Beyond principal component analysis: A trilinear decomposition model and least squares estimation

The paper derives sufficient conditions for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis.     

A method for simulating non-normal distributions

A method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived. The form of such a transformation on normal deviates [X N(0, 1)] isY =a +bX +cX ² +dX ³. Analytic and empirical validation of the method is demonstrated.This work was done while the author was at the University of Illinois at Champaign-Urbana.     

What Diagnostic Devices Do: The Case of Blood Sugar Measurement

Diagnostic devices do more than just passively register facts. They intervene in the situations in which they are put to use. The question addressed here is what this general remark may imply in specific cases. To answer this question a specific case is being analysed: that of the blood sugar measurement device that people with diabetes may use to monitor their own blood sugar levels. This device not only allows the patients concerned to better approach normal blood sugar levels, but alters what counts as normal in the first place. Using the device may shift people's attention away from their physical sensations towards the numbers measured, but it may also help them to increase their own physical self-awareness. Self-monitoring finally (something that the devices have made possible) makes patients less dependent on professionals, but it requires them to engage in self-disciplining and binds them to the outcomes of their measurement activities: their own blood sugar levels.     

Efficient nonparametric approaches for estimating the operating characteristics of discrete item responses

Rationale and the actual procedures of two nonparametric approaches, called Bivariate P.D.F. Approach and Conditional P.D.F. Approach, for estimating the operating characteristic of a discrete item response, or the conditional probability, given latent trait, that the examinee's response be that specific response, are introduced and discussed. These methods are featured by the facts that: (a) estimation is made without assuming any mathematical forms, and (b) it is based upon a relatively small sample of several hundred to a few thousand examinees.Some examples of the results obtained by the Simple Sum Procedure and the Differential Weight Procedure of the Conditional P.D.F. Approach are given, using simulated data. The usefulness of these nonparametric methods is also discussed.This research was mostly supported by the Office of Naval Research (N00014-77-C-0360, N00014-81-C-0569, N00014-87-K-0320, N00014-90-J-1456).     

On the subject of homosexuality: What Freud said

The article explores Freud's writing on homosexuality, from his early hypotheses, expressed in his letters to Fleiss to his last observations in The Outline of Psychoanalysis, published in 1940 after his death. We trace the continuities as well as changes in his thinking, and have organized the paper conceptually, under the headings: 1) Bisexuality 2) Narcissism and Object choice, 3) On Normality and Pathology, and 4) The Quantitative factor and Aggression. We show that Freud was the first to confirm the existence of homosexualities, that he offers no black and white solution to the question of normality and pathology, although he contributes to the understanding of the vehemence that surrounds the subject, and that, in the considerable body of work, he has offered a rich and varied foundation for further thinking on the subject.     

Particularism and Default Reasons

This paper addresses a recent suggestion that moral particularists can extend their view to countenance default reasons (at a first stab, reasons that are pro tanto unless undermined) by relying on certain background expectations of normality. I first argue that normality must be understood non-extensionally. Thus if default reasons rest on normality claims, those claims won't bestow upon default reasons any definite degree of extensional generality. Their generality depends rather on the contingent distributional aspects of the world, which no theory of reasons should purport to settle. Appeals to default reasons cannot therefore uniquely support particularism. But this argument also implies that if moral generalism entailed that moral reasons by necessity have invariant valence (in the natural extensional sense), it would be a non-starter. Since generalism is not a non-starter, my argument forces us to rethink the parameters of the generalism-particularism debate. Here I propose to clarify the debate by focusing on its modal rather than extensional aspects. In closing, I outline the sort of generalism that I think is motivated by my discussion, and then articulate some worries this view raises about the theoretical usefulness of the label ‘default reason’.     

Normische Gesetzeshypothesen und die wissenschaftsphilosophische Bedeutung des nichtmonotonen Schliessens

Normic Laws and the Significance of Nonmonotonic Reasoning for Philosophy of Science. Normic laws have the form ‘if A then normally B’. They have been discovered in the explanation debate, but were considered as empirically vacuous (§1). I argue that the prototypical (or ideal) normality of normic laws implies statistical normality (§2), whence normic laws have empirical content. In §3–4 I explain why reasoning from normic laws is nonmonotonic, and why the understanding of the individual case is so important here. After sketching some foundations of nonmonotonic reasoning as developed by AI-researchers (§5), Iargue that normic laws are also the best way to understand ceteris paribus laws (§6). §7 deals with the difference between physical and non-physical disciplines and §9 with the difference between normicity and approximation. In §8 it is shown how nonmonotonic reasoning provides a new understanding of the protection of theories against falsification by auxiliary hypotheses. §10, finally, gives a system- and evolution-theoretical explanation of the deeper reason for the omnipresence of normic laws in practice and science, and forthe connection between ideal and statistical normality. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

The Concept of Abnormality in Medical Genetics

This paper explores usage of the concept ofabnormality in medical genetics and proposesdirectives for more careful usage of this concept.The conceptual difficulties are first explored, thena model is developed to assess actual usage, followedby analysis of a sample of genetic textbooks andgenetics literature. It appears that fact andvaluation are often intermingled, that referencestandards used to define 'genetic abnormalities' areoften not clear and that the concept of abnormality isoften used independent of the degree of certainty withwhich the altered genetype develops into a (seriously)harmful phenotype. On the basis of these findings itis argued that more restraint and more careful use ofthe concept of genetic abnormality of medical geneticsis appropriate as well as more agreement on the use ofreference standards.     

A new estimator of the uniqueness in factor analysis

A closed form estimator of the uniqueness (unique variance) in factor analysis is proposed. It has analytically desirable properties—consistency, asymptotic normality and scale invariance. The estimation procedure is given through the application to the two sets of Emmett's data and Holzinger and Swineford's data. The new estimator is shown to lead to values rather close to the maximum likelihood estimator.