A brief review of various information criteria is presented for the detection of differential item functioning (DIF) under item response theory (IRT). An illustration of using information criteria for model selection as well as results with simulated data are presented and contrasted with the IRT likelihood ratio (LR) DIF detection method. Use of information criteria for general IRT model selection is discussed.
AkaikeH. (1973). Information theory and an extension of the maximum likelihood principle. In PetrovB. N.CsákeF. (Eds.), 2nd International Symposium on Information Theory (pp. 267-281). Budapest, Hungary: Akadémiai Kiadó.
2.
AkaikeH. (1976). On entropy maximization principle. In KrishnaiahP. R. (Ed.), Applications of statistics: Proceedings of the symposium held at Wright State University, Dayton, Ohio. (pp. 27-53) Amsterdam, The Netherlands: North-Holland.
3.
BakerF. B.KimS.-H. (2004). Item response theory: Parameter estimation techniques (2nd ed.). New York, NY: Dekker.
4.
BishopY. M. M.FienbergS. E.HollandP. W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: The MIT Press.
5.
BockR. D.AitkinM. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459; 47, 369 (Errata).
6.
BockR. D.LiebermanM. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179-197.
7.
BockR. D.MoustakiI. (2007). Item response theory in a general framework. In RaoC. R.SinharayS. (Eds.), Handbook of statistics (Vol. 26, pp. 469-513). Amsterdam, The Netherlands: Elsevier.
8.
BozdoganH. (1987). Model selection and Akaike’s Information Criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345-370.
9.
BurnhamK. P.AndersonD. R. (1998). Model selection and inference: A practical information-theoretic approach. New York, NY: Springer-Verlag.
10.
CaiL. (2012). flexMIRT: A numerical engine for multilevel item factor analysis and test scoring (Version 1.88) [Computer software]. Seattle, WA: Vector Psychometric Group.
11.
CaiL.ThissenD.du ToitM. (2011). IRTPRO: Item response theory for patient-reported outcomes [Computer software]. Lincolnwood, IL: Scientific Software International.
12.
CohenA. S.ChoS.-J. (2016). Information criteria. In van der LindenW. J. (Ed.), Handbook of item response theory (Vol. 2, pp. 363-378). Boca Raton, FL: CRC Press.
13.
CohenA. S.KimS.-H.WollackJ. A. (1996). An investigation of the likelihood ratio test for detection of differential item functioning. Applied Psychological Measurement, 20, 15-26.
14.
de AyalaR. J. (2009). The theory and practice of item response theory. New York, NY: The Guilford Press.
15.
deLeeuwJ. (1992). Introduction to Akaike (1973) information theory and an extension of the maximum likelihood principle. In KotzS.JohnsonN. L. (Eds.), Breakthroughs in statistics, Volume I: Foundations and basic theory (pp. 599-609). New York, NY: Springer-Verlag.
16.
FujikoshiY.SatohK. (1997). Modified AIC and Cp in multivariate linear regression. Biometrika, 84, 707-716.
HurvichC. M.TsaiC.-L. (1989). Regression and time series model selection in small samples. Biometrika, 76, 297-307.
19.
JudgeG. G.GriffithsW. E.HillR. C.LütkepohlH.LeeT.-C. (1985). The theory and practice of econometrics (2nd ed.). New York, NY: John Wiley.
20.
KangT.-H.CohenA. S. (2007). IRT model selection methods for dichotomous items. Applied Psychological Measurement, 31, 331-358.
21.
KangT.-H.CohenA. S.SungH.-J. (2009). IRT model selection methods for polytomous items. Applied Psychological Measurement, 33, 499-518.
22.
KimS.-H. (2007). Some posterior standard deviations in item response theory. Educational and Psychological Measurement, 67, 258-279.
23.
KimS.-H.CohenA. S. (1998). Detection of differential item functioning under the graded response model with the likelihood ratio test. Applied Psychological Measurement, 22, 345-355.
24.
Klein EntinkR. H.FoxJ.-P.van der LindenW. J. (2009). A multivariate multilevel approach to the modeling of accuracy and speed of test takers. Psychometrika, 74, 21-48.
25.
KullbackS. (1959). Information theory and statistics. New York, NY: John Wiley.
26.
LiF.CohenA. S.KimS.-H.ChoS.-J. (2009). Model selection methods for dichotomous mixture IRT models. Applied Psychological Measurement, 33, 353-373.
27.
LordF. M. (1968). An analysis of the Verbal Scholastic Aptitude Test using Birnbaum’s three-parameter logistic model. Educational and Psychological Measurement, 28, 989-1020.
28.
LordF. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
29.
MagisD.TuerlinckxF.De BoeckP. (2015). Detection of differential item functioning using the lasso approach. Journal of Educational and Behavioral Statistics, 40, 111-135.
30.
MayH. (2006). A multilevel Bayesian item response theory method for scaling socioeconomic status in international studies of education. Journal of Educational and Behavioral Statistics, 31, 63-79.
31.
MeadeA. W.WrightN. A. (2012). Solving the measurement invariance anchor item problem in item response theory. Journal of Applied Psychology, 97, 1016-1031.
32.
ParzenE.TanabeK.KitagawaG. (Eds.). (1998). Selected papers of Hirotugu Akaike. New York, NY: Springer-Verlag.
33.
RaoC. R. (1973). Linear statistical inference and its applications (2nd ed.). New York, NY: John Wiley.
34.
RaoC. R.WuY. (2001). On model selection (with discussions and rejoinder). In LahiriP. (Ed.), Model selection (pp. 1-64). Beachwood, OH: Institute of Mathematical Statistics.
35.
RissanenJ. (1978). Modeling by shortest data description. Automatica, 14, 465-471.
36.
SakamotoY.IshiguroM.KitagawaG. (1986). Akaike information criterion statistics. Tokyo, Japan: KTK Scientific Publishers.
37.
SchwartzG. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461-464.
38.
ScloveS. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333-343.
39.
ShibataR. (1989). Statistical aspects of model selection (IIASA Working Paper, No. WP-89-077). Laxenburg, Austria: International Institute for Applied Systems Analysis. Retrieved from http://pure.iiasa.ac.at/3267/1/WP-89-077.pdf
40.
SpiegelhalterD. J.BestN. G.CarlinB. P.van der LindeA. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B, 64, 353-616.
41.
SugiuraN. (1978). Further analysis of the data by Akaike’s information criterion and the finite corrections. Communications in Statistics: Part A–theory and Methods, A, 7, 13-26.
42.
ThissenD. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175-186.
43.
ThissenD. (1991). MULTILOG user’s guide: Multiple, categorical item analysis and test scoring using item response theory (Version 6.0). Chicago, IL: Scientific Software.
44.
ThissenD. (2001). IRTLRDIF v.2.0b: Software for the computation of the statistics involved in item response theory likelihood-ratio tests for differential item functioning. Chapel Hill: L. L. Thurstone Psychometric Laboratory, University of North Carolina.
45.
ThissenD.ChenW.-H.BockR. D. (2002). MULTILOG: Multiple, categorical item analysis and test scoring using item response theory [Computer software]. Lincolnwood, IL: Scientific Software International.
46.
ThissenD.SteinbergL.GerrardM. (1986). Beyond group differences: The concept of item bias. Psychological Bulletin, 99, 118-128.
47.
ThissenD.SteinbergL.WainerH. (1988). Use of item response theory in the study of group differences in trace lines. In WainerH.BraunH. I. (Eds.), Test validity (pp. 147-169). Hillsdale, NJ: Lawrence Erlbaum.
48.
ThissenD.WainerH. (1982). Some standard errors in item response theory. Psychometrika, 47, 397-412.
49.
TutzG.SchaubererG. (2015). A penalty approach to differential item functioning in Rasch models. Psychometrika, 80, 21-43.
50.
VenablesW. N.SmithD. M., & The R Development Core Team. (2009). An introduction to R (2nd ed.). La Vergne, TN: Network Theory.