The flat-maximum effect and generic linear scoring models: a test

Received on 1 July 1991. Predicting human behaviour patterns with linear correlationmodels has absorbed researchers for the past five decades. Althoughmost observers generally concede that humans are inferior tosuch models in combining information, linear scoring modelsare unfortunately, plagued by the flat-maximum effect or the‘curse of insensitivity’. As Lovie & Lovie(1986)observe: ‘The predictive ability of linear models is insensitiveto large variations in the size of regression weights and tothe number of predictors.’ In essence, seemingly differentscoringmodels tend to produce indistinguishable predictive outcomes. Since its demonstration by Dawes & Corrigan (1974), observershave cast the flat maximum in a decidedly negative light. Incontrast, Lovie & Lovie (1986) present a provocatively contrarianview of the flat maximum‘s positive potential. In thissame vein, we examine the predictive power of a generic credit-scoringmodel versus individual empirically derived systems. If, asWainer (1976) noted in regard to the flat maximum, ’itdon‘t make no nevermind’, generic credit-scoringmodels could provide cheaper alternatives to individual empiricallyderived models. During the period 1984–8, a series of linear credit-scoringmodels were developed for ten Southeastern U.S. credit unions.For each credit union, stepwise multiple regression was employedto select a subset of explanatory variables to be used in adiscriminant analysis. A generic credit-scoring equation wasdeveloped from the resulting discriminant analyses using weightedaverage coefficients from five systems. The predictive powerof the generic model was compared to the predictive power ofholdout sample of the five remaining credit-scoring models. In all cases, the generic model's performance was very closeto that of the empirically derived models. Thus, our findingssupport Lovie & Lovie's (1986) challenge to the conventionalwisdom that the flat maximum casts a pall on the successfulmodelling of judgement processes. Indeed, the flat maximum impliesa positive role for simpler, and hence cheaper, generic models.Although further research is needed, it should be possible todevelop hybrid models with generic cores that perform as wellas empirically derived linear models.     

Review of Chemometrics Applied to Spectroscopy: 1985-95, Part 2

INTRODUCTION

Before beginning Part 2 of this review, a caveat noted by Deming and Palasota is brought to the reader's attention: [1] “Press et al. [2] have emphasized that data ‘consist of numbers, of course. But these numbers are fed into the computer, not produced by it. These are numbers to be treated with considerable respect, never to be tampered with, nor subjected to a numerical process whose character you do not completely understand. You are well advised to acquire reverence for data that is rather diferent fiom the “sporty” attitude which is sometimes allowable, or even commendable, in other numerical tasks.’ Yet by and large within chemometrics, preprocessing often seems to be carried out with little understanding of its fundamental efect on the structure of the data.”     

Non-aqueous chromium acetylacetonate electrolyte for redox flow batteries

A single-metal redox flow battery employing chromium(III) acetylacetonate in tetraethylammonium tetrafluoroborate and acetonitrile has been investigated using electrochemical techniques. Cyclic voltammetry was used to evaluate electrode kinetics. Four redox couples were observed in the stable potential window. The Cr^II/Cr^III, Cr^I/Cr^II, Cr^III/Cr^IV and Cr^IV/Cr^V redox couples all appeared to be quasi-reversible, with the Cr^III/Cr^IV couple exhibiting comparatively slow kinetics. A cell potential of 3.4 V was measured for the one-electron disproportionation of the neutral Cr^III complex. The diffusion coefficient for chromium acetylacetonate in the supporting electrolyte solution was estimated to be in the range of 5.0–6.2 × 10^?7 cm² s^?1 at room temperature. The charge–discharge characteristics of this system were evaluated in an H-type glass cell, and coulombic and energy efficiencies of approximately 55% and 20%, respectively, were obtained.     

High-Modulus Wholly Aromatic Fibers. II. Partially Ordered Polyamide-Hydrazides

Partially ordered polyarnide-hydrazides were produced by the poly condensation of diacid chlorides with aminobenz-hydrazides, the order that results being a consequence of the considerably more rapid reaction of a diacid chloride with the hydrazide group in competition with the aromatic amine group of the aminobenzhydrazide. Fibers were produced from a series of such polymers containing from 50 mole % meta-oriented phenylene rings to 100 mole % para-oriented ones. Fiber from the wholly para-oriented type of polymer exhibited very high strength and modulus: 12.5 and 468 g/den, respectively, at 4.3% elongation-to-break. Although the crystallinity and density observed for hot-drawn fibers of partially ordered completely para-oriented polyarnide-hydrazides were comparable to the crystallinity and density of fibers of the isomeric wholly ordered polymer, the partially ordered polymers were more readily spun to the ultra-high strength and high modulus type fibers, probably because their greater solubility made them easier to spin.     

High-Modulus Wholly Aromatic Fibers. I. Wholly Ordered Polyamide-Hydrazides and Poly-1,3,4-oxadiazole—Amides

Several completely ordered polyamide-hydrazide copolymers were prepared via low temperature poly condensation of aromatic diacid chlorides with symmetrical aromatic diamines containing preformed dihydrazide linkages. Highly crystalline, hot-drawn fibers of the polyamide-hydrazide containing only para-oriented phenylene units showed unusually high strength and exceptionally high initial modulus: 10.8 and 508 g/den, respectively, at 2.9% elongation-to-break. The as-spun fibers also exhibited rather high tensile strength and unusually high initial modulus: 8.2 and 291 g/den, respectively, at 9.4% elongation-to-break. The hot-drawn fiber retained considerable strength at elevated temperatures, exhibiting a tenacity of 1.4 g/den and an initial modulus of 169 g/den at 350°C. Heat-aging of the as-spun fiber at 185°C in air showed that 66% of the original tenacity, 41% of the elongation, and 86% of the modulus were retained even after 336 hr. Substitution of as little as 25 mole % meta-oriented phenylene rings for para-oriented ones resulted in loss of the ultra-high strength and modulus, giving tensile properties comparable to those of fibers from wholly aromatic polyamides of the meta-oriented type. Fibers from the polyamide-hydrazides containing 50 mole % meta-oriented rings showed similar properties. Although ordered oxadiazole-amide copolymers were obtained from diamines containing two preformed oxadiazole linkages separated by m-phenylene rings, fibers could not be spun from them. Fiber of an ordered oxadiazole-amide copolymer was obtained, however, by heat treatment of the wholly p-phenylene ordered poly amide-hydrazide copolymer precursor fiber. Such a fiber exhibited a tenacity of 15.3 g/den, 3.6% elongation-to-break, and 564 g/den initial modulus.     

Highly luminescent europium(III) complexes with naphtoiltrifluoroacetone and dimethyl sulphoxide

The synthesis, luminescence properties, experimental determination and theoretical calculation of the emission quantum yield of Eu(NTA)₃.2L complexes, where NTA is naphtoiltri-fluroacetone and L denotes H₂O or DMSO (dimethyl sulphoxide), were reported. The compounds were characterized by elemental analysis (carbon, hydrogen and europium), thermal analysis, UV-visible absorption and photoluminescence spectroscopies. The experimental quantum yields were determined based on a method previously proposed by Bril and collaborators. The Eu(NTA)₃.2DMSO compound shows a high value for the Ω₂ intensity parameter (35.8 × 10^?20 cm²), reflecting the hypersensitive nature of the ⁵D₀ → ⁷F₂ transition and indicating that the lanthanide ion is in a highly polarizable chemical environment. The experimental quantum yield measured for that compound, 0.75, is one of the highest so far reported for solid-state europium complexes. The theoretical calculations of the quantum yield were carried out by solving an appropriate set of rate equations and by using empirical spectroscopic parameters and energy transfer rates. The theoretical results agree well with the experimental data for both complexes. The photostability of Eu(NTA)₃.2DMSO at 358K was evaluated in order to verify whether this complex can be applied as a phosphor for blue light emitting devices.     

Graft Copolymerizations of Polysaccharides. II. Acrylamide Grafting to Yellow Dextrin

Graft copolymers of acrylamide and yellow dextrin were prepared using cerium(IV) as initiator. The yellow dextrin had a very broad molecular weight distribution but was fractionated utilizing dialysis and ultrafiltration membranes. Initiator efficiencies were determined using size exclusion chromatography and were found to be between 2.4 and 34%. Initiator efficiency increased with acrylamide concentration at constant cerium (IV) and yellow dextrin concentrations, and decreased with increasing cerium(IV) concentration at constant acrylamide and yellow dextrin concentrations. Plots of acrylamide conversion and intrinsic viscosity vs initial acrylamide concentration at constant yellow dextrin and ceric ion concentrations showed a maximum at about 2.0 M.     

Organometallic Polymers. XXVII. Radical-Initiated Polymerization and Copolymerization of π-(2, 4-Hexadien-1-yl Acrylate) tricarbonyliron

The novel monomer, π-(2, 4-hexadiene- l-yl acrylate) tricarbonyliron (HATI), has been prepared by two routes. It was homopolymerized and copolymerized with acrylonitrile, vinyl acetate, styrene, and methyl acrylate in benzene solutions. In all cases azobisisobutyronitrile was the initiator. The relative reactivity ratios, where HATI is defined as M₁, were determined: r₁ = 0.34, r₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = vinyl acetate; r₁ = 0.26, r₂ = 1.81, M₂ = styrene; and r₁ = 0.30, r₂ = 0.74, M₂ = methyl acrylate. The homo-and copolymers had high values of T_g. When polymerizations are carried out at high concentrations, a very high molecular weight tail is observed in HATI hompolymerizations and in HATI-methyl acrylate copolymerizations. The polymers were characterized by IR, gel permeation chromatography, viscosity, and differential scanning calorimetry studies. Finally, thermal decompositions carried out in air resulted in decomposition of the Fe(CO)₃ group, producing Fe₂O₃ as a fine powder. Thermal decomposition under nitrogen (in solution and on solids ground into KBr pellets) resulted in slow destruction of the Fe(CO)₃ groups but the resulting polymer mass was insoluble, and the question of what form the iron exists in (Fe metal, oxides, carbides, etc.) has not been answered.     

Polymerization of Methane and Olefin Mixtures over Fluosulfonic Acid and Antimony Pentafluoride

Mixtures of methane and olefins (ethylene, propylene, butenes, butadiene, and styrene) have been polymerized over HSO₃ F-SbF₃ to yield an oily oligomer with a molecular weight ranging from 100 to 700. The NMR spectra of each polymer showed a sharp peak at or near 1.25 &, suggesting the presence of block methylene in the polymer. The formation of block methylene is surprising considering the fact that the polymerization reaction is carbonium ion in nature. A primary cation has been invoked to explain the results. The formation of this primary cation must involve some extraordinary stabilization by some component in the acid.