Stuart’s tau measure of effect size for ordinal variables: Some methodological considerations

The reporting of measures of effect size has become increasingly important in psychology. A Monte Carlo resampling permutation procedure is introduced to find near-optimum maximum values for Stuart’s τ _c measure for two-way ordinal contingency tables, also termed Kendall’s τ _c since Kendall introduced τ _a and τ _b . Comparisons between resampling and exact procedures demonstrate the accuracy and utility of resampling measures of effect size for two-way ordinal contingency tables. The resampling procedure is shown to be more precise than the traditional method of standardizing τ _c .     

Necessity and Relative Contingency

The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named KΔτ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of Δ and τ allows proving (i) that KΔτ is equivalent to a modal system named K□τ (ii) that both KΔτ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of KΔτ is exactly the deontic system KD. In §4 it is proved that the modal τ -free fragment of a system KΔτw weaker than KΔτ is exactly the minimal normal system K. Presented by Daniele Mundici     

A group-theoretical invariant for elementary equivalence and its role in representations of elementary classes

There is a natural map which assigns to every modelU of typeτ, (U ε St^τ) a groupG (U) in such a way that elementarily equivalent models are mapped into isomorphic groups.G(U) is a subset of a collection whose members are called Fraisse arrows (they are decreasing sequences of sets of partial isomorphisms) and which arise in connection with the Fraisse characterization of elementary equivalence. LetEC _λ ^U be defined as {U εStr ^τ: ℬ ≡U and |ℬ|=λ; thenEG _λ ^U can be faithfully (i.e. 1-1) represented onto G(U) ×π ^*, whereπ ^*, is a collection of partitions over λ∪λ²∪....     

The adequacy of the theories of deductive systems with respect to sentential calculi

Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS _r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS _r , the variablesX, Y, Z ... represent the subsets ofS _R . The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS _R δ(X) means, thatX is closed with respect to the modus ponens rule.A _R designates the class of allS _R -substitutions of the axioms of the sentential calculusR.     

Sorai and the will oftian

Conclusion My purpose has been more negative than positive. That is, I have challenged the view that Sorai understoodtian as an intentional agent. At minimum, Sorai’s philosophical views do not depend upon such a conception oftian, and he refrains from characterizingtian in such terms when he discusses the concept oftian directly. However, I do not claim to have proven that Sorai’s view oftian was completely naturalistic, or even that Sorai did not—at some level—believe thattian had intentions. I have, I hope, shown thatthe case that Sorai viewedtian as intentional has not been convincingly made. Further, something closer to a dynamic and indeterminate naturalistic view is a reasonable alternative. On my reading, Sorai steers a course between the Song Confucian view oftian as static and knowable (a view that he explicitly rejects) and a view oftian as intentional (a view he never unequivocally expresses)—indeed, he rejects the idea of personifyingtian. When Sorai speaks of thexin or “mind”of tian, he is best understood as employing a metaphor that implies complexity, mystery, activity, and perhaps moral structure, but not intentionality in the normal sense. The complexity, indeterminacy, and dynamism oftian, as these are expressed in Sorai’s writings, do not necessarily imply willful intent on the part oftian, for they are all consistent with the Xunzian interpretation oftian as a natural process, even iftian’s regularities have a moral character.     

Variance ofd′ for thesame-different method

Variance estimates ofd′ are derived toward thesame-different method based on Taylor-series expansion with one and two variables. The variance estimates can be used for statistical comparison ofd′s obtained from various discrimination paradigms. Formulas and tables for estimating variance ofd′ for the method are provided. One S-PLUS program, which can produce bothd′ and variance ofd′, is also provided.     

A case of extreme simplicity of the core matrix in three-mode principal components analysis

In three-mode Principal Components Analysis, theP ×Q ×R core matrixG can be transformed to simple structure before it is interpreted. It is well-known that, whenP=QR,G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, whenP=QR − 1,G can be transformed to have nearly all elements equal to values spectified a priori. A cllsed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation ofG are discussed. Constructive comments from anonymous reviewers are gratefully acknowledged.     

Locating the Extrema of Fungible Regression Weights

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of “fungible weights” (Waller, Psychometrica, in press) that yields identical SSE (sum of squared errors) and R ² values. When the R ² using the alternate weights is a fixed value, fungible weights (a _i ) that yield the maximum or minimum cosine with an OLS weight vector (b) are called “fungible extrema.” We describe two methods for locating fungible extrema and we report R code (R Development Core Team, 2007) for one of the methods. We then describe a new approach for populating a class of fungible weights that is derived from the geometry of alternate regression weights. Finally, we illustrate how fungible weights can be profitably used to gauge parameter sensitivity in linear models by locating the fungible extrema of a regression model of executive compensation (Horton & Guerard, Commun. Stat. Simul. Comput. 14:441–448, 1985).     

Restricted ranking

This paper is a study of certain aspects of restricted ranking, a method intended for use by a panel ofm judges evaluating the relative merits ofN subjects, candidates for scholarships, awards, etc. Each judge divides theN subjects intoR classes so thatn _i individuals receive a gradei (i = 1, 2, ...,R; Σn _i =N) where theR numbersn _i are close toN/R (n _i =N/R whenN is divisible byR) and are preassigned and the same for all judges. This method is superior in several respects to other likely alternatives. Under the null hypothesis that allnR =N subjects are of equal merit, four tests of significance are developed. The effectiveness of the method is investigated both theoretically by means of the asymptotic relative efficiency and more generally by simulation studies. When the numbersn _i are not restricted to values close to or equal toN/R but instead are given values conforming to a normally distributed pattern, the resulting method is known as theQ-sort, so designated by certain investigators in psychotherapy. The simulation studies reveal that restricted ranking is only slightly inferior to complete ranking and generally superior in the cases considered to theQ-sort, although there are likely to be other situations when the latter is superior. The authors are indebted to Dr. Clyde Kramer of Virginia Polytechnic Institute for bringing theQ-sort ranking technique of psychotherapy to their attention.     

A model and algorithm for multidimensional scaling with external constraints on the distances

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configurationX relative to the proximity dataP and the loss ofX relative to a pseudo-data matrixR. The matrixR is set up such that the side constraints to be imposed onX's distances are expressed by the relations amongR's numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solutionX. Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matricesP andR. Further generalizations are introduced by substitutingR by a set ofR matrices,R _i ,i=1, ...r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.     

On the Mind Dependence of Truth

The claim that truth is mind dependent has some initial plausibility only if truth bearers are taken to be mind dependent entities such as beliefs or statements. Even on that assumption, however, the claim is not uncontroversial. If it is spelled out as the thesis that “in a world devoid of mind nothing would be true”, then everything depends on how the phrase ‘true in world w’ is interpreted. If ‘A is true in w’ is interpreted as ‘A is true of w’ (i.e. ‘w satisfies A’s truth conditions’, the claim need not be true. If on the other hand it is interpreted as ‘A is true of w and exists in w’ then the claim is trivially true, though devoid of any antirealistic efficacy. Philosophers like Heidegger and Rorty, who hold that truth is mind dependent but reality is not, must regard such principles as “A if and only if it is true that A” as only contingently true, which may be a good reason to reject the mind dependence of truth anyway.     

On sensitive rank tests for comparing the effects of two treatments on a single group

The rank testR _n of Cronholm and Revusky [1965] in effect doubles the number of comparisons carried out in the Mann-Whitney test between Treated and Control subjects chosen from a single group ofn and triples the asymptotic Pitman efficiency against shift alternatives by using a series ofn — 1 subexperiments. However, the full series can be too costly or time-consuming. It is shown thatj appropriately chosen subexperiments will permit one to make at leastj/(j+1) of the number of comparisons possible underR _n, with large sample efficiency ofj/(j+2) relative toR _n against shift alternatives and small sample efficiency greater than that,j=2, 3, ...,n — 2. The resulting test criterion is a sum ofj independent Mann-Whitney test statistics. Its null distribution is tabulated forn10 and small sample efficiency comparisons are carried out forn=10.     

Reliability of a Longitudinal Sequence of Scale Ratings

Reliability captures the influence of error on a measurement and, in the classical setting, is defined as one minus the ratio of the error variance to the total variance. Laenen, Alonso, and Molenberghs (Psychometrika 73:443–448, 2007) proposed an axiomatic definition of reliability and introduced the R _T coefficient, a measure of reliability extending the classical approach to a more general longitudinal scenario. The R _T coefficient can be interpreted as the average reliability over different time points and can also be calculated for each time point separately. In this paper, we introduce a new and complementary measure, the so-called R _Λ , which implies a new way of thinking about reliability. In a longitudinal context, each measurement brings additional knowledge and leads to more reliable information. The R _Λ captures this intuitive idea and expresses the reliability of the entire longitudinal sequence, in contrast to an average or occasion-specific measure. We study the measure’s properties using both theoretical arguments and simulations, establish its connections with previous proposals, and elucidate its performance in a real case study. The authors are grateful to J&J PRD for kind permission to use their data. We gratefully acknowledge support from Belgian IUAP/PAI network “Statistical Techniques and Modeling for Complex Substantive Questions with Complex Data.”     

Semantic Information and the Correctness Theory of Truth

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained.     

Democracy and Education: About the Future of a Problem

In 20th century’s European theory of education there was little interest in philosophy ofdemocracy. John Dewey’sDemocracy and Education was translated in nearly every European language but did not become the center of discussion. Even “radical education” was much more childcentered than open to radical questions of political democracy. This article discusses the problem in two respects, first the tension between neo-liberalism’s concept of individuality and public education, and second the future problems of a theory of “democratic education”after Dewey. The aim is to overcome traditional European dualisms like that of “citizen”or “man” i.e. to pave the way for a post-Rousseauian theory of education. Inaugural lecture upon taking office at the University of Zurich on 22nd November 1999.     

The Geometry of Enhancement in Multiple Regression

In linear multiple regression, “enhancement” is said to occur when R ²=b′r>r′r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R _xx≠I, R _xx=E[xx′]=V Λ V′ (where V Λ V′ denotes the eigen decomposition of R _xx; λ ₁>λ ₂), the set B₁:={b_i:R²=b_i￠r_i=r_i￠r_i;0 < R² ￡ 1}\boldsymbol{B}_{1}:=\{\boldsymbol{b}_{i}:R^{2}=\boldsymbol{b}_{i}'\boldsymbol{r}_{i}=\boldsymbol{r}_{i}'\boldsymbol{r}_{i};0R² ￡ 1;R²l_p ￡ r_i￠r_i < R²}0p≥3 (and λ ₁>λ ₂>⋯>λ _p ), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B ₁ occurs at the intersection of two hyper-ellipsoids in ℝ ^p . Equations are provided for populating the sets B ₁ and B ₂ and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ _p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included in Appendices A and B.     

The <Emphasis Type="Italic">γ</Emphasis>-admissibility of Relevant Modal Logics I — The Method of Normal Models

The admissibility of Ackermann’s rule γ is one of the most important problems in relevant logic. While the γ-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the γ-admissibility. This paper discusses which relevant modal logics admit γ from the viewpoint of the method of normal models.     

Understanding consumer purchase of free‐of cosmetics: A value‐driven TRA approach

This study concerns the free‐of trend on the cosmetics market as expressed by a tendency among consumers to prefer cosmetics that are free of certain ingredients. Combining the Theory of Reasoned Action with a value‐driven approach, this study empirically investigates the association between consumers' personal values and their attitude and behaviour associated with purchasing free‐of cosmetics. A quantitative online survey of 250 Danish female consumers was conducted using self‐administering questionnaires. The findings indicate that consumers' willingness to purchase free‐of cosmetics (R² = .48) is both influenced by attitude (β = .65) and perceived subjective norm (β = .21) with attitude having the largest predictive power. Moreover, consumers' attitude towards willingness to purchase free‐of cosmetics seems to be value driven. Our results indicate that two values, self‐transcendence (β = .28) and self‐enhancement (β = ?.21), significantly influence attitude towards free‐of cosmetics purchase (R² = .10). Copyright © 2012 John Wiley & Sons, Ltd.     

Some necessary conditions for common-factor analysis

LetR be any correlation matrix of ordern, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrixU ² such thatG = R – U ² is Gramian and of minimum rankr. Lets ₁ be the number of latent roots ofR which are greater than or equal to unity. Then it is proved here thatr s ₁. Two further lower bounds tor are also established that are better thans ₁. Simple computing procedures are shown for all three lower bounds that avoid any calculations of latent roots. It is proved further that there are many cases where the rank of all diagonal-free submatrices inR is small, but the minimum rankr for a GramianG is nevertheless very large compared withn. Heuristic criteria are given for testing the hypothesis that a finiter exists for the infinite universe of content from which the sample ofn observed variables is selected; in many cases, the Spearman-Thurstone type of multiple common-factor structure cannot hold.This research was made possible in part by an uncommitted grant-in-aid from the Behavioral Sciences Division of the Ford Foundation.