An Application of the Three-Parameter IRT Model to Vertical Equating

Harris, Deborah J.; Hooker, Henry Daggett

doi:10.1177/014662168701100203

Cited by 11 publications

(12 citation statements)

References 15 publications

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“…This conclusion is supported by research described above by Harris and Kolen (1986) and Harris and Hoover (1987). These studies reported invariance with respect to examinee ability for three-parameter model horizontal equating but not for vertical equating.…”

Section: Discussionsupporting

confidence: 72%

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Effect of Examinee Ability on Test Equating Invariance

Skaggs

Lissitz

1988

Applied Psychological Measurement

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Previous research on the application of IRT methodology to vertical test equating has demonstrated conflicting results about the degree of invariance shown by these methods with respect to examinee ability. The purpose of this study was to examine IRT equating invariance by simulating the vertical equating of two tests under varying conditions. Rasch, three-parameter, and equipercentile equating methods were compared. Six equating cases, using different sets of item parameters, were replicated based on examinee samples of low, medium, or high ability or where ability was matched to the difficulty level of the test. The results showed that all three methods were reasonably invariant to examinee ability level under all conditions imposed. This suggests that multidimensionality is likely to be the cause of the lack of invariance found in real datasets.The equating of scores on two or more tests is fundamental to large testing programs. Scores on new forms of tests must be equated to scores on previous versions of the same test; this type of equating is typically referred to as &dquo;horizontal because new test forms are designed to be as similar as possible to previous forms in terms of their psychometric properties. The need for a different kind of equating, called 'b~~rt~c~l&dquo; equating, arises when it is desired to link scores across levels of achievement tests. These levels are likely to be targeted to grades in school, and tests corresponding to different levels differ intentionally both in content and difficulty. Obviously, from theoretical and operational perspectives, vertical equating is much more difficult to accomplish than horizontal equating.In recent years, a considerable quantity of research has investigated the application of item response theory (IRT) methodology to both types of test equating. Although a large number Of IRT models have been proposed, the research on test equating has been primarily limited to two models-the one-parameter logistic (Rasch) model and the three-parameter model.According to the Rasch model, the probability of an examinee with ability 0 (defined generically) answering item correctly is solely a function of the item's difficulty (bi) and the e~c~mi~~~'s ability (0):The three-parameter model incorporates two additional item parameters:at UNIV CALIFORNIA SANTA BARBARA on July 4, 2015 apm.sagepub.com Downloaded from

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Section: Discussionsupporting

confidence: 72%

“…On the other hand, Harris and Hoover (1987) examined vertical equating between levels of a mathematics achievement test. They replicated the equating of tests at adjacent levels using students at different grade levels.…”

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confidence: 99%

Effect of Examinee Ability on Test Equating Invariance

Skaggs

Lissitz

1988

Applied Psychological Measurement

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“…All equating procedures introduce error into score comparisons across different tests, test forms, or levels (Holland & Dorans, 2006;Skaggs & Lissitz, 1986). In general, the equipercentile equating method has performed well in many contexts (Kolen, 1981;O'Brien & Tohn, 1984;Yin, Brennan, & Kolen, 2004), including in vertical equating across ITBS levels when the examinees have high levels of ability for their age (Harris & Hoover, 1987). However, the impact of equipercentile equating on above-level test score interpretation is unknown.…”

Section: Limitationsmentioning

confidence: 99%

Using Above-Level Testing to Track Growth in Academic Achievement in Gifted Students

Warne

2013

Gifted Child Quarterly

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One widely accepted assessment practice in the field of gifted education is above-level testing, which has been defined as "the procedure of administering a test to a gifted child who is younger or in a lower grade than the group for which the test was originally designed" (Warne, 2012, p. 183). Also called out-of-level testing, off-grade testing, and off-level testing, above-level testing is used to screen students for Talent Search participation (

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“…The methods for the item-parameter linking are those described before under IRT calibration (see also Harris & Hoover, 1987). The only major difference between the use of IRT in horizontal linking and the use in vertical linking is that if concurrent calibration is used for linking the item parameters onto the same scale for all the tests taken by several very different populations of test takers, the estimation method should allow for estimation of the parameters of multiple ability distributions.…”

Section: Vertical Scalingmentioning

confidence: 99%

“…This particular type of linking is often called vertical linking in the field of educational measurement. In a vertical linking design, the examinees that take the two (or more) test forms are from representative samples of their cohorts, the examinees are assessed at the same point(s) in time, the samples of examinees that take different test forms differ significantly in ability, and the forms to be linked are not parallel Harris & Hoover, 1987;Kolen & Brennan, 2004;Yen & Burket, 1997 ACT, Inc., 2000). Vertical linking is a weaker type of linking than equating.…”

Section: Introductionmentioning

confidence: 99%

Linking Competencies in Educational Settings and Measuring Growth

Davier

Carstensen²,

Davier

2006

ETS Research Report Series

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Measuring and linking competencies require special instruments, special data collection designs, and special statistical models. The measurement instruments are tests or tests forms, which can be used in the following situations: The same test can be given repeatedly; two or more parallel tests forms (i.e., forms intended to be similar in difficulty and content and that still need to equated) can be given at different time points; or two or more test forms that may be less parallel to various degrees can be given at different points in time. In some circumstances, the goal of the analysis is to make the scores of parallel test forms comparable across different time points and different samples of relatively similar ability (horizontal equating). In other situations, we aim at the comparability of scores of tests forms that are not parallel, and although they are intended to measure the same competencies, they are of different difficulties and are taken by samples that show large differences in ability (vertical linking). In other cases, we want to evaluate the change in competencies over time (with or without covariates) for the same individuals measured by the same instrument or by different instruments (longitudinal linking). This paper will briefly discuss a variety of techniques for relating scale scores from different data collections points and will then discuss models for measuring growth. Each of these areas is a large field in itself, and each has a potential strong impact on educational policies such as the No Child Left Behind Act (for example, the vertical linking of state or national assessments and longitudinal studies are a potential basis for informative analyses for the policy makers), on the life of students and parents (equating of achievement tests), or on the life of professionals (equating of licensure tests). In these times when more and more standardized testing is used for assessing competencies in different domains nationally and internationally, we are also discovering more challenges in ensuring that the process and the results are fair and accurate. In turn, these challenges and these new social implications open the door toward more research in support of fair assessments, both in improving upon the test construction process and in advancing the statistical methods involved.

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An Application of the Three-Parameter IRT Model to Vertical Equating

Cited by 11 publications

References 15 publications

Effect of Examinee Ability on Test Equating Invariance

Effect of Examinee Ability on Test Equating Invariance

Using Above-Level Testing to Track Growth in Academic Achievement in Gifted Students

Linking Competencies in Educational Settings and Measuring Growth

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