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.     

On two integrable cellular automata

A representation-free approach to theq-analog of the quantum central limit theorem for is presented. It is shown that for certain functionals one can derive a version of a quantum central limit theorem (qclt) with as a scaling parameter, which may be viewed as aq-analog of qclt.     

Adsorbate influence on the coercive field of ultrathin Co/Cu{1 1 0}

We report on experimental coercive field measurements for ultrathin films of Co on Cu{1 1 0}, revealing a complex dependence upon the surface coverage of oxygen and hydrogen adatoms. With reference to first-principles calculations, we rationalise this behaviour in terms of initial reaction with surface contaminants and/or adsorption at defects, followed by (in the case of oxygen) subsequent surface ordering and eventual formation of surface oxide.     

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.”     

Twisted mannitol crystals establish homologous growth mechanisms for high-polymer and small-molecule ring-banded spherulites

D-Mannitol belongs to a large and growing family of crystals with helical morphologies (Yu, L. J. Am. Chem. Soc.2003, 125, 6380). Two polymorphs of D-mannitol, α and δ, when grown in the presence of additives such as poly(vinylpyrrolidone) (PVP) or D-sorbitol, form ring-banded spherulites composed of handed helical fibrils, where the helix axes correspond to the radial growth directions. The two polymorphs form helices with opposite senses in the presence of PVP but the same sense in the presence of D-sorbitol. The characteristic dimensions of the fibrils, including thickness, aspect ratio, and pitch, were determined by scanning probe and electron microscopies. These values must form the basis of any theory that presupposes what forces give rise to crystal twisting, a problem that has been broached but unsettled in the literature of polymer crystallization. The interdependence of the rhythmic variations of both linear and circular birefringence, as determined by Mueller matrix microscopy, informs the cooperative organization of mannitol fibers. The microstructure of mannitol ring-banded spherulites compares favorably to that of high polymers and is evaluated within the context of current theories of crystal twisting.