The essential process in a family of measurement models

Five members of the Rasch family of latent trait models which have appeared more or less independently in the literature are brought together and identified as one model. In addition to sharing the distinguishing characteristic of the dichotomous Rasch model—separable person and item parameters and hence sufficient statistics—all five models share a common algebraic form and have as their basic element the fundamental process defined by Rasch's simple logistic expression. In these models, the sufficient statistics for person and item parameters are counts of events constructed to be indicative of the variable being measured, and the measures they enable are ‘fundamental’.     

基于一般线性模型框架的心理统计教学

心理统计学教学中,不同的统计方法常常是独立教学,致使学生不易理解各种方法之间的关系。事实上,t检验、方差分析和多元线性回归等方法都可以统一到一般线性模型的框架下,而结构方程是对这个框架的最一般化的描述,且结构方程路径图是呈现这个框架的形象工具。因此,本文尝试用路径图的方式来呈现心理学研究中最常用的统计方法,并将结构方程分析结果与传统分析结果进行对照,帮助学生建立一般线性模型上位概念,将以往孤立的统计方法联系起来。     

Automatically deriving readers’ knowledge structures from texts

Latent semantic analysis (LSA) serves as both a theory and a method for representing the meaning of words based on a statistical analysis of their contextual usage (Foltz, 1996; Landauer & Dumais, 1997). In experiments in the domains of psychology and history, we compared the representation of readers’ knowledge structures of information learned from texts with the representation generated by LSA. Results indicated that LSA’s representation is similar to readers’ representations. In addition, the degree to which the reader’s representation is similar to LSA’s representation is indicative of the amount of knowledge the reader has acquired and of the reader’s reading ability. This approach has implications both as a model of learning from text and as a practical tool for performing knowledge assessment.     

Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model

Rasch models are characterised by sufficient statistics for all parameters. In the Rasch unidimensional model for two ordered categories, the parameterisation of the person and item is symmetrical and it is readily established that the total scores of a person and item are sufficient statistics for their respective parameters. In contrast, in the unidimensional polytomous Rasch model for more than two ordered categories, the parameterisation is not symmetrical. Specifically, each item has a vector of item parameters, one for each category, and each person only one person parameter. In addition, different items can have different numbers of categories and, therefore, different numbers of parameters. The sufficient statistic for the parameters of an item is itself a vector. In estimating the person parameters in presently available software, these sufficient statistics are not used to condition out the item parameters. This paper derives a conditional, pairwise, pseudo-likelihood and constructs estimates of the parameters of any number of persons which are independent of all item parameters and of the maximum scores of all items. It also shows that these estimates are consistent. Although Rasch’s original work began with equating tests using test scores, and not with items of a test, the polytomous Rasch model has not been applied in this way. Operationally, this is because the current approaches, in which item parameters are estimated first, cannot handle test data where there may be many scores with zero frequencies. A small simulation study shows that, when using the estimation equations derived in this paper, such a property of the data is no impediment to the application of the model at the level of tests. This opens up the possibility of using the polytomous Rasch model directly in equating test scores.     

The Implication of Popper’s Anti-inductive Theory for the Development of Indigenous Psychologies

Echoing Kumar’s advocacy that psychologists should not ignore Popper, this article received the methodological strategies for attaining the epistemological goal of universal psychology or global psychology as suggested by previous indigenous psychologists and argued that it is impossible for them to attain this goal by the inductive method. The significant implications of Popper’s anti-inductive theory for solving this dilemma are emphasized for future progress of indigenous psychologies.     

The many-facet Rasch model in the analysis of the go/no-go association task

This article provides a many-facet Rasch measurement (MFRM) analysis of go/no-go association task (GNAT)-based measures of implicit attitudes toward sweet and salty food. We describe the statistical model and the strategy we adopted to score the GNAT, and we emphasize that, when analyzing implicit measures, MFRM indexes have to be interpreted in a peculiar way. In comparison with traditional scoring algorithms, an MFRM analysis of implicit measures provides some additional information and suffers from fewer limitations and assumptions. MFRM might help to overcome some limitations of current implicit measures, since it directly addresses some known issues and potential confounds, such as those related to a rational zero point, to the arbitrariness of the metric, and to participants’ task-set switching ability.     

MATLAB and graphical user interfaces: Tools for experimental management

MATLAB is a convenient platform for the development and management of psychological experiments because of its easy-to-use programming language, sophisticated graphics features, and statistics and optimization tools. Through implementation of the Brainard-Pelli Psychophysics Toolbox, the MATLAB user gains close temporal and spatial control over the CRT, while retaining the simplicity of an interpreted language conducive to rapid program development. MATLAB’s abilities can be further utilized through easily programmable graphical user interfaces (GUIs). We illustrate how a GUI can serve as a powerful and intuitive tool for organizing and controlling all aspects of a psychological experiment, including design, data collection, data analysis, and theory fitting.     

On the Bayesian Nonparametric Generalization of IRT-Type Models

We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities’ distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general distribution generating the abilities, even for a finite number of probes. For the semiparametric Rasch model, only a finite number of properties of the general abilities’ distribution can be identified by a finite number of items, which are completely characterized. The full identification of the semiparametric Rasch model can be only achieved when an infinite number of items is available. The results are illustrated using simulated data.     

协单参数单维度Rasch模型的优势与意义

相比多参数多维度IRT模型通过增加参数的方式来提升模型拟合度和解释度，Rasch模型流派强调“理论驱动研究”和“数据符合模型”，推崇单参数单维度的测量模型能最大限度地减少额外因素对真实测量目的的影响和干扰，从而保证测量的客观性和准确性。Rasch模型关注测量目标与测量工具的对应关系，它的“简单”特性有助于研究者更准确地评估和解释被测目标与测量工具间的适配性，且在将非线性数据转化为等距数据时具有天然的优势。     

Statelessness and the Politics of Misrecognition

This article focuses on the account of disrespect found in Honneth’s theory of recognition. In it, I am particularly interested in the form of misrecognition or disrespect which is the negation of respect, and which is clearly represented by statelessness. Respect, for Honneth, is closely connected to legal recognition. Guided by Honneth’s view of critical theory as ‘not entirely without a foundation in social reality’, the article puts together an analysis of the political dynamics of his model of disrespect. This analysis is used to challenge certain aspects of Honneth’s political theory and in particular the implications of his conception of the state. The article argues that the way in which the state is used has the effect of obscuring significant political obstacles to recognition, and in particular, the way in which the state limits respect.     

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.     

Mark Graves <Emphasis Type="Italic">Mind,Brain and the Elusive Soul: Human Systems of Cognitive Science and Religion</Emphasis>

This article explores the use of Graves’ theory of the soul as an interdisciplinary tool to facilitate a holistic approach to healing. Graves’ discussion is applied to the use of therapeutic interventions to facilitate the emergent processes of healing and spiritual growth in traumatized persons.     

Monte Carlo tests of the Rasch model based on scalability coefficients

For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non‐parametric item response theory a natural starting‐point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using p‐values computed using Markov chain Monte Carlo methods. The power of the tests of unequal item discrimination, and their ability to distinguish between local dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.     

混合IRT潜在模型及其应用轨迹

项目反应理论是测量被试潜在特质的现代测量理论, 潜在类别分析是基于模型的潜在特质分类技术。混合项目反应理论将项目反应理论与潜在类别分析相结合, 能够同时对被试分类并量化其潜在特质。在阐述混合项目反应理论概念、原理的基础上, 介绍了MRM、mNRM和mPCM等几种常见混合模型及其参数估计方法, 并从心理与行为特征分类、项目功能差异检测、测验效度评价等方面评述了其在心理测验中的应用发展轨迹。     

On Keats' generalization of the rasch model

Parameter estimation for Keats generalization of the Rasch model that takes account of guessing behavior is investigated. It is shown that no minimal sufficient statistics for the ability parameters independent of the difficulty parameters exist. Thus Andersen's conditional inference technique for consistent estimation is not applicable to Keats' model. The notion of separability of the parameters is generalized.     

The statistical recommendations of the American Psychological Association Publication Manual: Effect sizes,confidence intervals,and meta‐analysis

Estimation based on effect sizes, confidence intervals, and meta‐analysis usually provides a more informative analysis of empirical results than does statistical significance testing, which has long been the conventional choice in psychology. The sixth edition of the American Psychological Association Publication Manual now recommends that psychologists should, wherever possible, use estimation and base their interpretation of research results on point and interval estimates. We outline the Manual's recommendations and suggest how they can be put into practice: adopt an estimation framework, starting with the formulation of research aims as ‘How much?’ or ‘To what extent?’ questions. Calculate from your data effect size estimates and confidence intervals to answer those questions, then interpret. Wherever appropriate, use meta‐analysis to integrate evidence over studies. The Manual's recommendations can assist psychologists improve they way they do their statistics and help build a more quantitative and cumulative discipline.     

Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory. Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.     

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Correlated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models, respectively, under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on ‘trust in the police’ selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan.     

Diagnosing item score patterns on a test using item response theory-based person-fit statistics

Person-fit statistics have been proposed to investigate the fit of an item score pattern to an item response theory (IRT) model. The author investigated how these statistics can be used to detect different types of misfit. Intelligence test data were analyzed using person-fit statistics in the context of the G. Rasch (1960) model and R. J. Mokken's (1971, 1997) IRT models. The effect of the choice of an IRT model to detect misfitting item score patterns and the usefulness of person-fit statisticsfor diagnosis of misfit are discussed. Results showed that different types of person-fit statistics can be used to detect different kinds of person misfit. Parametric person-fit statistics had more power than nonparametric person-fit statistics.