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.     

Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

题组反应理论及其在中学英语考试中的应用研究

题组作为众多测验中的一种常见题型,由于项目间存在一定程度的依赖性而违背了局部独立性假设,若用项目反应模型进行参数估计将会出现较大的偏差.题组反应理论将被试与题组的交互作用纳入到模型中,解决了项目间相依性的问题.笔者对题组反应理论的发展、基本原理及其相关研究进行了综述,并将其应用在中学英语考试中.与项目反应理论相对比,结果发现：（1）题组反应模型与项目反应模型在各参数估计值的相关系数较强,尤其是能力参数和难度参数;（2）在置信区间宽度的比较上,题组反应模型在各个参数上均窄于项目反应模型,即题组反应模型的估计精度优于项目反应模型.     

时间知觉与估计的认知理论综述

本文回顾时间知觉与估计的实验研究 ,总结该领域的国内外研究结果 ,对该领域的各主要认知模型作了较全面的考察和评述 ,并进一步探讨了时间认知领域研究的今后发展 ,尤其是时间知觉与估计研究的脑电研究思路。     

Relating tests given to different samples

Suppose a collection of standard tests is given to all subjects in a random sample, but a different new test is given to each group of subjects in nonoverlapping subsamples. A simple method is developed for displaying the information that the data set contains about the correlational structure of the new tests. This is possible to some extent, even though each subject takes only one new test. The method uses plausible values of the partial correlations among the new tests given the standard tests in order to generate plausible simple correlations among the new tests and plausible multiple correlations between composites of the new tests and the standard tests. The real data example included suggests that the method can be useful in practical problems.     

Errors in subtractions: judged and observed frequencies

In a first study 10 adults, aged 24-44 years, solved all 105 subtraction problems in the form M - N = , where 0 < or = M < or = 13, 0 < or = N < or = 13 and N < or = M. Each participant solved every problem 10 times and in total there were 10 500 answers. Answers, response latencies and errors were registered. Retrospective verbal reports were also given, indicating how a solution was reached: (1) via a (conscious) reconstructive cognitive process or (2) via an (unconscious) reproductive (retrieval) process. The participants made 291 errors (2.8%) when solving the subtractions in study 1. The rate of self-correction was very high, 92%. In a second study 27 undergraduate students estimated overall error rates, including self-corrected errors for the 105 subtraction problems used in the first study. Judged and actual error rates were compared. The participants systematically underestimated error rates for error prone problems and overestimated error rates for error free problems. The participants were fairly accurate when they predicted problems that were most error prone, with a hit rate of 0.67 for the (18) problems predicted as the most error prone ones. In contrast, predictions of which problems were error free were very poor with a hit rate of only 0.20 of the problems predicted as error free really having no errors in study 1. The correlation between judged error rates and frequencies for actually made errors was 0.69 for answers belonging to reconstructive solutions. In contrast, there was no significant correlation between judged and actual error rates at all for retrieved solutions, possibly reflecting the inaccessibility to consciousness of quick retrieval processes.     

Multilevel Modeling with Correlated Effects

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized method of moments (GMM) estimation techniques in multilevel modeling, the authors present a series of estimators along a robust to efficient continuum. This continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects. It is shown that the GMM approach provides an overarching framework that encompasses well-known estimators such as fixed and random effects estimators and also provides more options. These GMM estimators can be expressed as instrumental variable (IV) estimators which enhances their interpretability. Moreover, by exploiting the hierarchical structure of the data, the current technique does not require additional variables unlike traditional IV methods. Further, statistical tests are developed to compare the different estimators. A simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency. It further shows that not only are regression coefficients biased, but variance components may be severely underestimated in the presence of correlated effects. Empirical standard errors are employed as they are less sensitive to correlated effects when compared to model-based standard errors. An example using student achievement data shows that GMM estimators can be effectively used in a search for the most efficient among unbiased estimators. This research was supported by the National Academy of Education/Spencer Foundation and the National Science Foundation, grant number SES-0436274. We thank the editor, associate editor, and referees for detailed feedback that helped improve the paper.     

注意在短时距估计中的作用

注意一直是时间知觉研究的一个重要问题。本文综述了研究已经取得一些较为一致的结果：在双任务程序中对时间任务的注意越多,时距估计越准确;在单一任务中对目标刺激的时间属性注意越多,对该刺激的持续时距估计越准确;在时间导向任务中,个体可以有效地、主动把注意导向未来的某段时距,那么将对出现在那个时刻的刺激做出更好的反应。最后,讨论了现有研究中存在的、以及今后研究中需要着重考虑的问题。     

Semi‐parametric proportional hazards models with crossed random effects for psychometric response times

The semi‐parametric proportional hazards model with crossed random effects has two important characteristics: it avoids explicit specification of the response time distribution by using semi‐parametric models, and it captures heterogeneity that is due to subjects and items. The proposed model has a proportionality parameter for the speed of each test taker, for the time intensity of each item, and for subject or item characteristics of interest. It is shown how all these parameters can be estimated by Markov chain Monte Carlo methods (Gibbs sampling). The performance of the estimation procedure is assessed with simulations and the model is further illustrated with the analysis of response times from a visual recognition task.