A new solution to the problem of finding all numerical solutions to ordered metric structures

A new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling and ordinal multiple regression. The algorithm is computationally faster and numerically superior to previous algorithms.This research was supported in part by NIGMS grant GM-01231 to the University of Michigan. Authors' names are in alphabetic order.     

Piecewise method of reciprocal averages for dual scaling of multiple-choice data

The proposed method handles the classical method of reciprocal averages (MRA) in a piecewise (item-by-item) mode, whereby one can deal with smaller matrices and attain faster convergence to a solution than the MRA. A new concept the principle of constant proportionality is introduced to provide an interesting interpretation for scaling multiple-choice data a la Guttman. A small example is presented for discussion of the technique.This study was supported by the Natural Sciences and Engineering Research Council Canada Grant (No. A4581) to S. Nishisato. The authors are indebted to reviewers for valuable comments.     

A technique for the nonmetric analysis of paired comparisons of psychological intervals

A nonmetric coordinate adjustment technique is developed which determines scale values for objects whose interobject intervals (differences in subjective value) have been directly compared. In Monte Carlo simulations, the degree of metric determinancy of the scale values is shown to be quite high even when the amount of error is relatively high. This robustness under high-error conditions permitted the analysis of individual subject data in experiments on the direct comparison of loudness differences and loudness ratios where only one judgment per interval comparison was obtained per subject.This research was supported by a grant from the National Research Council of Canada.     

V.A. Smirnov’s Results in the Field of Modern Formal Logic

This paper is a survey of V.A. Smirnovs main results in modern logic.     

A Gibbs sampler for the multidimensional four-parameter logistic item response model via a data augmentation scheme

The four-parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three-parameter and two-parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open-source IRTlogit package.     

Conditional Covariance Theory and Detect for Polytomous Items

This paper extends the theory of conditional covariances to polytomous items. It has been proven that under some mild conditions, commonly assumed in the analysis of response data, the conditional covariance of two items, dichotomously or polytomously scored, given an appropriately chosen composite is positive if, and only if, the two items measure similar constructs besides the composite. The theory provides a theoretical foundation for dimensionality assessment procedures based on conditional covariances or correlations, such as DETECT and DIMTEST, so that the performance of these procedures is theoretically justified when applied to response data with polytomous items. Various estimators of conditional covariances are constructed, and special attention is paid to the case of complex sampling data, such as those from the National Assessment of Educational Progress (NAEP). As such, the new version of DETECT can be applied to response data sets not only with polytomous items but also with missing values, either by design or at random. DETECT is then applied to analyze the dimensional structure of the 2002 NAEP reading samples of grades 4 and 8. The DETECT results show that the substantive test structure based on the purposes for reading is consistent with the statistical dimensional structure for either grade. This research was supported by the Educational Testing Service and the National Assessment of Educational Progress (Grant R902F980001), US Department of Education. The opinions expressed herein are solely those of the author and do not necessarily represent those of the Educational Testing Service. The author would like to thank Ting Lu, Paul Holland, Shelby Haberman, and Feng Yu for their comments and suggestions. Requests for reprints should be sent to Jinming Zhang, Educational Testing Service, MS 02-T, Rosedale Road, Princeton, NJ 08541, USA. E-mail: jzhang@ets.org     

A Person Fit Test For Irt Models For Polytomous Items

A person fit test based on the Lagrange multiplier test is presented for three item response theory models for polytomous items: the generalized partial credit model, the sequential model, and the graded response model. The test can also be used in the framework of multidimensional ability parameters. It is shown that the Lagrange multiplier statistic can take both the effects of estimation of the item parameters and the estimation of the person parameters into account. The Lagrange multiplier statistic has an asymptotic χ²-distribution. The Type I error rate and power are investigated using simulation studies. Results show that test statistics that ignore the effects of estimation of the persons’ ability parameters have decreased Type I error rates and power. Incorporating a correction to account for the effects of the estimation of the persons’ ability parameters results in acceptable Type I error rates and power characteristics; incorporating a correction for the estimation of the item parameters has very little additional effect. It is investigated to what extent the three models give comparable results, both in the simulation studies and in an example using data from the NEO Personality Inventory-Revised.     

具有创造成就的科学家关于创造的概念结构

运用Q分类及多尺度分析方法,研究具有创造成就的科学家关于创造成就的概念结构。被试是30名来自物理、化学、数学、地学和生命科学领域的具有创造成就的科学家。研究发现,具有创造成就的科学家关于创造成就的概念结构由“成就取向/内心体验取向”、“主动进取/踏实肯干”两个维度构成;取得科学创造成就的重要特征是“成就取向”和“主动进取”。作者进一步讨论了主动进取对于取得创造性成就的意义     

First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years

There is evidence that spatial thinking is malleable, and that spatial and mathematical skills are associated (Mix et al. [2016] Journal of Experimental Psychology: General, 145, 1206; Mix et al. [2017] Journal of Cognition and Development, 18, 465; Uttal et al. [2013] Psychological Bulletin, 139, 352). However, few studies have investigated transfer of spatial training gains to mathematics outcomes in children, and no known studies have compared different modes of spatial instruction (explicit vs. implicit instruction). Based on a sample of 250 participants, this study compared the effectiveness of explicit and implicit spatial instruction in eliciting near transfer (to the specific spatial skills trained), intermediate transfer (to untrained spatial skills) and far transfer (to mathematics domains) at age 8. Spatial scaling and mental rotation skills were chosen as training targets as previous studies have found, and proposed explanations for, associations between these skills and mathematics in children of this age (Journal of Experimental Psychology: General, 145, 2016 and 1206). In this study, spatial training led to near, intermediate and far transfer of gains. Mental visualization and proportional reasoning were proposed to explain far transfer from mental rotation and spatial scaling skills respectively. For most outcomes, except for geometry, there was no difference in the effectiveness of implicit (practice with feedback) compared to explicit instruction (instructional videos). From a theoretical perspective, the study identified a specific causal effect of spatial skills on mathematics skills in children. Practically, the results also highlight the potential of instructional videos as a method of introducing spatial thinking into the classroom.