Local measures of association: Estimating the derivative of the regression line

A local measure of association that allows both heteroscedasticity and a non‐linear association was developed during the 1990s. The basic goal is to measure the strength of the association between X and Y, given X, when Y=θ(X)+τ(X)ε for some unknown functions θ(X) and τ(X). Application of this method requires the estimation of the derivative of θ(X). The focus in this paper is on four alternatives to a very slight modification of the method used by Doksum et al. when estimating this derivative. The main result is that in simulations, a certain robust analogue of their method dominates in terms of mean squared error, even under normality. The bias of the method is found to be small but a little larger than the bias associated with the method used by Doksum et al. The method is based in part on bootstrap bagging followed by a lowess smooth.     

Domain sampling formulation of cluster and factor analysis

Domain sampling principles permit formulation of a general method of multidimensional analysis. Cluster and factor analysis methods are special cases stemming from decisions made at different stages of the general method, especially in defining an independent dimension. Key cluster analyses define a dimension as a selection ofs variables drawn from the fulln set. Centroid, principal axes, and maximum likelihood analyses define it by then variables (raw or residual, weighted or unweighted); bifactor and second-order analysis, by both types of selection; square root analysis, by one variable. Key cluster methods can be designed to test hypotheses.     

The Perennial Freud: Method versus Myth and the Mischief of Freud Bashers

Nowadays Freud bashing is not only à la mode, in certain circles it has become de rigueur. Once a name of respect, Freud has become a name of ridicule. But like any scientific method, body of knowledge, and therapeutic procedure, psychoanalysis should be subjected to critical scrutiny. The recent crop of hostile Freud critics may have filled a vacuum left for decades by a psychoanalytic establishment which, like the Church of yesteryear, shunned all forms of criticism intramural and extramural. A central guiding idea of this essay is the distinction between the psychoanalytic method and psychoanalytic doctrines, hypotheses, and theories. This distinction has been invariably confused by both Freud's adherents and Freud's attackers. Moreover, arguments ad rem have been conflated with arguments ad hominem. A socially responsible criticism must seek to be constructive and not merely destructive. It is the latter course that was taken by the various hostile critics that came to be labeled as Freud bashers. The time has come to take a stand against the more egregious attacks on Freud and the psychoanalytic method.     

An analysis of Guttman's simplex

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically inton/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomesn/2 is contradictory to Guttman's contention that the minimal rank isn — 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.Prepared under Contract 816(02) between the Office of Naval Research and Washington University and presented in part at a meeting of the Southern Society for Philosophy and Psychology, St. Louis, Missouri, March 27, 1959. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

The detailed method of optimal regions

The detailed method of optimal regions is an extended form of the method of optimal regions which has been found effective in solving the personnel classification problem when the number of job categories is small. The automatic determination of the successive values of thev _i , made possible by the more exact techniques of the detailed method, provide easier solutions for the more complex problems and provide solutions, which, for the most part, can be mechanized. In a sense the detailed method of optimal regions is more than a detailed form of the method of optimal regions. It is essentially a method of transformations by which the original matrix is reduced to a matrix from which the solution is easily obtained.Much of the basic research covered in this paper was carried out while the author was working on the problem of personnel classification in his capacity as Consultant, Personnel Research Branch, Department of the Army. The author wishes to express his appreciation to the Department of the Army for permission to use these materials in this paper. The opinions expressed are those of the author and are not to be construed as official or as those of the Department of the Army.     

A multiple group method of factoring the correlation matrix

There are a number of methods of factoring the correlation matrix which require the calculation of a table of residual correlations after each factor has been extracted. This is perhaps the most laborious part of factoring. The method to be described here avoids the computation of residuals after each factor has been computed. Since the method turns on the selection of a set of constellations or clusters of test vectors, it will be calleda multiple group method of factoring. The method can be used for extracting one factor at a time if that is desired but it will be considered here for the more interesting case in which a number of constellations are selected from the correlation matrix at the start. The result of this method of factoring is a factor matrixF which satisfies the fundamental relationFF'=R.This study is one of a series of investigations in the development of multiple factor analysis and application to the study of primary mental abilities. We wish to acknowledge the financial assistance from the Social Science Research Committee of The University of Chicago which has made possible the work of the Psychometric Laboratory.     

The contribution of an orthogonal multiple factor solution to multiple correlation

A method is indicated by which multiple factor analysis may be used in determining a number,r, and then in selectingr predicting variables out ofn variables so that each of the remainingn-r variables may be predicted almost as well from ther variables as it could be predicted from all then—1 variables.     

A method of factor analysis by means of which all coordinates of the factor matrix are given simultaneously

In general, the methods of factor analysis developed during the past five years are based on the reduction of the correlational matrix by successive steps. The first factor loadings are determined and eliminated from the correlational matrix, giving a residual matrix. This process is continued for successive factor loadings until the elements of the last obtained residual matrix may be regarded as due to chance. The method outlined in this paper assumes the maximum number of factorsm in the correlational matrix. Them factor vectors are solved for simultaneously. Once them factor vectors are found, any vectors having only negligible factor loadings may be discarded.     

For Want of an ‘And’: A Puzzle about Non-Conservative Extension

The paper analyses Frege's approach to the identity conditions for the entity labelled by him as Sinn. It starts with a brief characterization of the main principles of Frege's semantics and lists his remarks on the identity conditions for Sinn. They are subject to a detailed scrutiny, and it is shown that, with the exception of the criterion of intersubstitutability in oratio obliqua, all other criteria have to be discarded. Finally, by comparing Frege's views on Sinn with Carnap's method of extension and intension and the method of intensional isomorphism, it is proved that these methods do not provide a criterion for the identity of Frege's Sinn, even for extensional contexts, that the concept of intension does not coincide, as stated by Carnap, in these contexts, with Frege's concept of Sinn, and that Carnap's claim that in oratio obliqua Frege's semantics leads to an infinite hierarchy of Sinn entities can be questioned at least hypothetically in the light of certain new historical facts.     

Balancing fit and parsimony to improve Q-matrix validation

The Q-matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q-matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q-matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut-off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for, PVAF) or a coefficient of determination (pseudo-R²). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut-off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q-matrix specification problem in applied settings. This proposal is illustrated using real data.     

Love as a Problem of Knowledge in Kierkegaard's Either/Or and Plato's Symposium

At the end of the essay “Silhouettes” in Either/Or, Kierkegaard writes, “only the person who has been bitten by snakes knows what one who has been bitten by snakes must suffer.” I interpret this as an allusion to Alcibiades' speech in Plato's Symposium. Kierkegaard invites the reader to compare Socrates with Don Giovanni, and Alcibiades with the seducer's women. Socrates' philosophical method, in this light, is a deceptive seduction: just as Don Giovanni's seduction leads his conquests to unhappy love—what Kierkegaard terms “reflective sorrow”—so the elenctic method leads Socrates' interlocutors to aporia, not to knowledge. I offer a critique of Socrates' ironic stance as a philosopher, which stance is reflected in the theory of love he presents in the Symposium, and suggest that philosophy should be modeled on the romantic love of persons—a love that can be reciprocated—not the love of an impersonal Form, a one-sided love.     

C. I. Lewis,Kant, and the reflective method of philosophy

ABSTRACT

If it seems unquestionable that C. I. Lewis is a Kantian in important respects, it is more difficult to determine what, if anything, is original about his Kantianism. For it might be argued that Lewis’ Kantianism simply reflects an approach to the a priori which was very common in the first half of the twentieth century, namely, the effort to make the a priori relative. In this paper, I will argue that Lewis’ Kantianism does present original features. The latter can be detected by focusing on Lewis’ account of the method of philosophy in the first chapter of Mind and the World Order. In that context, Lewis argues that the method of philosophy should be reflective and critical. It will be my contention that this understanding of philosophy involves a therapeutic perspective, which bears important resemblances to Kant’s account of transcendental reflection in the Amphiboly of the Critique of Pure Reason. I will illustrate how this therapeutic application of reflection works in Lewis’ metaphysics. In this context, reflection can correct errors of reasoning that occur when we are operating within a particular conceptual scheme and use the criteria of reality that are appropriate in another.     

When Sharing Is Not Caring: Does (un)Certainty About Bill Payment Method Lead Diners to Consume More and Spend More Money?

Previous work has demonstrated that unacquainted participants in an experimental, restaurant‐like setting consume more when they know in advance that the bill will be split evenly rather than paid according to individual consumption. Real life, however, often differs from these experimental settings in two important ways. First, unlike random groups of participants, diners who eat together are frequently friends or colleagues. Second, payment method (even vs. individual payment) is usually unknown (i.e. uncertain) at the time people place their orders, and is determined when the check arrives. The current research tests the ecological validity of the association between consumption amount and payment method. Study 1 was conducted in a natural setting with organic groups of diners. Some were asked to state their desired payment method before ordering (Certain condition); others did so only after asking for the check (Uncertain condition). In both conditions, even payment (as opposed to individual payment) was associated with greater consumption amount. However, overall, consumption amount was lower among diners in the Uncertain condition than among those in the Certain condition. Study 2 presents a controlled follow‐up experiment showing that eliminating diners' prior expectations regarding the payment method—by informing them that the payment method will be randomly determined after the consumption decision—eliminates the relationship between payment method and consumption amount. This study further indicates that when diners are uncertain what the payment method will be, even bill‐splitting has negative implications for their subsequent social interactions, expressed in retribution tendencies. Copyright © 2016 John Wiley & Sons, Ltd.     

Two Kinds of Definition in Spinoza's Ethics

Spinoza scholars have claimed that we are faced with a dilemma: either Spinoza's definitions in his Ethics are real, in spite of indications to the contrary, or the definitions are nominal and the propositions derived from them are false. I argue that Spinoza did not recognize the distinction between real and nominal definitions. Rather, Spinoza classified definitions according to whether they require a priori or a posteriori justification, which is a classification distinct from either the real/nominal or the intensional/extensional classification. I argue that Spinoza uses both a priori and a posteriori definitions in the Ethics and that recognizing both types of definitions allows us to understand Spinoza's geometric method in a new way. We can now understand the geometric method as two methods, one resulting in propositions that Spinoza considers to be absolutely certain and another resulting in propositions that Spinoza does not consider certain. The latter method makes use of a posteriori definitions and postulates, whereas the former method uses only a priori definitions and axioms.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

Rotational equivalence of factor loading matrices with specified values

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of results are given for the more complex case when the specified values are not necessarily zero. A method is given for constructing reflections to preserve specified rows and columns. When the appropriatek(k – 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2 ^k orthogonally equivalent matrices.This research was supported in part by the National Institute of Health Grant RR-3.     

Comparing variances of correlated variables

A test is proposed for the equality of the variances ofk 2 correlated variables. Pitman's test fork = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between thek normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.This research was supported by the fund for the promotion of research at the Technion.     

Congruence and temporal stability of multimiethod profiles: A new pair of personality variables

Congruence and temporal stability of multimethod profiles within the individual subject were studied as proposed new personality variables in a pool of seven small groups of graduate students in clinical psychology (N= 51) Sex differences were minimal A Stability Index was derived from (a) Q correlation stability coefficients obtained from the single method profiles of an inventory, self-ratings, and mean ratings by others, or (b) absolute difference scores between the composite profiles on occasion 1 and occasion 2 A Congruence Index was derived from (a) Q correlation coefficients obtained from each pair of profiles measured by the three methods for each subject, or (b) mean absolute difference scores obtained from each pair of method profiles These moderately correlated indices were used as dependent variables in stepwise multiple regression analyses, in which scores on a profile of 21 personality variables served as independent variables Although the difference score method was at least as effective as the correlational method in predicting congruence, the Q correlational method was superior in all other analyses conducted in this study Persons high in temporal stability seem to maintain an intellectually searching and interpersonally affiliative approach to the environment, showing little hostility and little tendency to seek change in current life circumstances The highly congruent individual seeks a positive nurturant interaction with other persons, gains pleasure from both sensory and interpersonal experiences, and shows little discontent with present life circumstances     

Formation of FeNi with L10-ordered structure using high-pressure torsion

FeNi with the L1₀-ordered structure is formed over an astronomical timescale in meteorites. In this study, severe plastic deformation using high-pressure torsion (HPT) is employed for the production of the L1₀ structure in the laboratory. Its formation is confirmed by X-ray diffraction analysis and transmission electron microscopy. Processing of elemental nanopowders by HPT is an effective method for the formation of the L1₀ phase, which is enhanced by the addition of Co to FeNi or annealing after HPT. The formation of the phase must be associated with enhanced diffusion through HPT.