Multidimensional rule, unidimensional rule, and similarity strategies in categorization: event-related brain potential correlates

Forty participants assigned artificial creatures to categories after explicit rule instruction or feedback alone. Stimuli were typical and atypical exemplars of 2 categories with independent prototypes, conflicting exemplars sharing features of both categories, and "Others" with only 1 or 2 features of the well-defined categories. Ten feedback-only participants spontaneously adopted a unidimensional rule; 10 used a multidimensional similarity strategy. Event-related potentials (ERPs) recorded during the transfer phase showed a commonality between multidimensional rule and similarity strategies in late frontal brain activity that differentiated both from unidimensional rule use. Multidimensional rule users alone showed an earlier prefrontal ERP effect that may reflect inhibition of responses based on similarity. The authors also discuss the role of declarative memory for features and exemplars.     

A multidimensional scaling program for distinctiveness and similarity based on stimulus classification and information measurement

When observers classify a set of multidimensional items on the basis of similarity, they generate information measures that are isomorphic to item vectors whose lengths correspond to the judged distinctiveness of each item and whose angles define the position of each item in a euclidean similarity space. The PROSCALE computer program calculates the item vectors and spatial positions from similarity classification data and then generates and rotates orthogonal dimensions of the similarity space. PROSCALE can also use variables associated with each item to generate oblique dimensions that span the space. PROSCALE carries out multidimensional similarity scaling or unidimensional magnitude estimation scaling on as many as 70 items for as many as 50 observers.     

Improving measurement precision of test batteries using multidimensional item response models

A conventional way to analyze item responses in multiple tests is to apply unidimensional item response models separately, one test at a time. This unidimensional approach, which ignores the correlations between latent traits, yields imprecise measures when tests are short. To resolve this problem, one can use multidimensional item response models that use correlations between latent traits to improve measurement precision of individual latent traits. The improvements are demonstrated using 2 empirical examples. It appears that the multidimensional approach improves measurement precision substantially, especially when tests are short and the number of tests is large. To achieve the same measurement precision, the multidimensional approach needs less than half of the comparable items required for the unidimensional approach.     

Perceptions of control, competence, and contingency as influences on the stress-behavior symptom relation in school-age children

Analyzed data from 154 school-age children and their mothers to examine the relations between stress, perceived competence and contingency, and behavior symptoms. Analyses focused on the relative merits of unidimensional vs multidimensional measures of control in predicting symptoms. The stress of undesirable life events and behavior symptoms were related in the expected direction. Multiple regression models with R2 ranging from .11 to .14 (all ps less than .0002) included significant main effects for stress, competence, and control. Analyses supported the relative superiority of the multidimensional measure of control. Models containing main effects and interaction terms were of equivalent magnitudes in accounting for variance in symptom scores. Findings support the idea of perceived control as a moderator of the stress-illness relation and are consistent with earlier suggestions that simple main effects models may be the most useful in examining these relations.     

Tasks of a feather flock together: Similarity effects in task switching

Recent research on task switching has paid little attention to how tasks are represented and how the relations between task representations might affect the executive processes engaged to achieve a task switch. Two experiments investigated the effect of task similarity on task switching. Similarity was defined in terms of shared component operations--attentional control settings in Experiment 1 and response modality in Experiment 2--with tasks sharing more component operations said to be more similar to each other than tasks sharing fewer component operations. Across both experiments, task similarity facilitated task switching, seen in reduced switch costs for switching between similar tasks as opposed to dissimilar tasks. These results indicate that task similarity defined in terms of component operations can be used to define a multidimensional task space in which the executive processes of task selection and implementation are active.     

Empirically indistinguishable multidimensional IRT and locally dependent unidimensional item response models

Multidimensionality is a core concept in the measurement and analysis of psychological data. In personality assessment, for example, constructs are mostly theoretically defined as unidimensional, yet responses collected from the real world are almost always determined by multiple factors. Significant research efforts have concentrated on the use of simulated studies to evaluate the robustness of unidimensional item response models when applied to multidimensional data with a dominant dimension. In contrast, in the present paper, I report the result from a theoretical investigation that a multidimensional item response model is empirically indistinguishable from a locally dependent unidimensional model, of which the single dimension represents the actual construct of interest. A practical implication of this result is that multidimensional response data do not automatically require the use of multidimensional models. Circumstances under which the alternative approach of locally dependent unidimensional models may be useful are discussed.     

Similarity and multidimensional ratio estimation with simultaneous qualitative and quantitative variation

Abstract.— Previous work on content models of multidimensional similarity have mostly been concerned with the case of only qualitative variation. In this study a set of emotion words that varied both in content and intensity was used as stimuli. Subjects gave multidimensional ratio estimations, similarity estimations and also unidimensional ratings of intensity. Both individual data and group data were collected. Five different previously suggested content models of similarity failed to fit these data that showed large individual idiosyncratic variability. It is pointed out that previous work, where some of the models fitted rather well, was concerned with cases that were largely insensitive to deviations fram the models.     

分类数据测量等价性检验方法及其比较：项目阈值(难度)参数的组间差异性检验

测量工具满足等价性是进行多组比较的前提, 测量等价性的检验方法主要有基于CFA的多组比较法和基于IRT的DIF检验两类方法。文章比较了单维测验情境下基于CCFA的DIFFTEST检验方法和基于IRT模型的IRT-LR检验方法, 以及多维测验情境下DIFFTEST和基于MIRT的卡方检验方法的差异。通过模拟研究的方法, 比较了几种方法的检验力和第一类错误, 并考虑了样本总量、样本量的组间均衡性、测验长度、阈值差异大小以及维度间相关程度的影响。研究结果表明：(1)在单维测验下, IRT-LR是比DIFFTEST更为严格的检验方法; 多维测验下, 在测验较长、测验维度之间相关较高时, MIRT-MG比DIFFTEST更容易检验出项目阈值的差异, 而在测验长度较短、维度之间相关较小时, DIFFTEST的检验力反而略高于MIRT-MG方法。(2)随着阈值差值增加, DIFFTEST、IRT-LR和MIRT-MG三种方法的检验力均在增加, 当阈值差异达到中等或较大时, 三种方法都可以有效检验出测验阈值的不等价性。(3)随着样本总量增加, DIFFTEST、IRT-LR和MIRT-MG方法的检验力均在增加; 在总样本量不变, 两组样本均衡情况下三种方法的检验力均高于不均衡的情况。(4)违背等价性题目个数不变时, 测验越长DIFFTEST的检验力会下降, 而IRT-LR和MIRT-MG检验力则上升。(5) DIFFTEST方法的一类错误率平均值接近名义值0.05; 而IRT-LR和MIRT-MG方法的一类错误率平均值远低于0.05。     

Functionally Unidimensional Item Response Models for Multivariate Binary Data

The problem of fitting unidimensional item response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that have a strong dimension but also contain minor nuisance dimensions. Fitting a unidimensional model to such multidimensional data is believed to result in ability estimates that represent a combination of the major and minor dimensions. We conjecture that the underlying dimension for the fitted unidimensional model, which we call the functional dimension, represents a nonlinear projection. In this article we investigate 2 issues: (a) can a proposed nonlinear projection track the functional dimension well, and (b) what are the biases in the ability estimate and the associated standard error when estimating the functional dimension? To investigate the second issue, the nonlinear projection is used as an evaluative tool. An example regarding a construct of desire for physical competency is used to illustrate the functional unidimensional approach.     

Bifactor models and rotations: exploring the extent to which multidimensional data yield univocal scale scores

The application of psychological measures often results in item response data that arguably are consistent with both unidimensional (a single common factor) and multidimensional latent structures (typically caused by parcels of items that tap similar content domains). As such, structural ambiguity leads to seemingly endless "confirmatory" factor analytic studies in which the research question is whether scale scores can be interpreted as reflecting variation on a single trait. An alternative to the more commonly observed unidimensional, correlated traits, or second-order representations of a measure's latent structure is a bifactor model. Bifactor structures, however, are not well understood in the personality assessment community and thus rarely are applied. To address this, herein we (a) describe issues that arise in conceptualizing and modeling multidimensionality, (b) describe exploratory (including Schmid-Leiman [Schmid & Leiman, 1957] and target bifactor rotations) and confirmatory bifactor modeling, (c) differentiate between bifactor and second-order models, and (d) suggest contexts where bifactor analysis is particularly valuable (e.g., for evaluating the plausibility of subscales, determining the extent to which scores reflect a single variable even when the data are multidimensional, and evaluating the feasibility of applying a unidimensional item response theory (IRT) measurement model). We emphasize that the determination of dimensionality is a related but distinct question from either determining the extent to which scores reflect a single individual difference variable or determining the effect of multidimensionality on IRT item parameter estimates. Indeed, we suggest that in many contexts, multidimensional data can yield interpretable scale scores and be appropriately fitted to unidimensional IRT models.     

识字能力的单维性检验研究

本研究以义务教育阶段学生识字量测验为工具,综合运用探索性结构方程建模(ESEM)以及非参数项目反应理论中的摩根量表(Mokken量表)和DETECT分析方法,探讨了识字能力的维度。探索性结构方程建模结果显示,识字的单维性模型优于多维模型,多维的结果更多的体现出一个难度维度的特征,即字频的作用。Mokken量表分析结果显示,1~2年级和3~9年级测验更倾向于单维量表的特征。DETECT分析结果显示,两个测验的D值趋近于零,表明识字能力是单维能力。结合三种分析方法,识字能力具有单维性。     

Converging evidence that fear of success is multidimensional

Fear of Success (FOS) was originally conceived as a unidimensional motive. However, there is both theoretical and empirical support for the hypothesis that FOS is multidimensional. We factor analyzed the responses of 236 undergraduates to twenty-oneConcern Over the Negative Consequences of Success items and found four factors. Our four factors show considerable overlap with dimensions based on theoretical accounts of FOS etiology as well as with the factor structures obtained from two other factor analytic studies. Thus, there is converging evidence that FOS is multidimensional. The relationship between multidimensional FOS and a multidimensional approach to achievement motivation is discussed.     

Converging evidence that fear of success is multidimensional

Fear of Success (FOS) was originally conceived as a unidimensional motive. However, there is both theoretical and empirical support for the hypothesis that FOS is multidimensional. We factor analyzed the responses of 236 undergraduates to twenty-oneConcern Over the Negative Consequences of Success items and found four factors. Our four factors show considerable overlap with dimensions based on theoretical accounts of FOS etiology as well as with the factor structures obtained from two other factor analytic studies. Thus, there is converging evidence that FOS is multidimensional. The relationship between multidimensional FOS and a multidimensional approach to achievement motivation is discussed.     

Validity of test score interpretations for three self-concept measures based on differing theoretical models

Three theoretical models have been proposed to represent self-concept: (a) unidimensional; (b) multidimensional; (c) multidimensional hierarchical. Inventories have been developed under each of the three competing theoretical models; which model best represents self-concept is unclear. Typically, self-concept construct validation has utilized various approaches including correlational, multitrait-multimethod, and factor analytic methods. Another method, however, for assessing validity would be to determine the consequences of score interpretations using different measures specific to each of the theoretical models. This paper examined Messick's notion (1989) of the validity of test-score interpretations as applied to three of the most widely used measures derived under each of the three different theoretical models of self-concept. Results suggest that overall multidimensional measures are more consistent in classifying individual's self-concept than unidimensional measures.     

Multiple imputation for item scores when test data are factorially complex

Multiple imputation under a two‐way model with error is a simple and effective method that has been used to handle missing item scores in unidimensional test and questionnaire data. Extensions of this method to multidimensional data are proposed. A simulation study is used to investigate whether these extensions produce biased estimates of important statistics in multidimensional data, and to compare them with lower benchmark listwise deletion, two‐way with error and multivariate normal imputation. The new methods produce smaller bias in several psychometrically interesting statistics than the existing methods of two‐way with error and multivariate normal imputation. One of these new methods clearly is preferable for handling missing item scores in multidimensional test data.     

Anatomy of a stimulus domain: The relation between multidimensional and unidimensional scaling of noise bands

Theoretically, there are many possible relationships between multidimensional scaling and unidimensional scalings of the same stimulus domain. In particular, it is uncertain what will happen if the number of psychological “dimensions” exceeds the number of physical variables. The multidimensional scaling of noise bands, unidimensionally a relatively well-understood domain, was done to explore these problems. In correspondence with the number of physical variables, a two-dimensional configuration was found to give a satisfactory account of the judgments of magnitude of stimulus difference. Axes of loudness, volume, and density were found to fit the configuration with a high degree of precision, lending support to the metric value of numbers produced in magnitude estimation. Pitch, or frequency, also had a simple relationship to the configuration, but was not an axis or dimension. Therefore, the usual conceptualization of judgments of overall similarity as the result of combining difference on separate dimensions is questioned. It is suggested that multidimensional configurations may sometimes correspond to internal representations of general importance.     

Critical Issues in the Assessment of Child Sexual Abuse

This article explores the feasibility of using standardized psychometric methods in the initial stages of an investigation of child sexual abuse; methods that are less intrusive and therefore less damaging to children and their families. We review the complex conceptual and research issues that arise from attempts to assess the many-sided aspects of child sexual maltreatment. Among those considered in both the clinical and research spheres are problems of definition and diagnosis; limitations of clinical interviews, and a variety of direct and indirect psychological instruments used for investigating sexual maltreatment and risk assessment; the inadequacies of experimental designs; and also the political, practical, and ethical restraints that hinder research in this area. It is argued that there is insufficient evidence based on controlled studies or standardized normative tests to advocate any simple, unidimensional methodology for the screening task. However, recommendations are put forward for the cautious, conjoint use of several procedures in a multidimensional approach to assessing child sexual abuse. Suggestions are also made for future research and development.     

An examination of the multidimensionality of supervisor and subordinate perceptions of leader‐member exchange

Research on leader‐member exchange (LMX) theory typically has measured LMX in a unidimensional manner and has neglected supervisor perceptions of the LMX relationship. The present study developed and validated a multidimensional scale of supervisor LMX based on Liden and Maslyn's (1998) multidimensional subordinate LMX scale. Confirmatory factor analyses supported a multidimensional factor structure for both supervisor and subordinate LMX scales with four distinct dimensions: affect, loyalty, contribution, and professional respect. Results further indicated that these dimensions differentially predicted various criteria indicating that different aspects of the LMX relationship are of greater or lesser importance depending upon the criterion of interest. Additionally, results indicated that multidimensional LMX scales measured from both supervisor and subordinate perspectives predict important individual job attitudes and behaviours above scales that are either unidimensional or measured from just one perspective.     

Choice and response time processes in the identification and categorization of unidimensional stimuli

Lacouture and Marley (1991, 1995, 2001) have successfully modeled the probabilities of correct responses and the mean correct response times (RTs) in unidimensional absolute identification tasks for various stimulus ranges and stimulus/response set sizes, for individual and group data. These fits include those to a set of phenomena often referred to as end-anchor effects. A revised model, with the independent accumulator decision process replaced by a leaky competing accumulator decision process, fits the probabilities of correct responses and the full distributions of RTs in unidimensional absolute identification. The revised model is also applied successfully to a particular class of unidimensional categorization tasks. We discuss possible extensions for handling sequential effects in unidimensional absolute identification, and other extensions of the given class of categorization tasks that are of potential empirical and theoretical importance as a supplement to the study of multidimensional absolute identification tasks.     

Human Rights Attitudes: Dimensionality and Psychological Correlates

This study assesses the dimensionality and correlates of individuals' attitudes toward human rights. In previous research, the Attitudes Toward Human Rights Inventory (ATHRI) was assumed to measure a unidimensional phenomenon and, as such, was used as an omnibus measure of human rights attitudes. In this study, factor analysis revealed the presence of 3 factors accounting for the variance in the measure, Personal Liberties, Civilian Constraint, and Social Security. This finding provided partial replication of results obtained by Diaz-Veizades, Widaman, Little, and Gibbs (1995) with their Human Rights Questionnaire and supports the contention that human rights attitudes should be considered multidimensional in nature. Correlation and regression analyses suggested that attitudes toward personal liberties are associated with political identification, whereas attitudes toward civilian constraint are related to moral judgment development and need for cognitive closure. Implications for ethics research and education are discussed.