Item information and discrimination functions for trinary pcm items

For trinary partial credit items the shape of the item information and the item discrimination function is examined in relation to the item parameters. In particular, it is shown that these functions are unimodal if ₂ – ₁ < 4 ln 2 and bimodal otherwi The locations and values of the maxima are derived. Furthermore, it is demonstrated that the value of the maximum is decreasing in ₂ – ₁. Consequently, the maximum of a unimodal item information function is always larger than the maximum of a bimodal one, and similarly for the item discrimination function.The work reported herein was partially supported under the National Assessment of Educational Progress (Grant No. R999G30002; CFDA No. 84.999G) as administered by the Office of Educational Research and Improvement, US Department of Education.     

Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.     

Varieties of Monadic Heyting Algebras Part II: Duality Theory

In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.     

汉语词汇测验中的项目功能差异初探

该文运用两种不同的方法对实际的汉语词汇测验中的３６个词汇进行了ＤＩＦ探测。对于１４００多劬的初三学生分别作了男女生与城郊学生间的比较。在男女组分析中检出７个属于一致性ＤＩＦ的项目;对于城郊学生组经两种方法同时确定的ＤＩＦ项目有７个,其中５个是一致性ＤＩＦ,２个是非一致性ＤＩＦ的项目。该文还讨论了产生ＤＩＦ的可能因素。     

Some critical observations of the test information function as a measure of local accuracy in ability estimation

The test information function serves important roles in latent trait models and in their applications. Among others, it has been used as the measure of accuracy in ability estimation. A question arises, however, if the test information function is accurate enough for all meaningful levels of ability relative to the test, especially when the number of test items is relatively small (e.g., less than 50). In the present paper, using the constant information model and constant amounts of test information for a finite interval of ability, simulated data were produced for eight different levels of ability and for twenty different numbers of test items ranging between 10 and 200. Analyses of these data suggest that it is desirable to consider some modification of the test information function when it is used as the measure of accuracy in ability estimation.     

Loglinear multidimensional IRT models for polytomously scored items

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.Hank Kelderman is currently affiliated with Vrije Universiteit, Amsterdam.We thank Linda Vodegel-Matzen of the Division of Developmental Psychology of the University of Amsterdam for making available the data used in the example in this article.     

A model-based standardization approach that separates true bias/DIF from group ability differences and detects test bias/DTF as well as item bias/DIF

A model-based modification (SIBTEST) of the standardization index based upon a multidimensional IRT bias modeling approach is presented that detects and estimates DIF or item bias simultaneously for several items. A distinction between DIF and bias is proposed. SIBTEST detects bias/DIF without the usual Type 1 error inflation due to group target ability differences. In simulations, SIBTEST performs comparably to Mantel-Haenszel for the one item case. SIBTEST investigates bias/DIF for several items at the test score level (multiple item DIF called differential test functioning: DTF), thereby allowing the study of test bias/DIF, in particular bias/DIF amplification or cancellation and the cognitive bases for bias/DIF.This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-90-J-1940, 4421-548 and National Science Foundation Mathematics Grant NSF-DMS-91-01436. The research reported here is collaborative in every respect and the order of authorship is alphabetical. The assistance of Hsin-hung Li and Louis Roussos in conducting the simulation studies was of great help. Discussions with Terry Ackerman, Paul Holland, and Louis Roussos were very helpful.     

Enhancing measurement validity in diverse populations: Modern approaches to evaluating differential item functioning

When developing and evaluating psychometric measures, a key concern is to ensure that they accurately capture individual differences on the intended construct across the entire population of interest. Inaccurate assessments of individual differences can occur when responses to some items reflect not only the intended construct but also construct-irrelevant characteristics, like a person's race or sex. Unaccounted for, this item bias can lead to apparent differences on the scores that do not reflect true differences, invalidating comparisons between people with different backgrounds. Accordingly, empirically identifying which items manifest bias through the evaluation of differential item functioning (DIF) has been a longstanding focus of much psychometric research. The majority of this work has focused on evaluating DIF across two (or a few) groups. Modern conceptualizations of identity, however, emphasize its multi-determined and intersectional nature, with some aspects better represented as dimensional than categorical. Fortunately, many model-based approaches to modelling DIF now exist that allow for simultaneous evaluation of multiple background variables, including both continuous and categorical variables, and potential interactions among background variables. This paper provides a comparative, integrative review of these new approaches to modelling DIF and clarifies both the opportunities and challenges associated with their application in psychometric research.     

Penalization approaches in the conditional maximum likelihood and Rasch modelling context

Recent detection methods for Differential Item Functioning (DIF) include approaches like Rasch Trees, DIFlasso, GPCMlasso and Item Focussed Trees, all of which - in contrast to well established methods - can handle metric covariates inducing DIF. A new estimation method shall address their downsides by mainly aiming at combining three central virtues: the use of conditional likelihood for estimation, the incorporation of linear influence of metric covariates on item difficulty and the possibility to detect different DIF types: certain items showing DIF, certain covariates inducing DIF, or certain covariates inducing DIF in certain items. Each of the approaches mentioned lacks in two of these aspects. We introduce a method for DIF detection, which firstly utilizes the conditional likelihood for estimation combined with group Lasso-penalization for item or variable selection and L1-penalization for interaction selection, secondly incorporates linear effects instead of approximation through step functions, and thirdly provides the possibility to investigate any of the three DIF types. The method is described theoretically, challenges in implementation are discussed. A dataset is analysed for all DIF types and shows comparable results between methods. Simulation studies per DIF type reveal competitive performance of cmlDIFlasso, particularly when selecting interactions in case of large sample sizes and numbers of parameters. Coupled with low computation times, cmlDIFlasso seems a worthwhile option for applied DIF detection.