Empirical bayes estimates of domain scores under binomial and hypergeometric distributions for test scores

We introduce two simple empirical approximate Bayes estimators (EABEs)— and —for estimating domain scores under binomial and hypergeometric distributions, respectively. Both EABEs (derived from corresponding marginal distributions of observed test scorex without relying on knowledge of prior domain score distributions) have been proven to hold -asymptotic optimality in Robbins' sense of convergence in mean. We found that, where and are the monotonized versions of and under Van Houwelingen's monotonization method, respectively, the convergence rate of the overall expected loss of Bayes risk in either or depends on test length, sample size, and ratio of test length to size of domain items. In terms of conditional Bayes risk, and outperform their maximum likelihood counterparts over the middle range of domain scales. In terms of mean-squared error, we also found that: (a) given a unimodal prior distribution of domain scores, performs better than both and a linear EBE of the beta-binomial model when domain item size is small or when test items reflect a high degree of heterogeneity; (b) performs as well as when prior distribution is bimodal and test items are homogeneous; and (c) the linear EBE is extremely robust when a large pool of homogeneous items plus a unimodal prior distribution exists.The authors are indebted to both anonymous reviewers, especially Reviewer 2, and the Editor for their invaluable comments and suggestions. Thanks are also due to Yuan-Chin Chang and Chin-Fu Hsiao for their help with our simulation and programming work.     

On the loss of information in conditional maximum likelihood estimation of item parameters

In item response models of the Rasch type (Fischer & Molenaar, 1995), item parameters are often estimated by the conditional maximum likelihood (CML) method. This paper addresses the loss of information in CML estimation by using the information concept of F-information (Liang, 1983). This concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss. For the dichotomous Rasch model, the derivations will be given in detail to show the use of the F-information concept for making comparisons for different estimation methods. It is shown that by using CML for item parameter estimation, some information is almost always lost. But compared to JML (joint maximum likelihood) as well as to MML (marginal maximum likelihood) the loss is very small. The reported efficiency in the use of information of CML to JML and to MML in several comparisons is always larger than 93%, and in tests with a length of 20 items or more, larger than 99%.     

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.     

Item Calibration Samples and the Stability of Achievement Estimates and System Rankings: Another Look at the PISA Model

Using an empirically-based simulation study, we show that typically used methods of choosing an item calibration sample have significant impacts on achievement bias and system rankings. We examine whether recent PISA accommodations, especially for lower performing participants, can mitigate some of this bias. Our findings indicate that standard operational methods, while not ideal, recover underlying proficiency reasonably well and generally outperform methods that more completely include all participants. Translating results onto the PISA scale, the calibration sample can induce bias of up to 12.49 points, which is important given that standard errors are around three points. Although ranking correlations are at least.95, we note the policy implications of slight ranking changes. Our findings indicate that limited accommodations targeted at low achieving educational systems do not outperform either of the other methods considered. Research that further explores accommodations for heterogeneous populations is recommended.     

How is the visual working memory load of driver influenced by information density of traffic signs?

The rapid development of urban roads has resulted in an increase in the amount of information that needs to be displayed on traffic signs. The overloading of information on traffic signs may increase drivers’ visual cognition burden and cause driving errors. It could be an important factor affecting driving safety and result in accidents. To enable drivers to cognize traffic signs, the information density that they could endure under reasonable workload levels should be determined. In this study, we designed and implemented trials to analyze drivers’ visual working memory load (VWML) caused by different information densities (including stimulus intensity (SI) and interval time of stimulus (IS)) of traffic signs. Twenty-four paid participants (12 females) with a mean age of 23.38 years (SD = 1.38) participated in laboratory simulation trials based on the memory retrieval approach. Subjective ratings (rating scale mental effort (RSME)), and performance measurement based on reaction time and accuracy of information-matching task were measured to reflect drivers’ VWML at different information densities. The results show that information density is an important factor affecting drivers’ VWML. The following are the significant observations of the study: (1) The subjective ratings on mental effort increased with increase in the SI. Meanwhile, it first decreased and then increased with increase in the IS. (2) The response accuracy results show that a high accuracy (≥0.7) was achieved by drivers in an IS of 15 s when the SI was at most 14.16 bit/m². Correspondingly, the drivers underwent less mental workload as a result of their better short-term memory characteristic. (3) The mean reaction time was over 1800 ms when the SI was over 14.16 bit/m². This indicated a reduction in the information-processing capability of the drivers. The results indicate that cognition of information of unreasonable density on traffic signs would increase drivers’ VWML. This would, in turn, result in an increase in their reaction time and decrease in accuracy. The threshold of information density was also determined through the experiment. It would satisfy the information demand of drivers and prevent information redundancy. The results contribute to an understanding of drivers’ VWML while cognizing traffic signs with different information densities and provide safety, effectiveness, and information continuity considerations for the design and setting of traffic signs.     

An experimental analysis of psychometric functions in a threshold discrimination task with four response categories1

An experiment on a threshold discrimination task with four response categories was conducted to check the implicit assumptions of a threshold discrimination task with three response categories. Consideration of a task with three response categories, for example, “stronger,”“don't know,” and “weaker,” leads us to anticipate a relation between position parameters and that between the sizes of scale parameters of a model for a task with four response categories, such as, “stronger,”“probably stronger,”“probably weaker,” and “weaker.” That is, position parameters will be equidistant between adjacent categories and the middle scale parameter will be the largest. The results of the experiment on a four‐category task did not support these anticipated relation, and a possibility of biases in the estimation of point of subjective equality (PSE), using a three‐category task is pointed out. As an alternative to a three‐category task, a four‐category task is suggested when more than two categories are required.     

4PLRT模型与3PLRT模型在瑞文标准推理测验中的比较研究

研究目的：考察反应时与智力的关系以及通过模型对比考察4PLRT模型特性。方法：以瑞文标准推理测验为例,对4PLRT模型与3PLRT模型作比较研究。结论：（1）项目时间参数与难度参数正相关,可以依据时间参数将瑞文标准测验划分成三大部分。（2）能力估计结果比较：由于项目参数和被试速度参数的作用,CTT条件下能力相等的不同被试在计时与非计时条件下存在差异。（3）关于被试的答题策略：被试会基于自身能力而充分权衡时间与准确性的关系。这两种不同模型下被试的能力值之间的比较也说明了时间是一个重要的智力评估因子。     

Dielectric and thermodynamic behaviour of binary mixtures of anisole with o-chlorophenol and with o-cresol

The molecular interactions in binary mixtures of anisole with o-chlorophenol and o-cresol have been studied at three different temperatures using dielectric measurements. The static permittivity and the permittivity at optical frequency have also been determined and used to obtain the Kirkwood correlation factors, the Bruggeman parameter, the excess permittivity and the excess free energy for different concentrations of two binary mixtures, namely (1) anisole + o-chlorophenol and (2) anisole + o-cresol. Using the effective Kirkwood correlation factor, parallel and anti-parallel alignments among the dipoles are identified. The corrective Kirkwood correlation factor, the excess permittivity and the Bruggeman parameter are used to explain the interaction between unlike molecules. The temperature dependences of the above parameters are also reported. The investigation shows systematic changes in the dielectric behaviour with variations in concentration and temperature.     

二参数逻辑斯蒂模型项目参数的估计精度

项目参数的估计精度对于测验的编制尤其是题库的建立十分重要。目前,国内外对项目参数估计精度的研究,大部分是基于在已知项目参数真值的情况下,运用各种参数估计方法产生新的估计值,再和真值进行偏度(BIAS)和均方根差(RMSE)的比较,从而说明该种估计方法的有效性。但是这种方法不能提供不同的参数真值之间的估计误差的变化规律。为了弥补这一缺陷,本文尝试从项目参数估计信息函数的角度出发研究项目参数的估计精度问题。本研究以二参数Logistic模型作为研究对象,首先定义了项目参数的估计信息函数,然后基于完全随机实验设计,通过模拟研究的方法探索影响项目参数的估计精度的因素,实验共设计了(2×3×2)种情形。研究结果表明：(1)项目参数(a,b)的估计精度均随着被试样本量的增大而提高;(2)被试的能力分布对难度参数的估计精度影响较大,对区分度参数的估计精度影响相对较小;(3)难度参数和区分度参数的估计精度都分别受到参数a和参数b的共同作用。     

Performance and Learning of Generalized Motor Programs: Relative (GMP) and Absolute (Parameter) Errors

The effects of practice (Experiment 1) and parameter variability (Experiment 2) on the learning of generalized motor programs (GMPs) and movement parameterization were investigated In each experiment, 2 tasks with different relative force-time structures were tested. Participants (N = 32, Experiment (N = 40, Experiment 2) attempted to exert a pattern of force that resembled in force and time a waveform that was displayed on a computer monitor. In both experiments, the analysis suggested that the GMP, although refined over practice, was relatively stable (i.e., resistant to decay and interference), even early in practice (after 20 trials). In addition, the results indicated that constant and variable parameter practice did not differentially affect GMP learning but did degrade the learning of the parameter that was not varied. The data provided additional evidence for the dissociation of the GMP and the parameterization processes proposed in GMP theory. Contrary to schema theory, the present data suggest an interdependence between the force and the time parameters: The manipulation of 1 of the parameters has a negative effect on the learning of the other parameter.