Marginal maximum likelihood estimation based on the expectation–maximization algorithm (MML/EM) is developed for the one-parameter logistic model with ability-based guessing (1PL-AG) item response theory (IRT) model. The use of the MML/EM estimator is cross-validated with estimates from NLMIXED procedure (PROC NLMIXED) in Statistical Analysis System. Numerical data are provided for comparisons of results from MML/EM and PROC NLMIXED.
AlbertJ. H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational and Behavioral Statistics, 17, 251-269.
2.
BakerF. B. (1998). An investigation of the item parameter recovery characteristics of a Gibbs sampling procedure. Applied Psychological Measurement, 22, 153-169.
3.
BirnbaumA. (1968). Some latent trait models and their use in inferring an examinee’s ability. In LordF. M.NovickM. R. (Eds.), Statistical theories of mental test scores (pp. 397-479). Reading, MA: Addison-Wesley.
4.
BockR. D.AitkinM. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
5.
BockR. D.LiebermanM. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179-197.
6.
GabrielsenA. (1978). Consistency and identifiability. Journal of Econometrics, 8, 261-263.
7.
HambletonR. K.SwaminathanH.RogersH. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage.
KieftenbeldV.NatesanP. (2012). Recovery of graded response model parameters a comparison of marginal maximum likelihood and Markov chain Monte Carlo estimation. Applied Psychological Measurement, 36, 399-419.
10.
KimS.-H. (2001). An evaluation of a Markov chain Monte Carlo method for the Rasch model. Applied Psychological Measurement, 25, 163-176.
11.
KoopmansT. C.ReiersolO. (1950). The identification of structural characteristics. The Annals of Mathematical Statistics, 21, 165-181.
12.
LordF. M.NovickM. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
13.
MarisG.BechgerT. (2009). On interpreting the model parameters for the three parameter logistic model. Measurement, 7, 75-88.
RijmenF.TuerlinckxF.De BoeckP.KuppensP. (2003). A nonlinear mixed model framework for item response theory. Psychological Methods, 8, 185-205.
16.
San MartínE.del PinoG.De BoeckP. (2006). IRT models for ability-based guessing. Applied Psychological Measurement, 30, 183-203.
17.
San MartínE.RolinJ.-M.CastroL. M. (2013). Identification of the 1PL model with guessing parameter: Parametric and semi-parametric results. Psychometrika, 78, 341-379.
ThissenD. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175-186.
20.
van der LindenW.HambletonR. K. (1997). Item response theory: Brief history, common models, and extensions. In van der LindenW.HambletonR. K. (Eds.), Handbook of modern item response theory (pp. 1-28). New York, NY: Springer.
21.
WalkerS. (1996). An EM algorithm for nonlinear random effects models. Biometrics, 52, 934-944.
