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Improving the Bandwidth Selection in Kernel Equating
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0002-9007-2440
Educational Testing Service.
2014 (English)In: Journal of educational measurement, ISSN 0022-0655, E-ISSN 1745-3984, Vol. 51, no 3, p. 223-238Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Blackwell Publishing, 2014. Vol. 51, no 3, p. 223-238
Keywords [en]
kernel equating, observed-score test equating
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-223988DOI: 10.1111/jedm.12044ISI: 000341592200001OAI: oai:DiVA.org:uu-223988DiVA, id: diva2:714694
Available from: 2014-04-29 Created: 2014-04-29 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Contributions to Kernel Equating
Open this publication in new window or tab >>Contributions to Kernel Equating
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The statistical practice of equating is needed when scores on different versions of the same standardized test are to be compared. This thesis constitutes four contributions to the observed-score equating framework kernel equating.

Paper I introduces the open source R package kequate which enables the equating of observed scores using the kernel method of test equating in all common equating designs. The package is designed for ease of use and integrates well with other packages. The equating methods non-equivalent groups with covariates and item response theory observed-score kernel equating are currently not available in any other software package.

In paper II an alternative bandwidth selection method for the kernel method of test equating is proposed. The new method is designed for usage with non-smooth data such as when using the observed data directly, without pre-smoothing. In previously used bandwidth selection methods, the variability from the bandwidth selection was disregarded when calculating the asymptotic standard errors. Here, the bandwidth selection is accounted for and updated asymptotic standard error derivations are provided.

Item response theory observed-score kernel equating for the non-equivalent groups with anchor test design is introduced in paper III. Multivariate observed-score kernel equating functions are defined and their asymptotic covariance matrices are derived. An empirical example in the form of a standardized achievement test is used and the item response theory methods are compared to previously used log-linear methods.

In paper IV, Wald tests for equating differences in item response theory observed-score kernel equating are conducted using the results from paper III. Simulations are performed to evaluate the empirical significance level and power under different settings, showing that the Wald test is more powerful than the Hommel multiple hypothesis testing method. Data from a psychometric licensure test and a standardized achievement test are used to exemplify the hypothesis testing procedure. The results show that using the Wald test can provide different conclusions to using the Hommel procedure.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. p. 24
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 106
Keywords
observed-score test equating, item response theory, R, equipercentile equating, asymptotic standard errors, non-equivalent groups with anchor test design
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-234618 (URN)978-91-554-9089-8 (ISBN)
Public defence
2014-12-12, Sal IV, Universitetshuset, Biskopsgatan 3, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2014-11-20 Created: 2014-10-21 Last updated: 2015-02-03

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Andersson, Björn

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