uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Item Response Theory Observed-Score Kernel Equating
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. Beijing Normal Univ, Beijing, Peoples R China..ORCID iD: 0000-0002-9007-2440
Department of Statistics, USBE, Umeå University, Sweden..
2017 (English)In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 82, no 1, 46-66 p.Article in journal (Refereed) Published
Abstract [en]

Item response theory (IRT) observed-score kernel equating is introduced for the non-equivalent groups with anchor test equating design using either chain equating or post-stratification equating. The equating function is treated in a multivariate setting and the asymptotic covariance matrices of IRT observed-score kernel equating functions are derived. Equating is conducted using the two-parameter and three-parameter logistic models with simulated data and data from a standardized achievement test. The results show that IRT observed-score kernel equating offers small standard errors and low equating bias under most settings considered.

Place, publisher, year, edition, pages
2017. Vol. 82, no 1, 46-66 p.
Keyword [en]
observed-score equating, item response theory, equipercentile equating, standard errors, NEAT design
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-233484DOI: 10.1007/s11336-016-9528-7ISI: 000394985400003PubMedID: 27743280OAI: oai:DiVA.org:uu-233484DiVA: diva2:757287
Funder
Swedish Research Council, 2014-578
Available from: 2014-10-21 Created: 2014-10-06 Last updated: 2017-04-20Bibliographically 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. 24 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 106
Keyword
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

Open Access in DiVA

No full text

Other links

Publisher's full textPubMed

Authority records BETA

Andersson, Björn

Search in DiVA

By author/editor
Andersson, Björn
By organisation
Department of Statistics
In the same journal
Psychometrika
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

doi
pubmed
urn-nbn

Altmetric score

doi
pubmed
urn-nbn
Total: 731 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf