral cyclic R2/4(8) pyrimidinium N-H...O interactions. These units are linked longitudinally to the sulfonate groups of the dianions through piperidinium N-H...O hydrogen bonds, giving a three-dimensional framework structure.

Order and disorder in the structures of two crystal polymorphs of the adduct bis(quinolinium-2-carboxylate) DL-malic acid

The structures of two polymorphs of the anhydrous cocrystal adduct of bis(quinolinium-2-carboxylate) DL-malic acid, one triclinic the other monoclinic and disordered, have been determined at 200 K. Crystals of the triclinic polymorph 1 have space group P-1, with Z = 1 in a cell with dimensions a = 4.4854(4), b = 9.8914(7), c = 12.4670(8)Å, α = 79.671(5), β = 83.094(6), γ = 88.745(6)deg. Crystals of the monoclinic polymorph 2 have space group P21/c, with Z = 2 in a cell with dimensions a = 13.3640(4), b = 4.4237(12), c = 18.4182(5)Å, β = 100.782(3)deg. Both structures comprise centrosymmetric cyclic hydrogen-bonded quinolinic acid zwitterion dimers [graph set R2/2(10)] and 50% disordered malic acid molecules which lie across crystallographic inversion centres. However, the oxygen atoms of the malic acid carboxylic groups in 2 are 50% rotationally disordered whereas in 1 these are ordered. There are similar primary malic acid carboxyl O-H...quinaldic acid hydrogen-bonding chain interactions in each polymorph, extended into two-dimensional structures but in l this involves centrosymmetric cyclic head-to-head malic acid hydroxyl-carboxyl O-H...O interactions [graph set R2/2(10)] whereas in 2 the links are through single hydroxy-carboxyl hydrogen bonds.

meso-Porphyrinylphosphine Oxides: Mono- and Bidentate Ligands for Supramolecular Chemistry and the Crystal Structures of Monomeric [10,20-Diphenylporphyrinatonickel(II)-5,15-diyl]-bis-[P(O)Ph2] and Polymeric Self-Coordinated ([10,20-Diphenylporphyrinatozinc(II)-5,15-diyl]-bis-[P(O)Ph2])

A series of porphyrins substituted in one or two meso-positions by diphenylphosphine oxide groups has been prepared by the palladium catalysed reaction of diphenylphosphine or its oxide with the corresponding bromoporphyrins. Compounds {MDPP-[P(O)Ph2]n} (M = H2, Ni, Zn; H2DPP = 5,15-diphenylporphyrin; n = 1, 2) were isolated in yields of 60-95%. The reaction is believed to proceed via the conventional oxidative addition, phosphination and reductive elimination steps, as the stoichiometric reaction of η1-palladio(II) porphyrin [PdBr(H2DPP)(dppe)] (H2DPP = 5,15-diphenylporphyrin; dppe = 1,2-bis(diphenylphosphino)ethane) with diphenylphosphine oxide also results in the desired mono-porphyrinylphosphine oxide [H2DPP-P(O)Ph2]. Attempts to isolate the tertiary phosphines failed due to their extreme air-sensitivity. Variable temperature 1H NMR studies of [H2DPP-P(O)Ph2] revealed an intrinsic lack of symmetry, while fluorescence spectroscopy showed that the phosphine oxide group does not behave as a "heavy atom" quencher. The electron withdrawing effect of the phosphine oxide group was confirmed by voltammetry. The ligands were characterised by multinuclear NMR and UV-visible spectroscopy as well as mass spectrometry. Single crystal X-ray crystallography showed that the bis(phosphine oxide) nickel(II) complex {[NiDPP-[P(O)Ph2]2} is monomeric in the solid state, with a ruffled porphyrin core and the two P=O fragments on the same side of the average plane of the molecule. On the other hand, the corresponding zinc(II) complex formed infinite chains through coordination of one Ph2PO substituent to the neighbouring zinc porphyrin through an almost linear P=O---Zn unit, leaving the other Ph2PO group facing into a parallel channel filled with disordered water molecules. These new phosphine oxides are attractive ligands for supramolecular porphyrin chemistry.

New palladium catalysed reactions of bromoporphyrins: synthesis and crystal structures of nickel(II) complexes of primary 5-aminoporphyrin, 5,5’-bis(porphyrinyl) secondary amine, and 5-hydroxyporphyrin

Primary aminoporphyrin, secondary bis(porphyrinyl)amine and hydroxyporphyrin complexes have been isolated and characterised both spectroscopically and crystallographically from the reaction of 5-bromo-10,15,20-triphenylporphyrinato-nickel(II) with hydrazine under palladium catalysis.

The hydrogen-bonded coordination polymer tetracesium bis(5-nitroisophthalate) heptahydrate

The coordination polymer complex tetracesium bis(5-nitroisophthalate) heptahydrate [Cs4(C8H3NO6)2 (H2O)7]n has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P21/c, with Z = 4 in a cell with dimensions a = 12.3213(3), b =6.7557(2) c = 36.2020(9) Å, β = 90.548(2)o. The complex is based on a repeating unit comprising four independent and different Cs coordination centres, two 6-coordinate, and two 8-coordinate [Cs-O, range 2.959(5)-3.386(5)Å], and seven water molecules, two of which are monodentate and the other five bridging, while all other oxygen atoms in the structure, including those of the nitro groups form inter-Cs bridges. Extensive water O-H…O hydrogen-bonding interactions give a three-dimensional framework. This structure represents the first of an alkali metal compound of 5-nitroisophthalic acid that has been reported.

Bis(guanidinium) 4,5-dichlorophthalate monohydrate

In the structure of the title hydrate salt 2(CH6N3)+ C8H2Cl2O42- . H2O, the planes of the carboxylate groups of the dianion are rotated out of the plane of the benzene ring [dihedral angles 48.42(10) and 55.64(9)deg.]. A duplex-sheet structure is formed through guanidinium-carboxylate N-H...O, guanidinium-water N-H...O, and water-carboxylate O-H..O hydrogen-bonding associations.