Testing the assumptions and interpreting the results of the Rasch model using log-linear procedures in SPSS

This paper shows how to use the log-linear subroutine of SPSS to fit the Rasch model. It also shows how to fit less restrictive models obtained by relaxing specific assumptions of the Rasch model. Conditional maximum likelihood estimation was achieved by including dummy variables for the total scores as covariates in the models. This approach greatly simplifies the specification of the Rasch models. We illustrate these procedures in an analysis of four items selected from the Reiss Premarital Sexual Permissiveness Scale. We found that a modified version of the Rasch model with item dependencies fits the data significantly better than the simple Rasch model. We also found that the item difficulties are the same for men and women, but that the item dependencies are significantly greater for men. Apart from any substantive issues these results raise, the value of this exercise lies in its demonstration of how researchers can use the procedures of popular, accessible software packages to study an increasingly important set of measurement models.     

WORK SAMPLE TESTS IN PERSONNEL SELECTION: A META‐ANALYSIS OF BLACK–WHITE DIFFERENCES IN OVERALL AND EXERCISE SCORES

Work sample exams are generally thought to have either low or comparatively low levels of ethnic group differences when used for personnel selection. Such exams are sometimes called “simulation exercises” and involve having applicants perform a set of tasks that are similar to those performed on the job. The nearly ubiquitous meta‐analytic value of Black–White subgroup differences in the literature is d= .38. Unfortunately, this estimate is plagued by a variety of problems (e.g., range restriction, inclusion of nonwork sample tests). Further, there are virtually no analyses that examine how the saturation of different constructs influence work sample tests. We gathered available data for Black–White ethnic group differences and found that overall work sample differences were markedly larger for samples of job applicants (d= .73) than previously thought. We also examined how different exercises and saturation of different constructs influenced work sample ds. For example, work sample test ratings of cognitive and job knowledge skills were associated with a mean observed d= .80, whereas ratings of various social skills were associated with mean observed ds that varied from .21 to .27. We urge scientists and practitioners to consider both the method and the constructs that are targeted when forecasting predictor ds.     

The role of processes and contents in human memory: An item response theory approach

This study investigated the specificities and communalities of visuospatial and verbal memory contents, as well as short-term memory and working memory (STM and WM) processes with the use of Rasch models as an alternative to the previous studies based on the classical test theory. A sample of 547 undergraduate students executed four computerised tasks, each consisting of verbal-numeric WM, visuospatial WM, verbal-numeric STM, and visuospatial STM content. Confirmatory factor analyses indicated that visuospatial and verbal-numeric memory are distinct, but correlated variables. Findings also support a domain-general view of WM capacity distinct from domain-specific storage. With the use of Rasch models, our results confirm previous experimental, psychometric, and neuropsychological studies, highlighting that memory span tasks can be divided into separate subsystems for content and processes. This study also shows that better results are obtained when models with person parameter estimates (provided from Rasch models) are adopted, rather than summed raw scores.     

Response style analysis with threshold and multi‐process IRT models: A review and tutorial

Two different item response theory model frameworks have been proposed for the assessment and control of response styles in rating data. According to one framework, response styles can be assessed by analysing threshold parameters in Rasch models for ordinal data and in mixture‐distribution extensions of such models. A different framework is provided by multi‐process item response tree models, which can be used to disentangle response processes that are related to the substantive traits and response tendencies elicited by the response scale. In this tutorial, the two approaches are reviewed, illustrated with an empirical data set of the two‐dimensional ‘Personal Need for Structure’ construct, and compared in terms of multiple criteria. Mplus is used as a software framework for (mixed) polytomous Rasch models and item response tree models as well as for demonstrating how parsimonious model variants can be specified to test assumptions on the structure of response styles and attitude strength. Although both frameworks are shown to account for response styles, they differ on the quantitative criteria of model selection, practical aspects of model estimation, and conceptual issues of representing response styles as continuous and multidimensional sources of individual differences in psychological assessment.     

Testing the Rasch model by means of the mixture fit index

Rudas, Clogg, and Lindsay (RCL) proposed a new index of fit for contingency table analysis. Using the overparametrized two‐component mixture, where the first component with weight 1?w represents the model to be tested and the second component with weight w is unstructured, the mixture index of fit was defined to be the smallest w compatible with the saturated two‐component mixture. This index of fit, which is insensitive to sample size, is applied to the problem of assessing the fit of the Rasch model. In this application, use is made of the equivalence of the semi‐parametric version of the Rasch model to specifically restricted latent class models. Therefore, the Rasch model can be represented by the structured component of the RCL mixture, with this component itself consisting of two or more subcomponents corresponding to the classes, and the unstructured component capturing the discrepancies between the data and the model. An empirical example demonstrates the application of this approach. Based on four‐item data, the one‐ and two‐class unrestricted latent class models and the one‐ to three‐class models restricted according to the Rasch model are considered, with respect to both their chi‐squared statistics and their mixture fit indices.     

Loglinear representations of multivariate Bernoulli Rasch models

In this paper, the extended Rasch model for dichotomously scored items is derived from the general multivariate Bernoulli distribution. The necessary and sufficient conditions for the multivariate Bernoulli distribution to be equal to the extended Rasch model provide a new loglinear representation of the extended Rasch model. Conditions are also given under which the extended Rasch model is equal to the random effects Rasch model, and it is shown under what conditions the extended Rasch model is equal to a random effects Rasch model in which the underlying variable has a normal distribution. In addition, alternative models for the construction of likelihood ratio tests are proposed. One of these alternative models is Haberman's extended interaction model. Furthermore, it is shown how both the SPSS and SAS programs can be used to estimate and test loglinear representations of extended Rasch models.     

Investigating population heterogeneity with factor mixture models

Sources of population heterogeneity may or may not be observed. If the sources of heterogeneity are observed (e.g., gender), the sample can be split into groups and the data analyzed with methods for multiple groups. If the sources of population heterogeneity are unobserved, the data can be analyzed with latent class models. Factor mixture models are a combination of latent class and common factor models and can be used to explore unobserved population heterogeneity. Observed sources of heterogeneity can be included as covariates. The different ways to incorporate covariates correspond to different conceptual interpretations. These are discussed in detail. Characteristics of factor mixture modeling are described in comparison to other methods designed for data stemming from heterogeneous populations. A step-by-step analysis of a subset of data from the Longitudinal Survey of American Youth illustrates how factor mixture models can be applied in an exploratory fashion to data collected at a single time point.     

Identifying Misfitting Achievement Estimates in Performance Assessments: An Illustration Using Rasch and Mokken Scale Analyses

Researchers apply individual person fit analyses as a procedure for checking model-data fit for individual test-takers. When a test-taker misfits, it means that the inferences from their test score regarding what they know and can do may not be accurate. One problem in applying individual person fit procedures in practice is the question of how much misfit it takes to make the test score an untrustworthy estimate of achievement. In this paper, we argue that if a person’s responses generally follow a monotonic pattern, the resulting test score is “good enough” to be interpreted and used. We present an approach that applies statistical procedures from the Rasch and Mokken measurement perspectives to examine individual person fit based on this good enough criterion in real data from a performance assessment. We discuss how these perspectives may facilitate thinking about applying individual person fit procedures in practice.     

多维Rasch模型在维度分数报告中的应用—对带宽-保真度困境的解决

分别采用四维度和十五维度Rasch模型分析包含项目内多维度结构的科学测验数据,估计两种维度结构下维度分数的信度.结果表明,对比相应的单维模型而言,四维度与十五维度Rasch模型均能够极大提高各内容维度上分数估计的信度.四维度与十五维度Rasch模型拟合结果的比较表明,对于总长度固定的测验,维度数目的增加能够补偿子维度长度减少引起的信度损失.但是这一作用必须以维度间较高的相关性为前提.     

Neglected questions in job design: How people design jobs,task-job predictability,and influence of training

Three questions important to job design interventions but neglected in research were explored. First, how do people design jobs? Internal processes (e.g., growth needs) from psychological (or job enrichment) models of job design were not apparent. Instead, groupings of tasks into jobs suggested simple cognitive categorization based on task similarity, reflecting an engineering (or work simplification) orientation. Second, can job design be predicted from task design? Separate measures for job and task designs were unrelated, indicating that the whole is not predictable from the parts in job design, Third, can job design principles be trained? Subjects easily learned and applied different job design approaches.     

Why are unemployed aged fifty and over less likely to find a job? A decomposition analysis

Reemployment chances for unemployed aged fifty and over are low compared to those of younger persons. To explain the different chances, the job search literature has largely focused on the job search behavior of unemployed individuals. Based on job search models, we propose that not only job search behavior, but also wage setting behavior, attitudinal variables and personal variables impact the difference in reemployment opportunities. Besides gaining insight into which variables explain the difference in reemployment opportunities, we also test how much of the difference each of these variables explains. We do this by drawing on a decomposition analysis. Using data from 647 recently unemployed, we find that about one third of the reemployment gap can be explained by the variables suggested by job search models, mostly in terms of age differences in search behavior, educational levels and reservation wage. Hence, about 70 % can be ascribed to other factors, such as employer preferences for those aged between 18 and 49. Implications of these results for theory, policy and practice are discussed.     

A person-fit index for polytomous rasch models,latent class models,and their mixture generalizations

A normally distributed person-fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution IRT models for dichotomous and polytomous data.This article extends previous work on the null distribution of person-fit indices for the dichotomous Rasch model to a number of models for categorical data. A comparison of two different approaches to handle the skewness of the person-fit index distribution is included.Major parts of this paper were written while the first author worked at the Institute for Science Education, Kiel, Germany. Any opinions expressed in this paper are those of the authors and not necessarily of Educational Testing Service. The results presented in this paper were improved by valuable comments from J. Rost, K. Yamamoto, N.D. Verhelst, E. Bedrick and two anonymous reviewers.     

Regularized Finite Mixture Models for Probability Trajectories

Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse. This work was supported in part by NIAAA grants R37 AA07065 and R01 AA12217 to RAZ.     

Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer-adaptive practice

We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person-by-item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer-adaptive practice mathematical environment.     

Process dissociation and mixture signal detection theory

The process dissociation procedure was developed in an attempt to separate different processes involved in memory tasks. The procedure naturally lends itself to a formulation within a class of mixture signal detection models. The dual process model is shown to be a special case. The mixture signal detection model is applied to data from a widely analyzed study. The results suggest that a process other than recollection may be involved in the process dissociation procedure.     

Defining Work Stress in Young People

Stress experienced by young workers can be very different from stress experienced by adults because of differing psychosocial developments. It is important to understand how early workplace experiences shape young workers' subsequent attitudes and behaviors, which may affect their psychological well‐being. This study examined how 18 young workers ages 17–29 perceive work stress. The authors found that young workers view job stress in 3 dimensions: lack of opportunity to learn, poor social interaction, and lack of opportunity to exercise initiative. Young workers also view work demands as challenging tasks and become job crafters to find more satisfaction in routine tasks.     

任职者任务绩效水平对其工作分析结果的影响

在控制了个体人口统计学变量和排除组织水平变量的影响下,探讨了电厂设计和编辑两个职位任职者的任务绩效水平对于他们Occupational Information Network (以下缩写为O*NET)工作分析问卷评价结果的影响。层次回归结果发现,控制了相关因素后,发电厂设计人员的任务绩效水平能显著影响其对技术性技能的水平评价,编辑的任务绩效水平能显著影响信息处理的重要性评价和水平评价,在一定程度上证实了“工作分析结果差异来源于真实差异”的理论