Conditionally Selective Dependence of Random Variables on External Factors

Selective influence of experimental factors upon observable or hypothetical random variables is a key concept in the analysis of processing architectures and response time decompositions. This paper deals with the notion of conditionally selective influence, defined as follows. Let {X1, em leader, Xn} be stochastically interdependent random variables (e.g., hypothetical components of response time), and let Phi be a set of external factors affecting the joint distribution of {X1, em leader, Xn}. A subset of factors &Lambdai conditionally selectively influences Xi if at any fixed values of the remaining random variables the conditional distribution of Xi only depends on factors inside &Lambdai. The notion of conditional selectivity generalizes the relationship between factors and random variables described in Townsend (1984) as "indirect nonselectivity." This paper establishes the structure of the joint distribution of {X1, em leader, Xn} that is necessary and sufficient for {X1, em leader, Xn} to be conditionally selectively influenced by (not necessarily disjoint) factor subsets {&Lambda1, em leader, Gamman}, respectively. The notion of conditional selectivity is compared to that of unconditional selectivity, defined as follows. A subset of factors &Gammai unconditionally selectively influences Xi if the latter can be presented as a deterministic function of &Gammai and of some random variables (the same for all Xi, i=1, em leader, n) whose joint distribution does not depend on any factors from Phi. The two forms of selective influence are generally incompatible. Copyright 1999 Academic Press.     

Cancellation Conditions for Finite Two-Dimensional Additive Measurement

It is well known that a weak order similar on a finite set X=X(1)xX(2) has an additive real-valued order-preserving representation if and only if similar on X satisfies a denumerable scheme of cancellation conditions C(2), C(3), em leader. Condition C(K) is based on K distinct ordered pairs in XxX. Given fixed cardinalities m and n for X(1) and X(2), there is a largest K, denoted by f(m, n), such that some similar on X satisfies C(2) through C(K-1) but violates C(K). It has been known for some time that f(2, n)=2 for all n>/=2, and f(3, 3)=3. It was proved recently that f(3, n)>/=n for all even n>/=4 and that f(m, n)/=2. The present paper shows that f(3, 4)=f(4, 4)=4, f(5, n)>/=n+1 for all odd n>/=5, and f(m, n)>/=m+n-10 for all odd m and n greater than or equal to 11. The last result in conjunction with the upper bound of m+n-1 shows that f(m, n) for most (m, n) is approximately m+n. Copyright 2001 Academic Press.     

Double Skew-Dual Scaling: A Conjoint Scaling of Two Sets of Objects Related by a Dominance Matrix

Consider two sets of objects, {alpha(1), em leader, alpha(n)} and {beta(1), em leader, beta(m), such as n subjects solving m tasks, or n stimuli presented first and m stimuli presented second in a pairwise comparison experiment. Let any pair (alpha(i), beta(j)) be associated with a real number a(ij), interpreted as the degree of dominance of alpha(i) over beta(j) (e.g., the probability of alpha(i) relating in a certain way to beta(j)). Intuitively, the problem addressed in this paper is how to conjointly, in a "naturally" coordinated fashion, characterize the alpha-objects and beta-objects in terms of their overall tendency to dominate or be dominated. The gist of the solution is as follows. Let A denote the nxm matrix of a(ij) values, and let there be a class of monotonic transformations straight phi with nonnegative codomains. For a given straight phi, a complementary matrix B is defined so that straight phi(a(ij))+straight phi(b(ij))=const, and one computes vectors D(alpha) and D(beta) (the dominance values for alpha-objects and beta-objects) by solving the equations straight phi(A) straight phi(D(beta))/Sigma;straight phi(D(beta))=straight phi(D(alpha)) and straight phi(B(T)) straight phi(D(alpha))/Sigmastraight phi(D(alpha))=straight phi(D(beta)), where (T) is transposition, Sigma is the sum of elements, and straight phi applies elementwise. One also computes vectors S(alpha) and S(beta) (the subdominance values for alpha-objects and beta-objects) by solving the equations straight phi(B) straight phi(S(beta))/Sigmastraight phi(S(beta))=straight phi(S(alpha)) and straight phi(A(T)) straight phi(S(alpha))/Sigmastraight phi(S(alpha))=straight phi(S(beta)). The relationship between S-vectors and D-vectors is complex: intuitively, D(alpha) characterizes the tendency of an alpha-object to dominate beta-objects with large dominance values, whereas S(alpha) characterizes the tendency of an alpha-objects to fail to dominate beta-objects with large subdominance values. For classes containing more than one straight phi-transformation, one can choose an optimal straight phi as the one maximizing some measure of discrimination between individual elements of vectors straight phi(D(alpha)), straight phi(D(beta)), straight phi(S(alpha)), and straight phi(S(beta)), such as the product or minimum of these vectors' variances. The proposed analysis of dominance matrices has only superficial similarities with the classical dual scaling (Nishisato, 1980). Copyright 1999 Academic Press.     

Mental architectures with selectively influenced but stochastically interdependent components

The way external factors influence distribution functions for the overall time required to perform a mental task (such as responding to a stimulus, or solving a problem) may be informative as to the underlying mental architecture, the hypothetical network of interconnected processes some of which are selectively influenced by some of the external factors. Under the assumption that all processes contributing to the overall performance time are stochastically independent, several basic results have been previously established. These results relate patterns of response time distribution functions produced by manipulating external factors to such questions as whether the hypothetical constituent processes in the mental architecture enter AND gates or OR gates, and whether pairs of processes are sequential or concurrent. The present study shows that all these results are also valid for stochastically interdependent component times, provided the selective dependence of these components upon external factors is understood within the framework of a recently proposed theory of selective influence. According to this theory each component is representable as a function of three arguments: the factor set selectively influencing it, a component-specific source of randomness, and a source of randomness shared by all the components.     

Congruence Lattices of Semilattices with Operators

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \({{\rm Con}(S,+,0,G) \cong^{d} {{\rm S}_{p}}(L,H)}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices satisfy the Jónsson–Kiefer property.     

Selective influence through conditional independence

Let each of several (generally interdependent) random vectors, taken separately, be influenced by a particular set of external factors. Under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by “its own” factor set? The answer proposed and elaborated in this paper is: One can say this if and only if one can find a factor-independent random vector given whose value the vectors in question are conditionally independent, with their conditional distributions selectively influenced by the corresponding factor sets. Equivalently, the random vectors should be representable as deterministic functions of “their” factor sets and of some mutually independent and factor-independent random variables, some of which may be shared by several of the functions.     

The Developmental Leadership Questionnaire (DLQ): some psychometric properties

The development leadership model (Larsson et al., 2003), designed to introduce refinements to the transformational leadership model, has been adopted for use in the Swedish Armed Forces. The Developmental Leadership Questionnaire (DLQ) was constructed to measure important parts of the model. The main aim of the study was to evaluate some psychometric properties of the DLQ. Most analyses are based on two subsets of individuals from a sample mostly consisting of male Swedish, military officers, each of whom has rated a given leader (n = 450 and 449 respectively). A second sample consisted of Swedish military cadets (n = 141). The dimensionality was assessed with a confirmatory factor analysis. Most DLQ scales were reasonably well reproduced and showed high or acceptable internal consistency. When related to perceived results of leadership (self-rated by leaders and rated by subordinates), results from multiple regression analyses supported what could be predicted by the theoretical model. It was concluded that the DLQ has acceptable psychometric properties and that the theoretical refinements introduced to the developmental leadership model were empirically supported.     

CDAscal: An algorithm for assessing the correspondence of one or more vectors to a symmetric matrix using ordinal regression

An algorithm for assessing the correspondence of one or more attribute rating variables to a symmetric matrix of dissimilarities is presented. The algorithm is useful as an alternative to fitting property variables into a multidimensional scaling space. Rather than requiring a two step process of first deriving a multidimensional space and then fitting variables individually into the space, the algorithm directly assesses the correspondence of each variable to the symmetric matrix and permits a regression extension such that a set of variables can be considered simultaneously. The relation between the matrix and the variables is determined by evaluating pairs of pairs relations, . Though the algorithm requires only ordinal assumptions, the correspondence may be computed intervally also. Multiple ordinal regression is performed with the values derived from the matrix serving as the dependent variable and those derived from the attribute ratings serving as the independent variables. Standard multiple regression statistics forR-square,F, andt are calculated as well as measures of ordinal association between the vectors and the matrix.     

Turing–Taylor Expansions for Arithmetic Theories

Turing progressions have been often used to measure the proof-theoretic strength of mathematical theories: iterate adding consistency of some weak base theory until you “hit” the target theory. Turing progressions based on n-consistency give rise to a \({\Pi_{n+1}}\) proof-theoretic ordinal \({|U|_{\Pi^0_{n+1}}}\) also denoted \({|U|_n}\). As such, to each theory U we can assign the sequence of corresponding \({\Pi_{n+1}}\) ordinals \({\langle |U|_n\rangle_{n > 0}}\). We call this sequence a Turing-Taylor expansion or spectrum of a theory. In this paper, we relate Turing-Taylor expansions of sub-theories of Peano Arithmetic to Ignatiev’s universal model for the closed fragment of the polymodal provability logic \({\mathsf{GLP}_\omega}\). In particular, we observe that each point in the Ignatiev model can be seen as Turing-Taylor expansions of formal mathematical theories. Moreover, each sub-theory of Peano Arithmetic that allows for a Turing-Taylor expansion will define a unique point in Ignatiev’s model.     

Foundationalism with infinite regresses of probabilistic support

There is a long-standing debate in epistemology on the structure of justification. Some recent work in formal epistemology promises to shed some new light on that debate. I have in mind here some recent work by David Atkinson and Jeanne Peijnenburg, hereafter “A&P”, on infinite regresses of probabilistic support. A&P show that there are probability distributions defined over an infinite set of propositions {\(p_{1}, p_{2}, p_{3}, {\ldots }, p_{n}, {\ldots }\}\) such that (i) \(p_{i}\) is probabilistically supported by \(p_{i+1}\) for all i and (ii) \(p_{1}\) has a high probability. Let this result be “APR” (short for “A&P’s Result”). A&P oftentimes write as though they believe that APR runs counter to foundationalism. This makes sense, since there is some prima facie plausibility in the idea that APR runs counter to foundationalism, and since some prominent foundationalists argue for theses inconsistent with APR. I argue, though, that in fact APR does not run counter to foundationalism. I further argue that there is a place in foundationalism for infinite regresses of probabilistic support.     

Nondeterministic three-valued logic: Isotonic and guarded truth-functions

Nondeterministic programs occurring in recently developed programming languages define nondeterminate partial functions. Formulas (Boolean expressions) of such nondeterministic languages are interpreted by a nonempty subset of {T (“true”), F (“false”), U (“undefined)}. As a semantic basis for the propositional part of a corresponding nondeterministic three-valued logic we study the notion of a truth-function over {T, F, U} which is computable by a nondeterministic evaluation procedure. The main result is that these truth-functions are precisely the functions satisfying four basic properties, called \( \subseteq \) -isotonic, \( \subseteq \) ^?-isotonic, hereditarily guarded, and hereditarily guard-using, and that a function satisfies these properties iff it is explicitly definable (in a certain normal form) from “if..then..else..fi”, binary choice, and constants.     

Contextual-Hierarchical Reconstructions of the Strengthened Liar Problem

In this paper we shall introduce two types of contextual-hierarchical (from now on abbreviated by ‘ch’) approaches to the strengthened liar problem. These approaches, which we call the ‘standard’ and the ‘alternative’ ch-reconstructions of the strengthened liar problem, differ in their philosophical view regarding the nature of truth and the relation between the truth predicates T r ⁿ and T r ⁿ⁺¹ of different hierarchy-levels. The basic idea of the standard ch-reconstruction is that the T r ⁿ⁺¹-schema should hold for all sentences of \(\mathcal {L}^{n}\). In contrast, the alternative ch-reconstruction, for which we shall argue in section four, is motivated by the idea that T r ⁿ and T r ⁿ⁺¹ are coherent in the sense that the same sentences of \(\mathcal {L}^{n}\) should be true according to T r ⁿ and T r ⁿ⁺¹. We show that instances of the standard ch-reconstruction can be obtained by iterating Kripke’s strong Kleene jump operator. Furthermore, we will demonstrate how instances of the alternative ch-reconstruction can be obtained by a slight modification of the iterated axiom system KF and of the iterated strong Kleene jump operator.     

Need for Meaning,Meaning Confusion,Meaning Anxiety,and Meaning Avoidance: Additional Dimensions of Meaning in Life

Two aspects of meaning in life have drawn much attention in previous research: presence of meaning and search for meaning. We proposed four additional aspects concerning individuals’ thoughts and feelings about meaning in life: need for meaning, meaning confusion, meaning avoidance, and meaning anxiety. We developed items to measure these dimensions. Exploratory and confirmatory factor analysis indicated that the data fit the factors well. Convergent and discriminant validities of the four dimensions were demonstrated though their distinct patterns of correlations with other variables, such as personality traits, need satisfaction, personal aspirations, life satisfaction, anxiety and depression. Moreover, cluster analysis revealed that individuals could be divided into meaningful groups according to these dimensions, with each group demonstrating unique psychological features. Implications for future studies on meaning in life are discussed.     

Tree inference with factors selectively influencing processes in a processing tree

We show how to systematically construct a processing tree using data from an experiment in which two experimental factors are intended to selectively influence two different processes. Only two arrangements are possible for the two selectively influenced processes: ordered and unordered. We show that there are only two standard trees that need be considered, one for each arrangement. Necessary and sufficient conditions are given for each tree to be applicable. If the conditions do not hold, no tree is possible. If the selectively influenced processes are ordered, their order is sometimes determined by the data. We consider two factors that selectively influence two processes in every tree in a set of trees, such that on a given trial, a tree is selected from the set at random. We show that if the influenced processes are ordered in every tree or unordered in every tree, then the mixture of trees is equivalent to one of the two standard trees. To illustrate the method, a tree is constructed from simulated data from a model of Batchelder and Riefer [Batchelder, W.H., Riefer, D.M. (1980). Separation of storage and retrieval factors in free recall of clusterable pairs. Psychological Review, 87, 375–397].     

新HSK书写成绩可靠性影响因素的概化理论分析

本研究以概化理论为视角,搜集了新HSK五级模拟书写题的作答和评分数据,估算了题型、题量、评卷员人数、评阅速度等潜在影响效应的方差分量,考察了新HSK书写成绩的可靠性,并探索了改善该分数可靠性的途径。基于概化理论和规划求解的数据分析发现了题量的调整方案以及题型、题量、评卷员人数的最优组合方案。本研究对评阅速度进行的分析属于前沿性的理论探索,而其他数据分析结果,则可能有益于旨在改进该测试质量的决策实践。     

An n-Player Semantic Game for an n + 1-Valued Logic

First we show that the classical two-player semantic game actually corresponds to a three-valued logic. Then we generalize this result and give an n-player semantic game for an n + 1-valued logic with n binary connectives, each associated with a player. We prove that player i has a winning strategy in game if and only if the truth value of is t _i in the model M, for 1 ≤ i ≤ n; and none of the players has a winning strategy in if and only if the truth value of is t ₀ in M.     

A Replication of the Reker and Cousins’ Study About the Complementarity Between the Purpose-In-Life Test (PIL) and the Seeking of Noetic Goals (SONG) Among Spanish Young People

The main aim of this study was to replicate the Reker and Cousins’ (1979) work about the complementarity between the the Purpose-In-Life Test (PIL), which indicates the degree to which the person has found meaning and purpose in life (presence of meaning), and the Seeking of Noetic Goals (SONG), which measures the degree to which the person is motivated to find meaning and purpose in life (search for meaning). Participants were 349 Spanish undergraduates (224 women, 64.20 %, and 125 men, 35.80 %) between 18 and 26 years old, M = 20.81, SD = 2.17. Principal Component Analysis showed eight factors: four mainly related to the presence of meaning and four mainly related to the search for meaning. The PIL contributed four factors to presence of meaning, whereas the SONG contributed four factors to the search for meaning. The results confirmed the factorial structure, internal consistency, and validity of both scales and their complementarity.     

Distinguishing Between the Facilitating and the Self-Serving Charismatic Group Leader

Winnicott informed us about the components of the facilitating environment. Kohut warned us to differentiate between the charismatic leader, who looks for enfeebled followers to further his own grandiose ambitions, and the idealizable leader whose actions are based on a sense of values. Findings from attachment theory and neurobiology indicate how specific developmental issues make for a perfect fit between the self-serving charismatic leader and those who have been deprived of attuned interactive regulation and secure attachment in early childhood. This article attempts to integrate the above ideas for application to group dynamics in therapeutic, supervisory, training, and institutional groups.