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1.
This article is a response to the commentaries on the position paper on observed‐score equating by van der Linden (this issue). The response focuses on the more general issues in these commentaries, such as the nature of the observed scores that are equated, the importance of test‐theory assumptions in equating, the necessity to use multiple equating transformations, and the choice of conditioning variables in equating.  相似文献   

2.
van der Linden (this issue) uses words differently than Holland and Dorans. This difference in language usage is a source of some confusion in van der Linden's critique of what he calls equipercentile equating. I address these differences in language. van der Linden maintains that there are only two requirements for score equating. I maintain that the requirements he discards have practical utility and are testable. The score equity requirement proposed by Lord suggests that observed score equating was either unnecessary or impossible. Strong equity serves as the fulcrum for van der Linden's thesis. His proposed solution to the equity problem takes inequitable measures and aligns conditional error score distributions, resulting in a family of linking functions, one for each level of θ. In reality, θ is never known. Use of an anchor test as a proxy poses many practical problems, including defensibility.  相似文献   

3.
Equating methods make use of an appropriate transformation function to map the scores of one test form into the scale of another so that scores are comparable and can be used interchangeably. The equating literature shows that the ways of judging the success of an equating (i.e., the score transformation) might differ depending on the adopted framework. Rather than targeting different parts of the equating process and aiming to evaluate the process from different aspects, this article views the equating transformation as a standard statistical estimator and discusses how this estimator should be assessed in an equating framework. For the kernel equating framework, a numerical illustration shows the potentials of viewing the equating transformation as a statistical estimator as opposed to assessing it using equating‐specific criteria. A discussion on how this approach can be used to compare other equating estimators from different frameworks is also included.  相似文献   

4.
We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners for being too complex and that it does not offer sufficient smoothing in certain cases. In addition, the bandwidth parameters have been treated as constants in the derivation of the standard error of equating even when they were selected by considering the observed data. Here, the bandwidth selection is simplified, and modified standard errors of equating (SEEs) that reflect the bandwidth selection method are derived. The method is illustrated with real data examples and simulated data.  相似文献   

5.
Local equating (LE) is based on Lord's criterion of equity. It defines a family of true transformations that aim at the ideal of equitable equating. van der Linden (this issue) offers a detailed discussion of common issues in observed‐score equating relative to this local approach. By assuming an underlying item response theory model, one of the main features of LE is that it adjusts the equated raw scores using conditional distributions of raw scores given an estimate of the ability of interest. In this article, we argue that this feature disappears when using a Rasch model for the estimation of the true transformation, while the one‐parameter logistic model and the two‐parameter logistic model do provide a local adjustment of the equated score.  相似文献   

6.
While agreeing with van der Linden (this issue) that test equating needs better theoretical underpinnings, my comments criticize several aspects of his article. His examples are, for the most part, worthless; he does not use well‐established terminology correctly; his view of 100 years of attempts to give a theoretical basis for equating is unreasonably dismissive; he exhibits no understanding of the role of the synthetic population for anchor test equating for the nonequivalent groups with anchor test design; he is obtuse regarding the condition of symmetry, requiring it of the estimand but not of the estimator; and his proposal for a foundational basis for all test equating, the “true equating transformation,” allows a different equating function for every examinee, which is way past what equating actually does or hopes to achieve. Most importantly, he appears to think that criticism of others is more important than improved insight that moves a field forward based on the work of many other theorists whose contributions have improved the practice of equating.  相似文献   

7.
Three local observed‐score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias—as defined by Lord's criterion of equity—and percent relative error. The local kernel item response theory observed‐score equating method, which can be used for any of the common equating designs, had a small amount of bias, a low percent relative error, and a relatively low kernel standard error of equating, even when the accuracy of the test was reduced. The local kernel equating methods for the nonequivalent groups with anchor test generally had low bias and were quite stable against changes in the accuracy or length of the anchor test. Although all proposed methods showed small percent relative errors, the local kernel equating methods for the nonequivalent groups with anchor test design had somewhat larger standard error of equating than their kernel method counterparts.  相似文献   

8.
In operational testing programs using item response theory (IRT), item parameter invariance is threatened when an item appears in a different location on the live test than it did when it was field tested. This study utilizes data from a large state's assessments to model change in Rasch item difficulty (RID) as a function of item position change, test level, test content, and item format. As a follow-up to the real data analysis, a simulation study was performed to assess the effect of item position change on equating. Results from this study indicate that item position change significantly affects change in RID. In addition, although the test construction procedures used in the investigated state seem to somewhat mitigate the impact of item position change, equating results might be impacted in testing programs where other test construction practices or equating methods are utilized.  相似文献   

9.
In spite of all of the technical progress in observed‐score equating, several of the more conceptual aspects of the process still are not well understood. As a result, the equating literature struggles with rather complex criteria of equating, lack of a test‐theoretic foundation, confusing terminology, and ad hoc analyses. A return to Lord's foundational criterion of equity of equating, a derivation of the true equating transformation from it, and mainstream statistical treatment of the problem of estimating the transformation for various data‐collection designs exist as a solution to the problem.  相似文献   

10.
IRT Equating Methods   总被引：1，自引：0，他引：1  
The purpose of this instructional module is to provide the basis for understanding the process of score equating through the use of item response theory (IRT). A context is provided for addressing the merits of IRT equating methods. The mechanics of IRT equating and the need to place parameter estimates from separate calibration runs on the same scale are discussed. Some procedures for placing parameter estimates on a common scale are presented. In addition, IRT true-score equating is discussed in some detail. A discussion of the practical advantages derived from IRT equating is offered at the end of the module.  相似文献   

11.
Calibration and equating is the quintessential necessity for most large‐scale educational assessments. However, there are instances when no consideration is given to the equating process in terms of context and substantive realization, and the methods used in its execution. In the view of the authors, equating is not merely an exhibit of the statistical methodology, but it is also a reflection of the thought process undertaken in its execution. For example, there is hardly any discussion in literature of the ideological differences in the selection of an equating method. Furthermore, there is little evidence of modeling cohort growth through an identification and use of construct‐relevant linking items’ drift, using the common item nonequivalent group equating design. In this article, the authors philosophically justify the use of Huynh's statistical method for the identification of construct‐relevant outliers in the linking pool. The article also dispels the perception of scale instability associated with the inclusion of construct‐relevant outliers in the linking item pool and concludes that an appreciation of the rationale used in the selection of the equating method, together with the use of linking items in modeling cohort growth, can be beneficial to the practitioners.  相似文献   

12.
曹文娟  白俊梅 《考试研究》2013,(3):79-85,33
本文使用R-2.15.2软件模拟研究锚测验难度参数方差特征对测验等值误差的影响,采用三种等值方法(链百分位等值法、Levine等值法和Tucker等值法)对锚测验不同类型的难度方差进行比较研究。结果显示,当锚测验难度方差小于全测验难度方差时,其等值的随机误差和系统误差与锚测验难度方差和全测验难度方差一致时(即锚测验为全测验的平行缩减版minitest时)的表现基本相同。因此,对锚测验而言,要求其与全测验具有相同的统计规格可能过于严格。  相似文献   

13.
In this article, linear item response theory (IRT) observed‐score equating is compared under a generalized kernel equating framework with Levine observed‐score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when using data from IRT models, linear IRT observed‐score equating is virtually identical to Levine observed‐score equating. This leads to the conclusion that poststratification equating based on true anchor scores can be viewed as the curvilinear Levine observed‐score equating.  相似文献   

14.
A resampling study was conducted to compare the statistical bias and standard errors of nonequivalent-groups linear test equating in small samples of examinees. Sample sizes of 15, 25, 50, and 100 were examined. One thousand samples of each size were drawn with replacement from each of 5 archival data files from teacher subject area tests. For each test, data files from 2 parallel forms were used. Results suggest trivial levels of equating bias even with small samples, but substantial increases in standard errors as sample size decreases. Results were interpreted in terms of applications to testing situations in which small numbers of examinees are available.  相似文献   

15.
Equatings were performed on both simulated and real data sets using the common-examinee design and two abilities for each examinee (i.e., two dimensions). Item and ability parameter estimates were found by using the Multidimensional Item Response Theory Estimation (MIRTE) program. The amount of equating error was evaluated by a comparison of the mean difference and the mean absolute difference between the true scores and ability estimates found on both tests for the common examinees used in the equating. The results indicated that effective equating, as measured by comparability o f true scores, was possible with the techniques used in this study. When the stability o f the ability estimates was examined, unsatisfactory results were found.  相似文献   

16.
Two methods of local linear observed‐score equating for use with anchor‐test and single‐group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed‐score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980) definition of equity was used. The local method for the anchor‐test design yielded minimum bias, even for considerable variation of the relative difficulties of the two test forms and the length of the anchor test. Among the traditional methods, the method of chain equating performed best. The local method for single‐group designs yielded equated scores with bias comparable to the traditional methods. This method, however, appears to be of theoretical interest because it forces us to rethink the relationship between score equating and regression.  相似文献   

17.
Test equating might be affected by including in the equating analyses examinees who have taken the test previously. This study evaluated the effect of including such repeaters on Medical College Admission Test (MCAT) equating using a population invariance approach. Three-parameter logistic (3-PL) item response theory (IRT) true score and traditional equipercentile equating methods were used under the random groups equating design. This study also examined whether or not population sensitivity of equating by repeater status varies depending on other background variables (gender and ethnicity). The results indicated that there was some evidence of repeaters' effect on equating with varying amounts of such effect by gender.  相似文献   

18.
Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed‐score equating, one which provides flexible control over how form difficulty is assumed versus estimated to change across the score scale. A general linear method is presented as an extension of traditional linear methods. The general method is then compared to other linear and nonlinear methods in terms of accuracy in estimating a criterion equating function. Results from two parametric bootstrapping studies based on real data demonstrate the usefulness of the general linear method.  相似文献   

19.
《教育实用测度》2013,26(4):383-407
The performance of the item response theory (IRT) true-score equating method is examined under conditions of test multidimensionality. It is argued that a primary concern in applying unidimensional equating methods when multidimensionality is present is the potential decrease in equity (Lord, 1980) attributable to the fact that examinees of different ability are expected to obtain the same test scores. In contrast to equating studies based on real test data, the use of simulation in equating research not only permits assessment of these effects but also enables investigation of hypothetical equating conditions in which multidimensionality can be suspected to be especially problematic for test equating. In this article, I investigate whether the IRT true-score equating method, which explicitly assumes the item response matrix is unidimensional, is more adversely affected by the presence of multidimensionality than 2 conventional equating methods-linear and equipercentile equating-using several recently proposed equity-based criteria (Thomasson, 1993). Results from 2 simulation studies suggest that the IRT method performs at least as well as the conventional methods when the correlation between dimensions is high (³ 0.7) and may be only slightly inferior to the equipercentile method when the correlation is moderate to low (£ 0.5).  相似文献   

20.
In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed‐score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the normality assumption, would be preferred, because it is asymptotically accurate regardless of the distribution of the data. In this article, an analytical formula for the standard error of linear observed‐score equating, which characterizes the effect of nonnormality, is obtained under elliptical distributions. Using three large‐scale real data sets as the populations, resampling studies are conducted to empirically evaluate the normal and general estimators of the standard error of linear observed‐score equating. The effect of sample size (50, 100, 250, or 500) and equating method (chained linear, Tucker, or Levine observed‐score equating) are examined. Results suggest that the general estimator has smaller bias than the normal estimator in all 36 conditions; it has larger standard error when the sample size is at least 100; and it has smaller root mean squared error in all but one condition. An R program is also provided to facilitate the use of the general estimator.  相似文献   

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