Estimating the standard errors of rotated factor loadings by jackknifing

The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood factor analysis. Simulations are performed in whicht-statistics based upon these jackknife estimates of the standard errors are computed. The validity of thet-statistics and their associated confidence intervals is assessed. Methods are given through which the computational efficiency of the jackknife may be greatly enhanced in the factor analysis model.Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources Grant RR-3.The author wishes to thank his doctoral committee co-chairmen, Drs James W. Frane and Robert I. Jennrich, UCLA, for their contributions to this research.     

Approximate confidence intervals for a robust scale parameter

A recent paper by Wainer and Thissen has renewed the interest in Gini's mean difference,G, by pointing out its robust characteristics. This note presents distribution-free asymptotic confidence intervals for its population value,γ, in the one sample case and for the difference Δ=(γ ₁?γ ₂) in the two sample situations. Both procedures are based on a technique of jackknifingU-statistics developed by Arvesen.     

A Logic for Multiple-source Approximation Systems with Distributed Knowledge Base

The theory of rough sets starts with the notion of an approximation space, which is a pair (U,R), U being the domain of discourse, and R an equivalence relation on U. R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U. The focus then is on approximations of concepts on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base, which is a tuple (U,R_P)_{Pßf N}(U,R_P)_{P\ss_f N}, where N is a set of sources and P ranges over all finite subsets of N. Each R _P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS ^D is proposed. In LMSAS ^D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS ^D are discussed and it is shown that the modal system KTB is embedded in LMSAS ^D . The epistemic logic S5^D_nS5^D_n is also embedded in LMSAS ^D , and cannot replace the latter to serve our purpose. The relationship of LMSAS ^D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed.     

On Iachello's model of cuprate superconductors

A U(3) model proposed by Iachello for superconductivity in cuprate materials is analyzed. The model consists of s and d pairs (approximated as bosons) in a two-dimensional Fermi system with a surface. The transition occurs between a phase in which the system is a condensate of one type of boson, and a phase which is a mixture of two types of bosons. In the current work we have investigated the validity of the Bogoliubov approximation, and we used a reduced Hamiltonian to determine a phase diagram, the symmetry of the phases, and the temperature dependence of the heat capacity.     

Approximating the conditional distribution of person FIT indexes for checking the rasch model

We present a simple approximation to the conditional distribution of goodness-of-fit statistics for the Rasch model, assuming that the item difficulties are known. The approximation is easily programmed, and gives relatively accurate assessments of conditionalp-values for tests of length 10 or more. A few generalizations are discussed.     

Mixed-valence impurity in a nanoscale particle

We consider a mixed-valence Anderson impurity with infinite U embedded into a small metallic particle. The nanosize of the system leads to discrete energy levels rather than to a continuum of energy eigenstates for the host. Using the Brillouin-Wigner approximation we show that the magnetic susceptibility, which arises from the van Vleck admixing of the magnetic configuration into the ground state, is only weakly affected by the finite spacing of energy levels, while the specific heat and the entropy display an exponential activation at low temperatures, that is have properties deviating from a Fermi liquid.     

The effect of strength of cognitive linkages on attitude change in a communication situation

Implicitly or explicitly, linkage is a basic concept in all theories of cognitive consistency — consistency or inconsistency can exist only with reference to entities which are cognitively linked through association or dissociation. The nature of cognitive linkages has not been systematically studied, but it seems evident that they may vary in many ways. One is the strength or intensity of perceived relationship between cognitive entities. The basic hypothesis in the present two experiments was that the effect of a communication in terms of attitude change would depend on the strength of linkage between concepts mentioned in the message. Results show no such effect when strength was manipulated through combination of linkages, whereas the hypothesis was confirmed when linkage strength was varied semantically. Also, previous studies on direct and mediated generalization of attitude change towards consistency were successfully replicated. Finally, it was found that amount of attitude change towards consistency was significantly higher for linkages involving affect (L-relations) than for linkages simply expressing unit formation (U-relations).     

On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient

In this paper a rapid and reliable method is found for estimating the value of the Bivariate Normal Correlation Coefficient, ρ, given values of the joint probability and the normal deviates,h andk, or the related areas. This technique finds useful application in the computational approximation of the tetrachoric correlation coefficient,r, when the underlying distributions may be assumed to be normal.     

Three-Valued Temporal Logic <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">t</Emphasis></Subscript> and Future Contingents

Prior’s three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic Q _t and give its axiomatization and semantics. We also argue that Q _t provides a smooth solution to the problem of future contingents. Presented by Daniele Mundici     

Optimal sequential designs for on-line item estimation

Replenishing item pools for on-line ability testing requires innovative and efficient data collection designs. By generating localD-optimal designs for selecting individual examinees, and consistently estimating item parameters in the presence of error in the design points, sequential procedures are efficient for on-line item calibration. The estimating error in the on-line ability values is accounted for with an item parameter estimate studied by Stefanski and Carroll. LocallyD-optimaln-point designs are derived using the branch-and-bound algorithm of Welch. In simulations, the overall sequential designs appear to be considerably more efficient than random seeding of items.This report was prepared under the Navy Manpower, Personnel, and Training R&D Program of the Office of the Chief of Naval Research under Contract N00014-87-0696. The authors wish to acknowledge the valuable advice and consultation given by Ronald Armstrong, Charles Davis, Bradford Sympson, Zhaobo Wang, Ing-Long Wu and three anonymous reviewers.     

Characterizing Simpler Recognizable Sets of Integers

For a given numeration system U, a set X of integers is said to be U-star-free if the language of the normalized U-representations of the elements in X is star-free. Adapting a result of McNaughton and Papert, we give a first-order logical characterization of these sets for various numeration systems including integer base systems and the Fibonacci system. For k-ary systems, the problem of the base dependence of this property is also studied. Finally, the case of k-adic systems is developed.     

Construct validity for the verbal associated pairs screen

The present study introduces the Verbal Associated Pairs Screen (VAPS) as a new measure for assessing performance validity in pediatric populations. This study presents initial data on psychometric properties and establishes construct validity for the VAPS in a sample of 30 adolescent healthy controls and 206 youths with traumatic brain injury (TBI: moderate/severe, N = 30; mild, N = 176). The control group’s age (M = 14.93, SD = 1.8) was significantly higher than the moderate/severe TBI (M = 13.9, SD = 2.8), t(68.508) = ?3.038, p = .003, and mild TBI (mTBI) groups (M = 14, SD = 2.8), t(54.147) = 2.038, p = .046. The TBI groups were administered the VAPS in accord with other established performance validity tests (PVTs) and well-established memory tests as part of routine clinical evaluations. The healthy control group was administered the VAPS only. VAPS score distributions for the control group were negatively skewed and highly kurtotic. VAPS scores from the moderate/severe TBI and control groups were indistinguishable for Trial 2 (U = 274, p < .01) and the Delay (U = 396, p = .218). In the mTBI group, convergent and divergent validity was established with other well-validated PVTs and memory tests, respectively. ROC curve analyses identified optimal cutoff scores for the VAPS Total Score, with acceptable sensitivity (55%) and excellent specificity (100%), as well as strong detectability (AUC = .829, 95% CI: 0.731 – 0.928, p < .001). Clinical applications, limitations, and directions for future research with the VAPS are discussed.     

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∪....     

Equating test scores—A maximum likelihood solution

Certain problems of equating are discussed. The maximum likelihood solution is presented for the following special equating problem: Two tests,U andV, are to be equated, making use of a third anchor test,W. The examinees are divided into two random halves. TestsU andW are administered to one half; testsV andW are administered to the other half. It is assumed that any practice effect or other effect, exerted byU andV onW, is the same forU and forV.     

An Excel sheet for inferring children’s number-knower levels from give-<Emphasis Type="Italic">N</Emphasis> data

Number-knower levels are a series of stages of number concept development in early childhood. A child’s number-knower level is typically assessed using the give-N task. Although the task procedure has been highly refined, the standard ways of analyzing give-N data remain somewhat crude. Lee and Sarnecka (Cogn Sci 34:51–67, 2010, in press) have developed a Bayesian model of children’s performance on the give-N task that allows knower level to be inferred in a more principled way. However, this model requires considerable expertise and computational effort to implement and apply to data. Here, we present an approximation to the model’s inference that can be computed with Microsoft Excel. We demonstrate the accuracy of the approximation and provide instructions for its use. This makes the powerful inferential capabilities of the Bayesian model accessible to developmental researchers interested in estimating knower levels from give-N data.     

Generalized concordance

Based on a simple nonparametric procedure for comparing two proximity matrices, a measure of concordance is introduced that is appropriate whenK independent proximity matrices are available. In addition to the development of a general concept of concordance and specific techniques for its evaluation within and between the subsets of a partition of theK matrices, several methods are also suggested for comparing and/or for fitting a particular structure to the given data. Finally, brief indications are provided as to how the well-known notion of concordance forK rank orders can be included within the more general framework.Partial support for this research was supplied by the National Science Foundation through SOC-77-28227.     

What is at Issue in Argumentation? Judgment in the Hellenistic Doctrine of <Emphasis Type="Italic">Krinomenon</Emphasis>

This paper offers an account of the Hellnistic doctrine of krinomenon, elaborating on the idea of rhetoric’s restoration as a major tool of contemporary research and philosophical study. As opposed to theories of argumentation that identify judgment with its propositional version and establish legitimization on speaker-audience identity, failing to acknowledge difference and controversy, the doctrine of krinomenon focuses on the question posed, connecting rhetoric to judgment. The crucial difference from classical rhetoric lies in the concept of zētēma: In the doctrine of krinomenon, participants in a common inquiry are reasonable, while logos refers to judgment itself – not the audience. Whereas a proposition dismisses its own problematization, controversy, i.e. non-identity that gives meaning to utterances, is inscribed in krinomenon, which is the product of dialectic between contradictory utterances. Beyond the two opposite logics of dogmatism and relativism, difference in the doctrine of krinomenon is judgment’s very condition.     

Use of the Jackknife Statistic to Evaluate Result Replicability

Result replicability has often been confused with significance testing because of a misinformed view that statistical significance evaluates result importance and result replicability. Several alternatives, of which the jackknife statistic is one, provide researchers with the tools for estimating result replicability. In the present study, an available data set from A. L. Edwards (1985, p. 57) is used to illustrate the use of the jackknife statistic to assess the replicability of multiple regression results in a concrete fashion. The jackknifed coefficients are computed to assess the stability of beta weights and the multiple R ² value. Confidence intervals and t statistics are also calculated to facilitate the interpretation of these jackknifed coefficients.     

The role of schizotypy and creativity in a group problem-solving task

The well-studied link between psychotic traits and creativity is a subject of much debate. The present study investigated the extent to which schizotypic personality traits – as measured by O-LIFE (Oxford–Liverpool Inventory of Feelings and Experiences) – equip healthy individuals to engage as groups in everyday tasks. From a sample of 69 students, eight groups of four participants – comprised of high, medium, or low-schizotypy individuals – were assembled to work as a team to complete a creative problem-solving task. Predictably, high scorers on the O-LIFE formulated a greater number of strategies to solve the task, indicative of creative divergent thinking. However, for task success (as measured by time taken to complete the problem) an inverted U shaped pattern emerged, whereby high and low-schizotypy groups were consistently faster than medium schizotypy groups. Intriguing data emerged concerning leadership within the groups, and other tangential findings relating to anxiety, competition and motivation were explored. These findings challenge the traditional cliché that psychotic personality traits are linearly related to creative performance, and suggest that the nature of the problem determines which thinking styles are optimally equipped to solve it.     

A note concerning the creager—Valentine paper

TheU _i statistic, discussed by Creager and Valentine in a recent paper, is defined as a standard error of estimate for the regression of a composite, consisting ofn components, on then–1 components, exclusive of thejth component. It is shown that this standard error equals the standard error of estimate for the prediction of thejth component from the othern–1 components. This equality is used to suggest an efficient procedure to compute all primary uniquenessesU _i .