A note on the item information function of the four-parameter logistic model

Magis, David

doi:10.1177/0146621613475471

Request a copy

Article (Scientific journals)

A note on the item information function of the four-parameter logistic model

Magis, David

2013 • In Applied Psychological Measurement, 37, p. 304-315

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/137218

DOI
10.1177/0146621613475471

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

Applied Psychological Measurement 37 (2013), 304-315.pdf

Publisher postprint (257.76 kB)

Request a copy

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Item response theory; Four-parameter lgistic model; Item information function; Maximization

Abstract :

[en] This paper focuses on four-parameter logistic (4PL) model (Barton & Lord, 1981) as an extension of the usual three-parameter logistic (3PL) model with an upper asymptote possibly different from one. For a given item with fixed item parameters, Lord (1980) derived the value of the latent ability level that maximizes the item information function under the 3PL model. The purpose of this paper is to extend this result to the 4PL model. A generic and algebraic method is developed for that purpose. The result is practically illustrated by an example and several potential applications of this result are outlined.

Disciplines :

Education & instruction

Author, co-author :

Magis, David ; Université de Liège - ULiège > Département d'éducation et formation > Psychométrie et édumétrie

Language :

English

Title :

A note on the item information function of the four-parameter logistic model

Alternative titles :

[fr] Une note sur la fonction d'information d'item du modèle logistique à quatre paramètres

Publication date :

2013

Journal title :

Applied Psychological Measurement

ISSN :

0146-6216

eISSN :

1552-3497

Publisher :

SAGE Publications

Volume :

Pages :

304-315

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 01 January 2013

Statistics

Number of views

151 (7 by ULiège)

Number of downloads

1 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Barton M. A.,Lord F. M.An upper asymptote for the three-parameter logistic item-response model. Princeton, NJ: Educational Testing Service; 1981:.
Birnbaum A.Statistical theories of mental test scores. Lord F. M.Novick M. R., ed. Reading, MA: Addison-Wesley; 1968:397-479.
Chang H.-H.,Yin Z.To weight or not to weight? Balancing influence of initial items in adaptive testing.Psychometrika. 2008;73:441-450.
Green B. F.A comment on early student blunders on computer-based adaptive tests.Applied Psychological Measurement. 2011;35:165-174.
Hambleton R. K.,Swaminathan H.Item response theory: Principles and applications. Boston, MA: Kluwer; 1985:.
Jacobson N.Basic algebra I. 1985). Basic algebra I (2nd ed.). San Francisco, CA: W. H. Freeman.San Francisco, CA: W. H. Freeman; 1985:.
Liao W.-W.,Ho R.-G.,Yen Y.-C.,Cheng H.-C.The four-parameter logistic item response theory model as a robust method of estimating ability despite aberrant responses.Social Behavior and Personality. 2012;40:1679-1694.
Linacre J. M.Discrimination, guessing and carelessness: Estimating IRT parameters with Rasch.Rasch Measurement Transactions. 2004;18:959-960.
Loken E.,Rulison K. L.Estimation of a four-parameter item response theory model.British Journal of Mathematical and Statistical Psychology. 2010;63:509-525.
Lord F. M.Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum; 1980:.
Lunn D. J.,Thomas A.,Best N.,Spiegelhalter D.WinBUGS-A Bayesian modeling framework: Concepts, structure, and extensibility.Statistics and Computing. 2000;10:325-337.
MagisD. (2012). Some robust ability estimators with logistic item response models. Unpublished manuscript, Department of Education, University of Liège, Liège, Belgium.
Magis D.,Raîche G.Random generation of response patterns under computerized adaptive testing with the R package catR.Journal of Statistical Software. 2012;48:1-19.
Mislevy R. J.,Bock R. D.Biweight estimates of latent ability.Educational and Psychological Measurement. 1982;42:725-737.
Osgood D.,McMorris B. J.,Potenza M. T.Analyzing multiple-item measures of crime and deviance I: Item response theory scaling.Journal of Quantitative Criminology. 2002;18:267-296.
R Development Core Team. (2012). R: A language and environment for statistical computing [Computer software]. Vienna, Austria: R Foundation for Statistical Computing
Reise S. P.,Waller N. G.How many IRT parameters does it take to model psychopathology items?.Psychological Methods. 2003;8:164-184.
Rulison K. L.,Loken E.I've fallen and I can't get up: Can high ability students recover from early mistakes in computerized adaptive testing?.Applied Psychological Measurement. 2009;33:83-101.
Rupp A. A.Item response modeling with BILOG-MG and MULTILOG for Windows.International Journal of Testing. 2003;3:365-384.
Schuster C.,Yuan K.-H.Robust estimation of latent ability in item response models.Journal of Educational and Behavioral Statistics. 2011;36:720-735.
Tavares H. R.,de Andrade D. F.,Pereira C. A.Detection of determinant genes and diagnostic via item response theory.Genetics and Molecular Biology. 2004;27:679-685.
Tendeiro J. N.,Meijer R. R.A CUSUM to detect person misfit: A discussion and some alternatives for existing procedures.Applied Psychological Measurement. 2012;36:420-442.
Waller N. G.,Reise S. P.New directions in psychological measurement with model-based approaches. Embretson S.Roberts J. S., ed. Washington, DC: American Psychological Association; 2009:147-173.
Yen Y.-C.,Ho R.-G.,Liao W.-W.,Chen L.-J.,Kuo C.-C.An empirical evaluation of the slip correction in the four parameter logistic models with computerized adaptive testing.Applied Psychological Measurement. 2012;36:75-87.