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Extensions of the kernel method of test score equating
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis makes contributions within the area of test score equating and specifically kernel equating. The first paper of this thesis studies the estimation of the test score distributions needed in kernel equating. There are currently two families of models implemented within kernel equating for this purpose, namely log-linear models and item response theory models. The impact of model selection criteria for these models on the equated scores are studied using both empirical and simulated data.

The second paper focuses on the continuization of the estimated score distributions, where different bandwidth selection methods are studied. The study considers multiple data collection designs, sample sizes and score distributions and investigates how large impact the bandwidth selection has on the equated scores.

When the test groups differ in their ability distributions it is necessary to adjust for such differences to make fair comparisons possible. The most common way of adjusting for ability imbalance is by using items that are common for both test forms, known as anchor items. If no such items are available, it has been suggested to use background information about the test-takers instead. However, when the covariate vector of background information increases, the combination of covariates with no observations tends to increase as well. The third paper of this thesis therefore suggests to transform the covariate vector into a scalar propensity score. Two equating estimators are suggested under this setting and the standard error of equating (SEE) for both estimators are given.

The SEE for kernel equating has previously been derived using the delta method. The fourth paper revisits the Bahadur representation of sample quantiles to derive the SEE. Both methods of calculating the SEE are compared, and it is shown that they are equivalent for all common data collection designs when the terms of the Bahadur SEE are estimated using Taylor expansions. An implementation of an alternative estimator of the Bahadur SEE for which the equivalence result does not hold is also included to illustrate when the two methods differ.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2019. , p. 25
Series
Statistical studies, ISSN 1100-8989 ; 55
Keywords [en]
Test equating, Nonequivalent groups, Standard error of equating, bandwidth selection, log-linear models, item response theory
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-166359ISBN: 978-91-7855-126-2 (print)OAI: oai:DiVA.org:umu-166359DiVA, id: diva2:1378833
Public defence
2020-01-17, S213H, Samhällsvetarhuset, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2019-12-18 Created: 2019-12-14 Last updated: 2019-12-17Bibliographically approved
List of papers
1. Model Selection for Presmoothing of Bivariate Score Distributions in Kernel Equating
Open this publication in new window or tab >>Model Selection for Presmoothing of Bivariate Score Distributions in Kernel Equating
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-166355 (URN)
Available from: 2019-12-14 Created: 2019-12-14 Last updated: 2019-12-17
2. How Important is the Choice of Bandwidth in Kernel Equating?
Open this publication in new window or tab >>How Important is the Choice of Bandwidth in Kernel Equating?
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-166356 (URN)
Available from: 2019-12-14 Created: 2019-12-14 Last updated: 2019-12-17
3. Kernel Equating Using Propensity Scores for Nonequivalent Groups
Open this publication in new window or tab >>Kernel Equating Using Propensity Scores for Nonequivalent Groups
2019 (English)In: Journal of educational and behavioral statistics, ISSN 1076-9986, E-ISSN 1935-1054, Vol. 44, no 4, p. 390-414Article in journal (Refereed) Published
Abstract [en]

When equating two test forms, the equated scores will be biased if the test groups differ in ability. To adjust for the ability imbalance between nonequivalent groups, a set of common items is often used. When no common items are available, it has been suggested to use covariates correlated with the test scores instead. In this article, we reduce the covariates to a propensity score and equate the test forms with respect to this score. The propensity score is incorporated within the kernel equating framework using poststratification and chained equating. The methods are evaluated using real college admissions test data and through a simulation study. The results show that propensity scores give an increased equating precision in comparison with the equivalent groups design and a smaller mean squared error than by using the covariates directly. Practical implications are also discussed.

Place, publisher, year, edition, pages
Sage Publications, 2019
Keywords
kernel equating, background variables, nonequivalent groups, NEC design, propensity scores
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-157869 (URN)10.3102/1076998619838226 (DOI)000486857200001 ()
Funder
Swedish Research Council, 2014-578
Available from: 2019-04-04 Created: 2019-04-04 Last updated: 2019-12-14Bibliographically approved
4. Revisiting the Bahadur Representation of Sample Quantiles for the Standard Error of Kernel Equating
Open this publication in new window or tab >>Revisiting the Bahadur Representation of Sample Quantiles for the Standard Error of Kernel Equating
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-166357 (URN)
Available from: 2019-12-14 Created: 2019-12-14 Last updated: 2019-12-17

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