An item response model with internal restrictions on item difficulty

An IRT model based on the Rasch model is proposed for composite tasks, that is, tasks that are decomposed into subtasks of different kinds. There is one subtask for each component that is discerned in the composite tasks. A component is a generic kind of subtask of which the subtasks resulting from the decomposition are specific instantiations with respect to the particular composite tasks under study. The proposed model constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the corresponding subtask items, which are estimated together with the weights used in the linear combinations, one weight for each kind of subtask. Although the model does not belong to the exponential family, its parameters can be estimated using conditional maximum likelihood estimation. The approach is demonstrated with an application to spelling tasks. We thank Eric Maris for his helpful comments.     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.     

The Analysis of Intervention Change in Children and Families: Methodological and Conceptual Issues Embedded in Intervention Studies

This article provides an overview of methodological and conceptual issues underlying the assessment of change during psychotherapy with children and families. Three central considerations are discussed: (1) What changes do we measure? (2) When do we measure change? (3) How do we measure change? The difficulties with the traditional methods of assessing change are highlighted, and suggestions for a new paradigm that calls for expansion of the nomological network relevant to the analysis of change, as well as the inclusion of more assessment points and more reliable and valid measures of the change process, are presented. Illustrations of key points are provided from the Adolescent Transitions Program, a theoretically based intervention program targeting high-risk youth.     

画人智力测验评分项目的再确定

该研究参照国内外已有的画人测验材料 ,并在以往使用绘人智能测验的基础上 ,重新设计 ,提出了一份包含 80个评分项目的画人评分标准。新标准首先在课题组内试用修改 ,然后又用于 9名标准评分员的培训 ,最后运用总计 2 5 8名 ,年龄为 6～ 1 2岁的小学儿童作预试 ,进行系统的项目分析。在上述过程中 ,对项目进行反复推敲删改 ,最终形成了一份供制订画人智力测验常模用的画人评分标准。该标准分有无、细节、比例、奖励四个维度 ,按身体部位分成头、头发、眼、耳、鼻、口、颈、躯干、上肢、手、下肢、脚以及连接和服饰共十四个大类 ,每大类包含 4～ 8个评分点 ,总计 75个评分点。     

An investigation of hierarchical Bayes procedures in item response theory

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters. Simulated data sets were analyzed via two joint and two marginal Bayesian estimation procedures. The marginal Bayesian estimation procedures yielded consistently smaller root mean square differences than the joint Bayesian estimation procedures for item and ability estimates. As the sample size and test length increased, the four Bayes procedures yielded essentially the same result.The authors wish to thank the Editor and anonymous reviewers for their insightful comments and suggestions.     

Optimal sequential designs for on-line item estimation

Replenishing item pools for on-line ability testing requires innovative and efficient data collection designs. By generating localD-optimal designs for selecting individual examinees, and consistently estimating item parameters in the presence of error in the design points, sequential procedures are efficient for on-line item calibration. The estimating error in the on-line ability values is accounted for with an item parameter estimate studied by Stefanski and Carroll. LocallyD-optimaln-point designs are derived using the branch-and-bound algorithm of Welch. In simulations, the overall sequential designs appear to be considerably more efficient than random seeding of items.This report was prepared under the Navy Manpower, Personnel, and Training R&D Program of the Office of the Chief of Naval Research under Contract N00014-87-0696. The authors wish to acknowledge the valuable advice and consultation given by Ronald Armstrong, Charles Davis, Bradford Sympson, Zhaobo Wang, Ing-Long Wu and three anonymous reviewers.     

Caution indices based on item response theory

A new family of indices was introduced earlier as a link between two approaches: One based on item response theory and the other on sample statistics. In this study, the statistical properties of these indices are investigated and then the relationships to Guttman Scales, and to item and person response curves are discussed. Further, these indices are standardized, and an example of their potential usefulness for diagnosing students' misconceptions is shown.This research was sponsored by the Personnel and Training Research Program, Psychological Sciences Division, Office of Naval Research, under contract No. N00014-82-K-0604.     

A comment on ‘some standard errors in item response theory’

In maximum likelihood estimation the standard error of the location parameter of the three parameter logistic model can be large, due to inaccurate estimation of the lower asymptote. Thissen and Wainer who demonstrated this effect, suggested that the introduction of a prior distribution for the lower asymptote might alleviate the problems. Here it is demonstrated in some detail that the standard error of the location parameter can be made acceptably small in this way.The author thanks Pieter Vijn for his helpful comments.     

Optimal item difficulty for the three-parameter normal ogive response model

In tailored testing, it is important to determine the optimal difficulty of the next item to present to the examinee. This paper shows that the difference that maximizes information for the three-parameter normal ogive response model is approximately 1.7 times the optimal difference –b for the three-parameter logistic model. Under the normal model, calculation of the optimal difficulty for minimizing the Bayes risk is equivalent to maximizing an associated information function.The views expressed herein, are those of the author and do not necessarily reflect those of the Department of the Navy.     

The bias function of the maximum likelihood estimate of ability for the dichotomous response level

Samejima has recently given an approximation for the bias function for the maximum likelihood estimate of the latent trait in the general case where item responses are discrete, generalizing Lord's bias function in the three-parameter logistic model for the dichotomous response level. In the present paper, observations are made about the behavior of this bias function for the dichotomous response level in general, and also with respect to several widely used mathematical models. Some empirical examples are given.