Residualanalysis in the polytomous rasch model

Residuals for check of model fit in the polytomous Rasch model are examined. Comparisons are made between using counts for all response pattern and using item totals for score groups for the construction of the residuals. Comparisons are also, for the residuals based on score group totals, made between using as basis the item totals, or using the estimated item parameters. The developed methods are illustrated by two examples, one from a psychiatric rating scale, one from a Danish Welfare Study.     

Testing unidimensionality in polytomous Rasch models

A fundamental assumption of most IRT models is that items measure the same unidimensional latent construct. For the polytomous Rasch model two ways of testing this assumption against specific multidimensional alternatives are discussed. One, a marginal approach assuming a multidimensional parametric latent variable distribution, and, two, a conditional approach with no distributional assumptions about the latent variable. The second approach generalizes the Martin-Löf test for the dichotomous Rasch model in two ways: to polytomous items and to a test against an alternative that may have more than two dimensions. A study on occupational health is used to motivate and illustrate the methods.The authors would like to thank Niels Keiding, Klaus Larsen and the anonymous reviewers for valuable comments to a previous version of this paper. This research was supported by a grant from the Danish Research Academy and by a general research grant from Quality Metric, Inc.     

Logistic加权模型的理论构建与模拟分析

试题难度、试题考查重要性程度加权是多级记分试题的两个基本属性, 因而在IRT项目特征函数中需用不同参数来表示。以往多级记分模型用多个难度参数来描述多级记分试题的难度, 不能有效的表达多级记分试题的分数权重作用。从多级记分试题的分数加权作用角度, 本文提出Logistic加权模型并论述了理论构建思想。在Logistic加权模型下对项目参数估计的EM算法进行推导并编写了相应的参数估计程序。在Logistic加权模型下进行测验模拟, 发现项目参数估计的模拟返真性能良好。     

多级计分测验中基于残差统计量的被试拟合研究

本文提出一种多级计分项目下的个人拟合统计量R, 考察它在检测6种常见的异常作答模式(作弊、猜测、随机、粗心、创新作答、混合异常)下的表现, 并与标准化对数似然统计量l_zp进行比较。结果表明：(1) 在异常作答覆盖率较低并且异常作答类型为作弊和猜测时, R的检测率显著高于l_zp; (2) 随着测验长度和被试异常程度的增加, 两种统计量的检测率都会上升; (3) 在一些条件下, R与l_zp检测效果接近。实证数据分析进一步展示了R统计量的使用方法和过程, 结果也表明R统计量具有较好的应用前景。     

A sequential cognitive diagnosis model for polytomous responses

This paper proposes a general polytomous cognitive diagnosis model for a special type of graded responses, where item categories are attained in a sequential manner, and associated with some attributes explicitly. To relate categories to attributes, a category‐level Q‐matrix is used. When the attribute and category association is specified a priori, the proposed model has the flexibility to allow different cognitive processes (e.g., conjunctive, disjunctive) to be modelled at different categories within a single item. This model can be extended for items where categories cannot be explicitly linked to attributes, and for items with unordered categories. The feasibility of the proposed model is examined using simulated data. The proposed model is illustrated using the data from the Trends in International Mathematics and Science Study 2007 assessment.     

Ideal Point Discriminant Analysis Revisited with a Special Emphasis on Visualization

Ideal point discriminant analysis is a classification tool which uses highly intuitive multidimensional scaling procedures. However, in the last paper, Takane wrote about it. He concludes that the interpretation is rather intricate and calls that a weakness of the model. We summarize the conditions that provide an easy interpretation and show that in maximum dimensionality they can be obtained without any loss. For reduced dimensionality, it is conjectured that loss is minor which is examined using several data sets. This research was conducted while the author was sponsored by the Netherlands Organisation for Scientific Research (NWO), Innovational Grant, no. 452-06-002.     

Ordinal state-trait regression for intensive longitudinal data

In many psychological studies, in particular those conducted by experience sampling, mental states are measured repeatedly for each participant. Such a design allows for regression models that separate between- from within-person, or trait-like from state-like, components of association between two variables. But these models are typically designed for continuous variables, whereas mental state variables are most often measured on an ordinal scale. In this paper we develop a model for disaggregating between- from within-person effects of one ordinal variable on another. As in standard ordinal regression, our model posits a continuous latent response whose value determines the observed response. We allow the latent response to depend nonlinearly on the trait and state variables, but impose a novel penalty that shrinks the fit towards a linear model on the latent scale. A simulation study shows that this penalization approach is effective at finding a middle ground between an overly restrictive linear model and an overfitted nonlinear model. The proposed method is illustrated with an application to data from the experience sampling study of Baumeister et al. (2020, Personality and Social Psychology Bulletin, 46, 1631).     

Spatial-temporal analysis of pedestrian injury severity with geographically and temporally weighted regression model in Hong Kong

This study intended to (1) investigate the pedestrian injury severity involved in traffic crashes; and (2) address the spatial and temporal heterogeneity simultaneously. To achieve the objectives, geographically and temporally weighted regression (GTWR) model was proposed to deal with both spatial and temporal heterogeneity simultaneously. The pedestrian crash data of Hong Kong metropolitan area from 2008 to 2012 were collected, involving 1652 pedestrian-related injury samples. By comparing GTWR model and standard geographically weighted regression (GWR) model and temporally weighted regression (TWR) model, the proposed GTWR model showed potential benefits in modeling both spatial and temporal non-stationarity simultaneously in terms of goodness-of-fit and F statistics. Results revealed that number of vehicles, number of pedestrian-related casualties, speed limit, vehicle movement and injury location have significant influence on pedestrian injury severity in different areas. The conclusions are reached that GRWR model can address the relationship between pedestrian injury severities and influencing factors, as well as accommodating spatial and temporal heterogeneity simultaneously. The findings provide useful insights for practitioners and policy makers to improve pedestrian safety.     

The Creativity Matrix: Spotlights and Blind Spots in Our Understanding of the Phenomenon

In this paper, we organize past and present theories and models of creativity by using a new conceptual framework—the creativity matrix—with the aim of highlighting the dimensions of creativity we know a lot about and those we tend to either ignore or find difficult to study. This matrix is formed by bringing together a developmental model of creativity (the 4 C's) and a structural one (the 5 A's). We start by briefly describing these two conceptual frameworks, and then, we proceed to exploring the matrix itself by describing how the 5 A's are dynamically organized at each “level” of the 4 C's. Importantly, our overview of the matrix is informed by existing models and concepts that address one of more of the C's and the A's. This gives us a unique opportunity to take stock of what has been studied so far and, toward the end, consider new avenues for the development of theory and research agendas within creativity studies.     

Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.     

Bayesian estimation in the two-parameter logistic model

A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. Through simulation studies it is shown that Bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are (a) more meaningful since they do not drift out of range, and (b) more accurate in that they result in smaller mean squared differences between estimates and true values.The research reported here was performed pursuant to Grant No. N0014-79-C-0039 with the Office of Naval Research.     

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.     

Robust regression: Testing global hypotheses about the slopes when there is multicollinearity or heteroscedasticity

A well-known concern regarding the usual linear regression model is multicollinearity. As the strength of the association among the independent variables increases, the squared standard error of regression estimators tends to increase, which can seriously impact power. This paper examines heteroscedastic methods for dealing with this issue when testing the hypothesis that all of the slope parameters are equal to zero via a robust ridge estimator that guards against outliers among the dependent variable. Included are results related to leverage points, meaning outliers among the independent variables. In various situations, the proposed method increases power substantially.     

心理距离对判断预测中的趋势阻尼的影响

三个实验考察了不同心理距离（空间、社会、时间）和序列特征（趋势和发展速度）对判断预测中的趋势阻尼的影响。结果发现,当个体对人工时间序列做出预测时,会出现趋势阻尼;下降序列的阻尼大于上升序列,序列发展速度越快阻尼越大;不同心理距离对趋势阻尼的影响不一致,空间距离对趋势阻尼的影响不显著,为他人预测时的阻尼小于为自己预测,时间距离远时的阻尼大于时间距离近。     

Properties of the maximum likelihood solution in factor analysis regression

Algebraic properties of the normal theory maximum likelihood solution in factor analysis regression are investigated. Two commonly employed measures of the within sample predictive accuracy of the factor analysis regression function are considered: the variance of the regression residuals and the squared correlation coefficient between the criterion variable and the regression function. It is shown that this within sample residual variance and within sample squared correlation may be obtained directly from the factor loading and unique variance estimates, without use of the original observations or the sample covariance matrix.     

Reciprocal Markov Modeling of Feedback Mechanisms Between Emotion and Dietary Choice Using Experience-Sampling Data

With intensively collected longitudinal data, recent advances in the experience-sampling method (ESM) benefit social science empirical research, but also pose important methodological challenges. As traditional statistical models are not generally well equipped to analyze a system of variables that contain feedback loops, this paper proposes the utility of an extended hidden Markov model to model reciprocal the relationship between momentary emotion and eating behavior. This paper revisited an ESM data set (Lu, Huet, &; Dube, 2011 Lu, J., Huet, C., &; Dubé, L. (2011). Emotional reinforcement as a protective factor for healthy eating in home settings. The American Journal of Clinical Nutrition, 94(1), 254–261. http://dx.doi.org/10.3945/ajcn.110.006361[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) that observed 160 participants' food consumption and momentary emotions 6 times per day in 10 days. Focusing on the analyses on feedback loop between mood and meal-healthiness decision, the proposed reciprocal Markov model (RMM) can accommodate both hidden (“general” emotional states: positive vs. negative state) and observed states (meal: healthier, same or less healthy than usual) without presuming independence between observations and smooth trajectories of mood or behavior changes. The results of RMM analyses illustrated the reciprocal chains of meal consumption and mood as well as the effect of contextual factors that moderate the interrelationship between eating and emotion. A simulation experiment that generated data consistent with the empirical study further demonstrated that the procedure is promising in terms of recovering the parameters.     

Adult reflection in a graduate-level online distance education course

This study examined adult learners’ ability to engage in critical reflection concerning their own learning in a graduate-level online instructional technology course. The online course was facilitated through asynchronous discussions, and the course topic was about the design and delivery of distance education. The data for this study consisted of four critical reflection papers about students’ perception of their learning. The Periodic Reflection Tool, based on activity systems analysis, was introduced to participants as a guide for engaging in in-depth reflection about their learning process and completing their course assignment. After course completion and during data analysis, we applied instrumental learning and communicative learning theories to evaluate how participants used the tool to reflect on their personal learning in the course. At the conclusion of an analysis of their reflection statements, it was found that purposeful reflections guided by the Periodic Reflection Tool could help guide adult learners to reflect on many aspects of their learning and we suggest that the tool could be used to examine adults’ transition from traditional to online settings.     

互动公平对员工幸福感的影响:心理授权的中介作用与权力距离的调节作用

近些年,由于积极心理学的兴起,员工幸福感的研究得到了广泛的关注。本论文从互动公平这一特定的组织公平概念出发,以公平理论为主体,并结合自我决定理论,从心理授权的视角既分析了互动公平影响员工幸福感的内在机制,又探讨了权力距离对整个影响机制的调节作用。通过对国内一家制造业企业的199名员工多时点匹配问卷的调查,结果表明:互动公平与员工幸福感之间呈现正相关关系;心理授权中介了互动公平对员工幸福感的影响作用;权力距离不仅负向调节了互动公平与心理授权之间的关系,而且还负向调节了互动公平—心理授权—员工幸福感这一中介机制。本研究的发现有利于充分了解互动公平影响员工幸福感的内在机制和边界条件,同时能为管理实践提供更好的指导,有效地提高员工幸福感。     

The 30¢ Deal of a Lifetime: Using Luther's Small Catechism with Teenagers to Engage Consumerist Culture

Abstract : This article explores the interaction of teenagers in the current consumerist culture, and how Martin Luther's Small Catechism offers multiple entry points to begin conversation around the illusions of consumerism. It examines motives behind consumption and what the church has to say in response to the consumerist “catechism.” Suggestions pertaining to the Ten Commandments, Apostles’ Creed, and Lord's Prayer are provided for pastors and teachers of catechetical students.