Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • 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
Optimal Item Calibration for Computerized Achievement Tests
Stockholm University, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0003-2889-0263
Stockholm University, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0003-4161-7851
2019 (English)In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 84, no 4, p. 1101-1128Article in journal (Refereed) Published
Abstract [en]

Item calibration is a technique to estimate characteristics of questions (called items) for achievement tests. In computerized tests, item calibration is an important tool for maintaining, updating and developing new items for an item bank. To efficiently sample examinees with specific ability levels for this calibration, we use optimal design theory assuming that the probability to answer correctly follows an item response model. Locally optimal unrestricted designs have usually a few design points for ability. In practice, it is hard to sample examinees from a population with these specific ability levels due to unavailability or limited availability of examinees. To counter this problem, we use the concept of optimal restricted designs and show that this concept naturally fits to item calibration. We prove an equivalence theorem needed to verify optimality of a design. Locally optimal restricted designs provide intervals of ability levels for optimal calibration of an item. When assuming a two-parameter logistic model, several scenarios with D-optimal restricted designs are presented for calibration of a single item and simultaneous calibration of several items. These scenarios show that the naive way to sample examinees around unrestricted design points is not optimal.

Place, publisher, year, edition, pages
2019. Vol. 84, no 4, p. 1101-1128
Keywords [en]
achievement tests, computerized tests, item calibration, optimal restricted design, two-parameter logistic model
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-169646DOI: 10.1007/s11336-019-09673-6ISI: 000492593800010OAI: oai:DiVA.org:su-169646DiVA, id: diva2:1323669
Available from: 2019-06-12 Created: 2019-06-12 Last updated: 2019-11-11Bibliographically approved
In thesis
1. Achievement tests and optimal design for pretesting of questions
Open this publication in new window or tab >>Achievement tests and optimal design for pretesting of questions
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Achievement tests are used to measure the students' proficiency in a particular knowledge. Computerized achievement tests (e.g. GRE and SAT) are usually based on questions available in an item bank to measure the proficiency of students. An item bank is a large collection of items with known characteristics (e.g. difficulty). Item banks are continuously updated and revised with new items in place of obsolete, overexposed or flawed items over time. This thesis is devoted to updating and maintaining the item bank with high-quality questions and better estimations of item parameters (item calibration). 

The thesis contains four manuscripts. One paper investigates the impact of student ability dimensionality on the estimated parameters and the other three deal with item calibration.

In the first paper, we investigate how the ability dimensionality influences the estimates of the item-parameters. By a case and simulation study, we found that a multidimensional model better discriminates among the students.

The second paper describes a method for optimal item calibration by efficiently selecting the examinees based on their ability levels. We develop an algorithm which selects intervals for the students' ability levels for optimal calibration of the items. We also develop an equivalence theorem for item calibration to verify the optimal design.  

The algorithm developed in Paper II becomes complicated with the increase of number of calibrated items. So, in Paper III we develop a new exchange algorithm based on the equivalence theorem developed in Paper II.

Finally, the fourth paper generalizes the exchange algorithm described in Paper III by assuming that the students have multidimensional abilities to answer the questions.

Place, publisher, year, edition, pages
Department of Statistics, Stockholm University, 2019. p. 26
Keywords
Achievement test, Equivalence theorem, Exchange algorithm, Item calibration, Item response theory model, Optimal experimental design
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-174079 (URN)978-91-7797-879-4 (ISBN)978-91-7797-880-0 (ISBN)
Public defence
2019-11-15, William-Olssonsalen, Geovetenskapens hus, Svante Arrhenius väg 14, floor 1, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2019-10-23 Created: 2019-10-02 Last updated: 2019-10-16Bibliographically approved

Open Access in DiVA

fulltext(0 kB)40 downloads
File information
File name FULLTEXT01.pdfFile size 0 kBChecksum
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Ul Hassan, MahmoodMiller, Frank
By organisation
Department of Statistics
In the same journal
Psychometrika
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 40 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 95 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • 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