On the need for negative local item dependence

While negative local item dependence (LID) has been discussed in numerous articles, its occurrence and effects often go unrecognized. This is due in part to confusion over what unidimensional latent trait is being utilized in evaluating the LID of multidimensional testing data. This article addresses this confusion by using an appropriately chosen latent variable to condition on. It then provides a proof that negative LID must occur when unidimensional ability estimates (such as number right score) are obtained from data which follow a very general class of multidimensional item response theory models. The importance of specifying what unidimensional latent trait is used, and its effect on the sign of the LIDs are shown to have implications in regard to a variety of foundational theoretical arguments, to the simulation of LID data sets, and to the use of testlet scoring for removing LID.This paper is based in part on a chapter in the first author's doctoral dissertation, written at the University of Illinois at Urbana-Champaign under the supervision of William Stout. Part of this research has been presented at the annual meeting of the National Council on Measurement in Education, San Diego, California, April 14–16, 1998.The research of the first author was partially supported by a Harold Gulliksen Psychometric fellowship through Educational Testing Service and by a Research and Productive Scholarship award from the University of South Carolina.     

The phenotypic and genotypic relation between working memory speed and capacity

This study examined the phenotypic and genotypic relationship between working memory speed (WMS) and working memory capacity (WMC) in 12-year-old twins and their siblings (N = 409). To asses WMS all children performed a reaction time task with three memory loads from which a basic mental speed measure and the derived slope were used. WMC was measured with two subtests of the WISC-R, namely Arithmetic and Digit Span. The phenotypic correlations among the WMS and WMC indices were around − 0.30. Heritabilities for all variables ranged from 43% to 56%. Structural equating modelling revealed that a model with two genetic factors, representing WMS and WMC, which were correlated (− 0.54) fitted the data best, indicating that WMS and WMC are partly mediated by the same set of genes and partly by separate sets of genes. When general IQ was simultaneously analysed with the data the correlation between the genetic factors for WMS and WMC decreased (− 0.25), but was still significant. This means that  50% of the genetic correlation between WMS and WMC is explained by IQ.     

认知诊断中的Q矩阵及其作用

Q矩阵作为连接认知和测量的桥梁,在认知诊断中起重要作用。本文梳理了应用Q矩阵解决认知诊断相关问题的理论与方法。首先整理Q矩阵的相关概念、算法、性质及其在认知诊断中的作用;并根据Q矩阵可计算理论构念效度、可以构成格等,指出Q矩阵是特殊的关联矩阵;接着介绍Q矩阵理论研究方面的几个近期发展;并对Q矩阵未来的应用研究作出展望。期望本文能为测量工作者更灵活地利用Q矩阵提供参考和帮助。     

The role of secondary covariates when estimating latent trait population distributions

The U.S. National Assessment of Educational Progress (NAEP), the Third International Mathematics and Science Study (TIMSS), and the U.S. Adult Literacy Survey collect probability samples of students (or adults) who are administered brief examinations in subject areas such as mathematics and reading (cognitive variables), along with background demographic (primary) and educational environment (secondary) questions. The demographic questions are used in the primary reporting, while the numerous explanatory secondary variables, or covariates, are only directly utilized in subsequent secondary analyses. The covariates are also used indirectly to create the plausible values (multiple imputations) that are an integral part of analyses because of the use of sparse matrix sampling of cognitive items. The improvement in the precision of the primary reporting due to the inclusion of the covariates is assessed here and contrasted with the precision of reporting using plausible values created using only the primary demographic variables.The results demonstrate that the improvement in precision depends on the matrix sampling designs for the cognitive assessments. The improvements range from essentially none for the most common designs, to moderate for some less common designs. Consequently, two potential changes in the reporting procedures that could improve the statistical and operational efficiency of primary reporting are (a) eliminate or reduce the collection of covariates and increase the number of cognitive items, (b) to avoid delays, eliminate the covariates from the creation of plausible values used for the primary reports, but include them later when creating public-use files for secondary analyses. The potential improvements in statistical and operational efficiency must be weighed against the intrinsic interest in the covariates, and the potential for small discrepancies in the primary and secondary reporting.Thanks to Donald Rubin, Robert Mislevy, and John Barnard for their helpful comments and computing assistance. This work was supported by NCES Grant 84.902B980011.     

Multiple timescales of body schema reorganization due to plastic surgery

Plastic surgery modifies the distribution of mass centers of a person’s body segments, changing his or her posture. The functional reorganization processes that lead subjects to re-integrate these body changes into a new stable body (posture) schema is poorly understood but current theories suggest the possible contribution of two components: a feedback mechanism that strongly depends on sensory input and an internal model that is relatively less dependent on sensory input and improves posture control, for example by compensating for delayed feedback. To assess the relative contributions of these two mechanisms during the functional reorganization of a posture scheme, we have conducted a longitudinal postural study in a population of healthy adults who were subject to breast plastic surgery to reduce or augment body weight. We measured participants’ orthostatic posture and ground reaction force immediately after, after 4 months, and 1 year after the surgery. To investigate the role of visual sensory information in the reorganization process we tested the participants with eyes open and closed. Our results indicate that participants find a new dynamical equilibrium within a few days. However, posture maintenance remains sub-optimal long after the center of masses and the resultant of ground reaction force stop changing; in some cases, for more than 4 months. Furthermore, the re-adaptation process is faster and more efficient in the eyes-open than in the eyes-closed condition. These results suggest that the reorganization involves different subsystems (responsible for the biomechanical changes, the re-calibration of feedback mechanisms, and the re-adaptation of internal models), which act at different timescales.     

A model of saccadic landing positions in reading under the influence of sensory noise

During reading, saccadic eye movements are produced to move the high acuity foveal region of the eye to words of interest for efficient word processing. Distributions of saccadic landing positions peak close to a word's centre but are relatively broad compared to simple oculomotor tasks. Moreover, landing-position distributions are modulated both by distance of the launch site and by saccade type (e.g., one-step saccade, word skipping, refixation). Here we present a mathematical model for the computation of a saccade intended for a given target word. Two fundamental assumptions are related to (1) the sensory computation of the word centre from inter-word spaces and (2) the integration of sensory information and a priori knowledge using Bayesian estimation. Our model was developed for data from a large corpus of eye movements from normal reading. We demonstrate that the model is able simultaneously to account for a systematic shift of saccadic mean landing position with increasing launch-site distance and for qualitative differences between one-step saccades (i.e., from a given word to the next word) and word-skipping saccades.     

Divergence Behaviour of the Successive Geometric Mean Method of Pairwise Comparison Matrix Generation for a Multiple Stage,Multiple Objective Optimization Problem

This paper focuses on the divergence behaviour of the successive geometric mean (SGM) method used to generate pairwise comparison matrices while solving a multiple stage, multiple objective (MSMO) optimization problem. The SGM method can be used in the matrix generation phase of our three‐phase methodology to obtain pairwise comparison matrix at each stage of an MSMO optimization problem, which can be subsequently used to obtain the weight vector at the corresponding stage. The weight vectors across the stages can be used to convert an MSMO problem into a multiple stage, single objective (MSSO) problem, which can be solved using dynamic programming‐based approaches. To obtain a practical set of non‐dominated solutions (also referred to as Pareto optimal solutions) to the MSMO optimization problem, it is important to use a solution approach that has the potential to allow for a better exploration of the Pareto optimal solution space. To accomplish a more exhaustive exploration of the Pareto optimal solution space, the weight vectors that are used to scalarize the MSMO optimization problem into its corresponding MSSO optimization problem should vary across the stages. Distinct weight vectors across the stages are tied directly with distinct pairwise comparison matrices across the stages. A pairwise comparison matrix generation method is said to diverge if it can generate distinct pairwise comparison matrices across the stages of an MSMO optimization problem. In this paper, we demonstrate the SGM method's divergence behaviour when the three‐phase methodology is used in conjunction with an augmented high‐dimensional, continuous‐state stochastic dynamic programming method to solve a large‐scale MSMO optimization problem. Copyright © 2013 John Wiley & Sons, Ltd.     

On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models

In item response theory, the classical estimators of ability are highly sensitive to response disturbances and can return strongly biased estimates of the true underlying ability level. Robust methods were introduced to lessen the impact of such aberrant responses on the estimation process. The computation of asymptotic (i.e., large‐sample) standard errors (ASE) for these robust estimators, however, has not yet been fully considered. This paper focuses on a broad class of robust ability estimators, defined by an appropriate selection of the weight function and the residual measure, for which the ASE is derived from the theory of estimating equations. The maximum likelihood (ML) and the robust estimators, together with their estimated ASEs, are then compared in a simulation study by generating random guessing disturbances. It is concluded that both the estimators and their ASE perform similarly in the absence of random guessing, while the robust estimator and its estimated ASE are less biased and outperform their ML counterparts in the presence of random guessing with large impact on the item response process.     

The Role of Numeracy and Intelligence in Health‐Risk Estimation and Medical Data Interpretation

Despite ample evidence that numeracy is an important influence on patient understanding and use of health‐related information, there is a dearth of studies examining the concept's relationship to other individual differences measures that may underlie complex judgments in the health domain. In this study, we compared the relative contributions of selected extant numeracy measures and general intelligence and other measures to varied judgment and decision‐making outcomes. Two hundred participants completed numeracy items, subscales of the Wechsler Adult Intelligence Scales, the need for cognition scale, and four relevant outcome measures including risk estimation and medical data interpretation. A numeracy scale constructed using item response and confirmatory factor analyses was consistently the strongest predictor across all outcome measures and accounted for unique variance over and above general intelligence. The results support the concept of numeracy as an independent construct that merits consideration in patient communication. Copyright © 2013 John Wiley & Sons, Ltd.