High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.     

汉语转折复句的命题表征项目互换效应研究

采用句子一图画验证任务(sentence-picture verification task)探讨了汉语转折复句的命题表征项目互换效应。结果表明,汉语倒装转折复句的项目表达顺序为“(但是)B→虽然A”,命题表征中项目存在着互换的倾向,所形成的命题表征为“虽然A→但是B”。本研究结果初步表明,读者理解汉语转折复句可能是一个按照“虽然A(事实让步)→但是B(转折)”固定方向进行系列认知加工的过程。     

汉语因果复句的心理表征项目互换效应研究

采用句子-图画验证任务(sentence picture verification task)探讨了汉语因果复句的心理表征项目互换效应。结果表明,汉语因果复句的项目表达顺序为"结果→原因"时,所形成的心理表征中项目发生互换,其结果为"原因→结果"。本研究结果初步表明,读者理解汉语因果复句是一个按照"原因→结果"固定方向进行系列加工的认知过程。     

Data, model, conclusion, doing it again

This paper explores the robustness of conclusions from a statistical model against variations in model choice (rather than variations in random sampling and random assignment to treatments, which are the usual variations covered by inferential statistics). After the problem formulation in section 1, section 2 presents an example from Box and Tiao in which variation in parent distribution is modeled for a one sample location problem. An adaptive Bayesian procedure permits to use a weighted mixture of parent distributions rather than choosing just one, such as a normal or a uniform distribution.In section 3 similar considerations are applied to an event history model for the influence of education and gender on age at first marriage, but here the conclusions are hardly influenced by the choice of the duration distribution. In section 4 a brief discussion of model choice in factor analysis and structural equation models is followed by a more elaborate treatment of the choice of integer valued slopes for item response functions in the OPLM model which is an extension of the Rasch model. A modest simulation study suggests that Adaptive Bayesian Modeling with a mixture of sets of slopes works better than fixing one set of postulated slopes.The paper concludes with some remarks on the roles and sources of prior distributions followed by a short epilogue which argues that simultaneous consideration of a class of models for the same data is sometimes superior to exclusively analyzing the data under one specific model chosen from such a class.This article is based on the Presidential Address Ivo W. Molenaar gave on June 20, 1998 at the 1998 Annual Meeting of the Psychometric Society held at the University of Illinois in Champaign, Illinois. Thanks is given to John Wiley & Sons and George C. Tiao for granting permission to reprint three figures from the book George C. Tiao wrote with George E. P. Box titled Bayesian Inference in Statistical Analysis.—EditorThanks are due to Anne Boomsma, Jeffrey Hoogland, Mark Huisman, Tom Snijders, Marijtje Van Duijn, and Norman Verhelst for suggesting improvements and/or assisting with data analyses.     

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.