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.     

Cu(I) complexes based on cis, cis-1,3,5-tris(arylideneamino)cyclohexane ligands: synthesis, structure and CO binding

A new series of sterically bulky, facially coordinating N(3)-donor tach-based ligands (tach; cis,cis-1,3,5-triaminocyclohexane) [2.1; cis,cis-1,3,5-tris(2,4-dimethylbenzylideneamino)cyclohexane, 4.1; cis,cis-1,3,5-tris(pentamethylbenzylideneamino)cyclohexane, 5.1; cis,cis-1,3,5-tris(2,6-dimethoxybenzylideneamino)cyclohexane, 6.1; cis,cis-1,3,5-tris(pentafluorobenzylideneamino)cyclohexane, 7.1; cis,cis-1,3,5-tris(3,5-bis(ditrifluoromethyl)benzylideneamino)cyclohexane, 8.1; cis,cis-1,3,5-tris(2-trifluoromethylbenzylideneamino)cyclohexane, 9.1; cis,cis-1,3,5-tris(2-methoxybenzylideneamino)cyclohexane] have been obtained from the condensation of tach with three equivalents of the appropriate substituted benzaldehyde. Reaction with [Cu(NCCH(3))(4)]PF(6) gives Cu(I) complexes of tach-based ligands {2.2-9.2, eg; 2.2; [Cu(2.1)(NCCH(3))]PF(6)}. Displacement of the acetonitrile ligand by CO was achieved successfully for all the Cu(I) complexes of tach-based ligands and the resulting complexes have been shown to bind carbon monoxide {2.3-9.3, eg; 2.3; [Cu(2.1)(CO)]PF(6)}. The X-ray single crystal structures of 5.1, 8.1, 9.1, 3.2, 7.2, 8.2, 9.2, 3.3, 5.3 and 6.3 have been determined.     

Coordination chemistry of N-heterocyclic stannylenes: a combined synthetic and Mössbauer spectroscopy study

The N-heterocyclic stannylenes (NHSns), [(Dipp) N(CH(2))(n)N(Dipp)S n] (Dipp = 2,6- (i)Pr(2)C(6)H(3); n = 2, 1; n = 3, 5) and [((t)Bu) N(CHMe)(2)N((t)Bu)S n] (10) are competent ligands toward a variety of transition metal centers, as seen in the complexes [W(CO)(5)·1] (2), [(OC)(4)Fe(μ-1)(2)Fe(CO)(4)] (3), [(OC)(4)Fe(μ-1)Fe(CO)(4)] (4), [Fe(CO)(4)·5](n) (6, n = 1 or 2), [(OC)(4)Fe(μ-5)Fe(CO)(4)] (7), [Ph(3)PPt(μ-1)(2)PtPPh(3)] (8), [Fe(CO)(4)·10] (11), and [(η(5)-C(5)H(5))(OC)(2)Mn·10] (12). X-ray crystallographic studies show that the NHSns are structurally largely unperturbed binding to the metal, but in contrast to the parent NHCs, NHSns often adopt a bridging position across dinuclear metal units. The balance between terminal and bridging positions for the stannylene is evidently closely balanced as shown by the observation of both monomers and dimers for 6 in the solid state and in solution. (119)Sn and (57)Fe Mo?ssbauer spectroscopy of the complexes shows the tin atoms in such complexes to be consistent with electron deficient Sn(II) centers.     

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.     

DIFFRACTION STUDIES OF SOME CONVENTIONAL AND NOVEL MICROPHONE BAFFLES

A directional microphone system for field recording of sounds in the air often involves a parabolic reflector to focus the sound waves on the microphone (transducer) element. Some deficiencies of such a system are noted with respect to reproduction of spectra. The reflector system, involving as it does a structure comparable to a wavelength in linear dimension, is not susceptible to traditional high- or low-frequency approximate methods of computation. Modern numerical techniques now permit precise calculation of the directional responses of small reflectors of various shapes. One result is a proposal for a very economical and effective system involving a plane reflector. Other baffle shapes are also investigated, which may be of interest in special applications.