The tunneling method for global optimization in multidimensional scaling

This paper focuses on the problem of local minima of the STRESS function. It turns out that unidimensional scaling is particularly prone to local minima, whereas full dimensional scaling with Euclidean distances has a local minimum that is global. For intermediate dimensionality with Euclidean distances it depends on the dissimilarities how severe the local minimum problem is. For city-block distances in any dimensionality many different local minima are found. A simulation experiment is presented that indicates under what conditions local minima can be expected. We introduce the tunneling method for global minimization, and adjust it for multidimensional scaling with general Minkowski distances. The tunneling method alternates a local search step, in which a local minimum is sought, with a tunneling step in which a different configuration is sought with the same STRESS as the previous local minimum. In this manner successively better local minima are obtained, and experimentation so far shows that the last one is often a global minimum.This paper is based on the 1994 Psychometric Society's outstanding thesis award of the first author. The authros would like to thank Robert Tijssen of the CWTS Leiden for kindly making available the co-citation data of the Psychometric literature. This paper is an extended version of the paper presented at the Annual Meeting of the Psychometric Society at Champaign-Urbana, Illin., June 1994.     

Loglinear Rasch models for the analysis of stability and change

Loglinear unidimensional and multidimensional Rasch models are considered for the analysis of repeated observations of polytomous indicators with ordered response categories. Reparameterizations and parameter restrictions are provided which facilitate specification of a variety of hypotheses about latent processes of change. Models of purely quantitative change in latent traits are proposed as well as models including structural change. A conditional likelihood ratio test is presented for the comparison of unidimensional and multiple scales Rasch models. In the context of longitudinal research, this renders possible the statistical test of homogeneity of change against subject-specific change in latent traits. Applications to two empirical data sets illustrate the use of the models.The author is greatly indebted to Ulf Böckenholt, Rolf Langeheine, and several anonymous reviewers for many helpful suggestions.     

Robust multidimensional scaling

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. To illustrate the efficacy of the procedure, some Monte Carlo simulation results are presented. The method is shown to perform well when outliers are present, even in relatively large numbers, and also to perform comparably to other approaches when no outliers are present.This research was supported by Grant A8351 from the Natural Sciences and Engineering Research Council of Canada to Ian Spence.     

Increasing item complexity: A possible cause of scale shrinkage for unidimensional item response theory

When the three-parameter logistic model is applied to tests covering a broad range of difficulty, there frequently is an increase in mean item discrimination and a decrease in variance of item difficulties and traits as the tests become more difficult. To examine the hypothesis that this unexpected scale shrinkage effect occurs because the items increase in complexity as they increase in difficulty, an approximate relationship is derived between the unidimensional model used in data analysis and a multidimensional model hypothesized to be generating the item responses. Scale shrinkage is successfully predicted for several sets of simulated data.The author is grateful to Robert Mislevy for kindly providing a copy of his computer program, RESOLVE.     

高中英语学习策略量表编制与Rasch多维度分析

当前,语言学习策略已成为我国中学英语教学的一项重要目标。该研究通过科学设计的问卷,调查了406名高三学生的英语学习策略掌握情况,并进一步分三个分维度、十个子维度,进行了深入的分析。研究表明,问卷提供的多维度的详细信息可以帮助详细了解学生对策略的掌握情况,从而进行有针对性的指导。同时,问卷的设计,维度划分等,也为研究人员,高中英语学习策略的教材编写和教学提供可靠有用的参考。     

Latent variable selection in multidimensional item response theory models using the expectation model selection algorithm

The aim of latent variable selection in multidimensional item response theory (MIRT) models is to identify latent traits probed by test items of a multidimensional test. In this paper the expectation model selection (EMS) algorithm proposed by Jiang et al. (2015) is applied to minimize the Bayesian information criterion (BIC) for latent variable selection in MIRT models with a known number of latent traits. Under mild assumptions, we prove the numerical convergence of the EMS algorithm for model selection by minimizing the BIC of observed data in the presence of missing data. For the identification of MIRT models, we assume that the variances of all latent traits are unity and each latent trait has an item that is only related to it. Under this identifiability assumption, the convergence of the EMS algorithm for latent variable selection in the multidimensional two-parameter logistic (M2PL) models can be verified. We give an efficient implementation of the EMS for the M2PL models. Simulation studies show that the EMS outperforms the EM-based L₁ regularization in terms of correctly selected latent variables and computation time. The EMS algorithm is applied to a real data set related to the Eysenck Personality Questionnaire.     

A multidimensional approach to measuring well-being in students: Application of the PERMA framework

Seligman recently introduced the PERMA model with five core elements of psychological well-being: positive emotions, engagement, relationships, meaning, and accomplishment. We empirically tested this multidimensional theory with 516 Australian male students (age 13–18). From an extensive well-being assessment, we selected a subset of items theoretically relevant to PERMA. Factor analyses recovered four of the five PERMA elements, and two ill-being factors (depression and anxiety). We then explored the nomological net surrounding each factor by examining cross-sectional associations with life satisfaction, hope, gratitude, school engagement, growth mindset, spirituality, physical vitality, physical activity, somatic symptoms, and stressful life events. Factors differentially related to these correlates, offering support for the multidimensional approach to measuring well-being. Directly assessing subjective well-being across multiple domains offers the potential for schools to more systematically understand and promote well-being.     

The moderating effects of gender on the associations between multidimensional hostility and psychosomatic symptoms: a Chinese case

The purpose of this study was to examine the effects of gender on the relationship between multidimensional hostility and psychosomatic symptoms in Chinese culture. The participants in this study were 398 Chinese college students (40% female) recruited from Taiwan. Four dimensions of multidimensional hostility-hostility cognition, hostility affect, expressive hostility behavior, and suppressive hostility behavior-were measured by the Chinese Hostility Inventory. After controlling for the effects of depression and anxiety, the results of path analysis revealed that the multidimensional hostility predicted psychosomatic symptoms directly, and predicted psychosomatic symptoms indirectly through negative health behavior. Furthermore, gender moderated the relationships between multidimensional hostility and health outcomes. Expressive hostility exacerbated psychosomatic symptom in females but buffered it in males, while affective hostility exacerbated psychosomatic symptoms in males. Additionally, suppressive hostility behavior was correlated to psychosomatic symptoms indirectly through negative health behavior in females. Moreover, expressive hostility was correlated to psychosomatic symptoms indirectly through negative health behavior more in males than in females.     

Multilevel multidimensional item response model with a multilevel latent covariate

In a pre‐test–post‐test cluster randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre‐test scores and other related covariates while estimating an intervention effect at post‐test. In many applications in education, the total post‐test and pre‐test scores, ignoring measurement error, are used as response variable and covariate, respectively, to estimate the intervention effect. However, these test scores are frequently subject to measurement error, and statistical inferences based on the model ignoring measurement error can yield a biased estimate of the intervention effect. When multiple domains exist in test data, it is sometimes more informative to detect the intervention effect for each domain than for the entire test. This paper presents applications of the multilevel multidimensional item response model with measurement error adjustments in a response variable and a covariate to estimate the intervention effect for each domain.     

Ethical Academic Judgments and Behaviors: Applying a Multidimensional Ethics Scale to Measure the Ethical Academic Behavior of Graduate Students

Using Reidenbach and Robin's Multidimensional Ethics Scale, this study investigated the relationships between background variables and students' ethical evaluations, judgments, and behavioral intentions using 3 scenarios involving dilemmas related to academic dishonesty. The sample included 436 master's students and 142 doctoral students. The study found that the participants used a combination of ethical philosophies to make ethical decisions. The respondents judged improper citations more harshly than acts of inappropriate authorship or the falsification of data. The doctoral students generally considered behaviors related to plagiarism and falsification to be more unethical than the master's students did, though no gender differences were found.