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.     

Measurement invariance,factor analysis and factorial invariance

Several concepts are introduced and defined: measurement invariance, structural bias, weak measurement invariance, strong factorial invariance, and strict factorial invariance. It is shown that factorial invariance has implications for (weak) measurement invariance. Definitions of fairness in employment/admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness/equity to exist. Implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers.Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.     

An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete

Lord developed an approximation for the bias function for the maximum likelihood estimate in the context of the three-parameter logistic model. Using Taylor's expansion of the likelihood equation, he obtained an equation that includes the conditional expectation, given true ability, of the discrepancy between the maximum likelihood estimate and true ability. All terms of orders higher thann ^?1 are ignored wheren indicates the number of items. Lord assumed that all item and individual parameters are bounded, all item parameters are known or well-estimated, and the number of items is reasonably large. In the present paper, an approximation for the bias function of the maximum likelihood estimate of the latent trait, or ability, will be developed using the same assumptions for the more general case where item responses are discrete. This will include the dichotomous response level, for which the three-parameter logistic model has been discussed, the graded response level and the nominal response level. Some observations will be made for both dichotomous and graded response levels.     

信度系数与观测分数和潜在特质的相关比

在经典真分数模型中,信度系数R=D(T)/D(X)。通常认为,信度系数与项目反应理论没有什么联系。事实上,信度系数恰好等于考生观测分数与潜在特质分数的非线性相关比η_(xθ)~2=1-MD(x|θ)/D(X),据此我们得出估计信度系数的一种新途径,同时讨论了x、θ的相关系数与相关比η_(xθ)~2的关系。     

An exact and optimal standardized person test for assessing consistency with the rasch model

The Rasch model predicts that an individual's ability level is invariant over subtests of the total test, and thus, all subtests measure the same latent trait. A person test of this invariance hypothesis is discussed that is uniformly most powerful and standardized in the sense that the conditional distribution of the test statistic, given a particular level of ability, does not depend on the absolute value of the examinee's ability parameter. The test can be routinely performed by applying a computer program designed by and obtainable from the author. Finally, a suboptimal test is derived that is extremely easy to use, and an overall group test of the invariance hypothesis discussed. All tests considered do not rely on asymptotic approximations; hence, they may be applied when the test is of only moderate length and the group of examinees is small.     

An extension of the rating scale model with an application to the measurement of change

The polytomous unidimensional Rasch model with equidistant scoring, also known as the rating scale model, is extended in such a way that the item parameters are linearly decomposed into certain basic parameters. The extended model is denoted as the linear rating scale model (LRSM). A conditional maximum likelihood estimation procedure and a likelihood-ratio test of hypotheses within the framework of the LRSM are presented. Since the LRSM is a generalization of both the dichotomous Rasch model and the rating scale model, the present algorithm is suited for conditional maximum likelihood estimation in these submodels as well. The practicality of the conditional method is demonstrated by means of a dichotomous Rasch example with 100 items, of a rating scale example with 30 items and 5 categories, and in the light of an empirical application to the measurement of treatment effects in a clinical study.Work supported in part by the Fonds zur Förderung der Wissenschaftlichen Forschung under Grant No. P6414.     

不同情绪背景下来源记忆的ERPs研究*

使用事件相关电位(ERP)技术和测试来源记忆的多键范式,探讨不同情绪效价背景下来源提取的认知神经机制。学习阶段,同时呈现汉字和3种效价情绪图片(重叠);测验阶段,只呈现汉字,要求被试进行四键判断：旧字且背景为中性,旧字且背景为正性,旧字且背景为负性,新字。结果发现：在提取阶段,刺激呈现后300~500 ms,3种情绪背景下来源判断正确项目和来源判断错误项目都比新项目诱发了更正的ERPs(即都存在新旧效应),这一结果反映出刺激呈现后300~500 ms 是一个早期的项目提取阶段,它独立于来源提取。并且,在中性背景下,两种新旧效应没有差别;而在正性和负性背景下,来源判断正确项目的新旧效应显著大于来源判断错误项目。说明相比于中性背景,情绪背景下被试可能更早对来源信息产生熟悉感。在500~650 ms,3种情绪背景下都存在来源判断正确项目的新旧效应,在来源判断错误项目和新项目之间没有显著差异,来源正确与来源错误有显著的新旧效应差异,但二者在头皮分布上是类似的,这反映了晚期的来源提取过程。同时来源正确的新旧效应在这两个时段有显著不同的头皮分布,表明这两个时段有不同加工过程。另外,在500~650 ms,存在显著的情绪效应,正性背景下正确判断来源诱发的ERPs比中性和负性背景下的更正,而且来源判断错误条件下没有情绪效应。综上所述,来源正确和来源错误可能仅仅反映了大脑激活在量上的不同,并不能推断两者存在质的差异;大脑神经活动的早期不仅反映了对记忆项目的熟悉性,而且也受情绪效应的影响,500 ms之后大脑神经活动反映的是对记忆项目回想的过程,这一回想过程也与情绪效应有关,受到情绪效应的调节。