Showing papers on "Equivalence (measure theory) published in 2003"

Beyond alpha: an empirical examination of the effects of different sources of measurement error on reliability estimates for measures of individual differences constructs.

Abstract: On the basis of an empirical study of measures of constructs from the cognitive domain, the personality domain, and the domain of affective traits, the authors of this study examine the implications of transient measurement error for the measurement of frequently studied individual differences variables. The authors clarify relevant reliability concepts as they relate to transient error and present a procedure for estimating the coefficient of equivalence and stability (L. J. Cronbach, 1947), the only classical reliability coefficient that assesses all 3 major sources of measurement error (random response, transient, and specific factor errors). The authors conclude that transient error exists in all 3 trait domains and is especially large in the domain of affective traits. Their findings indicate that the nearly universal use of the coefficient of equivalence (Cronbach's alpha; L. J. Cronbach, 1951), which fails to assess transient error, leads to overestimates of reliability and undercorrections for biases due to measurement error.

Computing Gaussian Mixture Models with EM Using Equivalence Constraints

Abstract: Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, indicating whether the points arise from the same source (positive constraints) or from different sources (negative constraints). Such constraints can be gathered automatically in some learning problems, and are a natural form of supervision in others. For the estimation of model parameters we present a closed form EM procedure which handles positive constraints, and a Generalized EM procedure using a Markov net which handles negative constraints. Using publicly available data sets we demonstrate that such side information can lead to considerable improvement in clustering tasks, and that our algorithm is preferable to two other suggested methods using the same type of side information.

Measurement Equivalence Of 10 Value Types From The Schwartz Value Survey Across 21 Countries

Abstract: Equivalence of measurement across cultures is a prerequisite for the generalization of an instrument. The measurement equivalence of 10 value types derived from Schwartz's structural model of values and measured with the Schwartz Value Survey questionnaire is evaluated in 21 countries. Based on previous research by Schwartz and colleagues, the measurement equivalence of the 10 value types is tested separately using nested multigroup confirmatory factor analyses. Results indicate that it is possible for most value types to reach acceptable levels of configural and metric equivalence; only the dimension of Hedonism is rejected at these two levels of equivalence. Four value types (Benevolence, Conformity, Self-Direction, and Universalism) also show factor variance equivalence. The hypotheses of scalar and reliability equivalence are rejected for all value types. Indications are also given of the number of items to be included for measuring the value types at the different levels of equivalence.

On the use of 'borrowed' scales in cross-national research: a cautionary note.

Abstract: Cross‐national studies may be flawed through “borrowing” scales used in domestic studies, without examining their relevance and equivalence in other countries and contexts. Examining construct equivalence is an essential first step in the design of cross‐national and multi‐country studies. An important aspect is examining the equivalence in meaning and salience of a construct in all countries or contexts studied. Unless this is established, erroneous or misleading conclusions about the nature and significance of the construct in that context are likely to result. The importance of examining construct equivalence in cross‐national research is illustrated, based on a series of studies applying the CETSCALE in The Netherlands.

Existence and continuous dependence of large solutions for the magnetohydrodynamic equations

Abstract: Global solutions of the nonlinear magnetohydrodynamic (MHD) equations with general large initial data are investigated. First the existence and uniqueness of global solutions are established with large initial data in H 1. It is shown that neither shock waves nor vacuum and concentration are developed in a finite time, although there is a complex interaction between the hydrodynamic and magnetodynamic effects. Then the continuous dependence of solutions upon the initial data is proved. The equivalence between the well-posedness problems of the system in Euler and Lagrangian coordinates is also showed.

Flat systems, equivalence and trajectory generation

Abstract: Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft.

Construct Equivalence of Multiple-Choice and Constructed-Response Items: A Random Effects Synthesis of Correlations

Abstract: A thorough search of the literature was conducted to locate empirical studies investigating the trait or construct equivalence of multiple-choice (MC) and constructed-response (CR) items. Of the 67 studies identified, 29 studies included 56 correlations between items in both formats. These 56 correlations were corrected for attenuation and synthesized to establish evidence for a common estimate of correlation (true-score correlations). The 56 disattenuated correlations were highly heterogeneous. A search for moderators to explain this variation uncovered the role of the design characteristics of test items used in the studies. When items are constructed in both formats using the same stem (stem equivalent), the mean correlation between the two formats approaches unity and is significantly higher than when using non-stem-equivalent items (particularly when using essay-type items). Construct equivalence, in part, appears to be a function of the item design method or the item writer's intent.

Adjustment for Acquiescence in the Assessment of the Construct Equivalence of Likert-Type Score Items

Abstract: Survey research often uses Liker-type score items to measure respondents' attitudes with respect to certain topics. This type of item has been shown to be susceptible to an acquiescent response bias. The purpose of this article is to point out the importance of controlling for this type of response bias when evaluating the equivalence of the construct measured by the items across (cultural) groups. More specifically, it is shown how and when omitting a factor accounting for the acquiescent response bias leads to a biased assessment of the invariance of the loadings of the content factor across the groups under study. On the basis of these results, a procedure for controlling for acquiescence is proposed and illustrated on a large data set of nine West European countries.

Testing Statistical Hypotheses of Equivalence

Abstract: (2003). Testing Statistical Hypotheses of Equivalence. Technometrics: Vol. 45, No. 3, pp. 271-272.

Competitive Risk Sharing Contracts with One-Sided Commitment

Abstract: This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex-ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex-post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. Contrary to intuition, we demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment effectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogoff (1989). From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.

The Spanish Translation and Cultural Adaptation of Five Mental Health Outcome Measures

Abstract: In this paper we report on the process of translating five mental health outcome measures into Spanish and adapting them to Latino culture. The instruments considered are the World Health Organization-Disability Assessment Scale, the Burden Assessment Scale, the Family Burden Scale, Lehman's Quality of Life Interview and the Continuity of Care in Mental Health Services Interview. A systematic process of translation and adaptation of the instruments was followed with the goal of achieving cultural equivalence between the English and Spanish versions of the instruments in five dimensions: semantic, content, technical, construct, and criterion equivalence. In this paper we present data about the semantic, content, and technical equivalence. Various steps were taken to achieve equivalence in these dimensions, including the use of a bilingual committee, a multi-national bilingual committee, back-translation, and focus groups with mental health patients and their relatives.

Uniform Equivalence of Logic Programs under the Stable Model Semantics

Abstract: In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q∪ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to stable models (which is the particular case for R= ∅), and has an application in program optimization. In this paper, we consider the more liberal notion of uniform equivalence, in which R ranges only over the sets of facts rather than all sets of rules. This notion, which is well-known, is particularly useful for assessing whether programs P and Q are equivalent as components in a logic program which is modularly structured. We provide semantical characterizations of uniform equivalence for disjunctive logic programs and some restricted classes, and analyze the computational cost of uniform equivalence in the propositional (ground) case. Our results, which naturally extend to answer set semantics, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for input-based problem solving.

A Psychometric Analysis of the Maslach Burnout Inventory-General Survey in the South African Police Service

Abstract: The objectives of this study, which was undertaken by two members of the WorkWell Research Unit, were to validate the Maslach Burnout Inventory-General Survey (MBI-GS) for the South African Police Service and to determine the construct equivalence of this Inventory and bias for different race groups. A cross-sectional survey design was used. Stratified random samples (N=2396) were taken of police members from nine provinces in South Africa. The study was based on the MBI-GS and a biographical questionnaire. Structural equation modelling confirmed a 3-factor model of burnout, consisting of Exhaustion, Cynicism and Professional Efficacy. All three factors showed acceptable internal consistencies. An exploratory factor analysis with target rotations confirmed the construct equivalence of the three factors for different race groups in the SAPS. No evidence was found for uniform or non-uniform bias of the items of the MBI-GS for different race groups.

Testing and Assessment in Cross-Cultural Psychology

Abstract: This chapter begins with some basic distinctions in cross-cultural and multicultural psychology, including the concepts of Etic and Emic. The use of tests and assessments for research and applied use in cross-cultural psychology is described. The nature of equivalence is depicted in detail with more than four types of equivalence differentiated: linguistic equivalence, conceptual equivalence, functional equivalence, and metric equivalence. A few other types of equivalence are also mentioned. The nature of bias in cross-cultural assessment is next clarified, with construct, method, and item bias acknowledged. The translation and adaptation of tests is reviewed from a procedural perspective, with emphasis upon the role of language and the role of culture in the understanding of behavior and, hence, the appreciation of testing and the interpretation of test results. Procedures for adapting tests from one culture to another and for evaluating the equivalence of the two versions are discussed. Several research designs for establishing the linkage of test scores across forms are also briefly provided. Keywords: cross-cultural testing; multicultural psychology; test adaptation; test bias; test equivalence; test translation

Geometric characterizations of Gromov hyperbolicity

Abstract: We prove the equivalence of three different geometric properties of metric-measure spaces with controlled geometry. The first property is the Gromov hyperbolicity of the quasihyperbolic metric. The second is a slice condition and the third is a combination of the Gehring–Hayman property and a separation condition.

Geodesic equivalence via integrability

Abstract: We suggest a construction that, given an orbital diffeomorphism between two Hamiltonian systems, produces integrals of them. We treat geodesic equivalence of metrics as the main example of it. In this case, the integrals commute; they are functionally independent if the eigenvalues of the tensor giαg¯αj are all different; if the eigenvalues are all different at least at one point then they are all different at almost each point and the geodesic flows of the metrics are Liouville integrable. This gives us topological obstacles to geodesic equivalence.

On tests of equivalence via non-unity relative risk for matched-pair design.

Abstract: Matched-pair design is often used in clinical trials to increase the efficiency of treatment comparison. We consider the problem of equivalence test with a relative risk endpoint in matched-pair studies with binary outcomes, and develop several score and Wald-type statistics for testing a hypothesis of non-unity relative risk. Examples from an assessment of HIV screening test and a cross-over clinical trial of soft contact lenses are used to illustrate the proposed methods. Through simulations we compare the empirical performance of these tests with the test proposed by Lachenbruch and Lynch. We show that a score test based on a reparameterized multinomial model by Tango performs best in the sense that the test satisfactorily controls the type I error rate and its empirical type I error rates are generally much closer to the prespecified nominal significance level than those of the other tests.

Equivalence Scales Reconsidered

Abstract: The paper proposes a new and normative approach for adjusting households' incomes in order to account for the heterogeneity of needs across income recipients when measuring inequality and welfare We derive the implications for the structure of the adjustment method of two conditions concerned with the way the ranking of situations is modified by a change in the reference household type and by more equally distributed living standards across households Our results suggest that concern for greater equality in living standards conflicts with the basic welfarist principle of symmetrical treatment of individuals that is at the core of the standard equivalence scale approach

Robust Mechanism Design

Abstract: The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with more higher order uncertainty. We study the "ex post equivalence" question: When is interim implementation on all possible type spaces equivalent to requiring ex post implementation on the space of payoff types? We show that ex post equivalence holds when the social choice correspondence is a function and in simple quasi-linear environments. When ex post equivalence holds, we identify how large the type space must be to obtain the equivalence. We also show that ex post equivalence fails in general, including in quasi-linear environments with budget balance. For quasi-linear environments, we provide an exact characterization of when interim implementation is possible in rich type spaces. In this environment, the planner can fully extract players' belief types, so the incentive constraints reduce to conditions distinguishing types with the same beliefs about others' types but different payoff types.

Correlation clustering: Minimizing disagreements on arbitrary weighted graphs

Abstract: We solve several open problems concerning the correlation clustering problem introduced by Bansal, Blum and Chawla [1]. We give an equivalence argument between these problems and the multicut problem. This implies an O(log n) approximation algorithm for minimizing disagreements on weighted and unweighted graphs. The equivalence also implies that these problems are APX-hard and suggests that improving the upper bound to obtain a constant factor approximation is non trivial. We also briefly discuss some seemingly interesting applications of correlation clustering.

Three-dimensional Cauchy?Riemann structures and second-order ordinary differential equations

Abstract: The equivalence problem for second-order ordinary differential equations (ODEs) given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate three-dimensional Cauchy–Riemann structures. This approach enables an analogue of the Fefferman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second-order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs.

Equivalence relations in individuals with language limitations and mental retardation.

Abstract: The study of equivalence relations exhibited by individuals with mental retardation and language limitations holds the promise of providing information of both theoretical and practical significance. We reviewed the equivalence literature with this population, defined in terms of subjects having moderate, severe, or profound mental retardation. The literature includes 55 such individuals, most of whom showed positive outcomes on equivalence tests. The results to date suggest that naming skills are not necessary for positive equivalence test outcomes. Thus far, however, relatively few subjects with minimal language have been studied. Moreover, we suggest that the scientific contributions of studies in this area would be enhanced with better documentation of language skills and other subject characteristics. With recent advances in laboratory procedures for establishing the baseline performances necessary for equivalence tests, this research area is poised for rapid growth.

Correlation clustering: Minimizing disagreements on arbitrary weighted graphs

Abstract: We solve several open problems concerning the correlation clustering problem introduced by Bansal, Blum and Chawla [1]. We give an equivalence argument between these problems and the multicut problem. This implies an O(log n) approximation algorithm for minimizing disagreements on weighted and unweighted graphs. The equivalence also implies that these problems are APX-hard and suggests that improving the upper bound to obtain a constant factor approximation is non trivial. We also briefly discuss some seemingly interesting applications of correlation clustering.

Equivalence of linear approaches in bioelectromagnetic inverse solutions

Abstract: Several different techniques have appeared in the magnetoencephalography (MEG) literature for solving the ambiguous inverse problem. We show that if the same second order statistics are uniformly applied in each case, then the resulting solutions are the same. Additionally, for the common assumption of independent sources, then the "noise significance " measure emphasises the need to select the data and noise covariance statistics, not the specific values of source statistics. Thus such algorithms as "dynamic SPM" and "synthetic aperture magnetoencephalography " are theoretically equivalent and differ in practice by practical matters of specification or estimation of data covariances.