Hülya Olmuş, Ezgi Nazman, Semra Erbaş
2.104 308


Our aim is to evaluate parameter estimation of two parameters item response theory (2-PL IRT) model using Joint Maximum Likelihood (JML). A simulation study is approached in terms of different sample sizes, number of items and levels of ability parameters for different level of discirimination parameter. As a result of this simulation study examinee ability parameter, item discrimination and difficulty parameters are obtained as well as Test Information Function and Point-biserial Correlation. One of the highlighted results shows that the level of discrimination parameter plays an important role in parameter estimation for 2-PL IRT models. 


two-parameter item response theory, joint maximum likelihood estimation, parameter estimation, discrimination parameter, ability parameter

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Andersen, E. B., “Sufficient Statistics and Latent Trait Models”, Psychometrica, 42, 69-81, (1977).

Baker, F. B., The Basics of Item Response Theory, ERIC Clearinghouse on Assessment and Evaluation, ( 2001).

Baker, F. B. and Kim, S. H., Item Response Theory: Parameter Estimation Techniques, Second Edition, (2004).

Baur, T. and Lukes, D., 2009. An Evaluation of the IRT Models Through Monte Carlo Simulation, Journal of Undergraduate Research XII.

Birnbaum, A., Some Latent Trait Models and Their Use in Inferring an Examinee’s Ability, In F.M. Lord & M.R. Novick (Eds.), Statistical Theories of Mental Test Scores, (1968).

Cai, L., and Thissen, D., Modern Approaches to Parameter Estimation in Item Response Theory. In S. P. Reise & D. A. Revicki (Eds.), Handbook of Item Response Theory Modeling: Applications to Typical Performance Assessment (pp. 41-59). New York, NY: Routledge, (2014).

Hambleton, R.K., “Item Response Theory: Introduction and Bibliography”, Psicothema, 2(1), 97-107, (1990).

Harris, D., Comparison of 1-,2- and 3-Parameter IRT Models, Instructional Topics in Educational Measurement, An NCME Instructional Module on, (1989).

Hulin, C. L., Drasgow, F., and Parsons, C. K., Item Response Theory: Application to Psychological Measurement, Homewood, I11: Dow Jones-Irwin, (1983).

Mellenberg, G.J., “Generalized Linear Item Response Theory”, American Psychological Association, 115 (2), 300-307,( 1994).

Le, D. T., Applying Item Response Theory Modeling in Educational Research, Iowa State University Digital Repository, (2013).

Paolino, J. P., “Penalized Joint Maximum Likelihood Estimation Applied to Two Parameter Logistic Item Response Models”, Graduate School of Arts and Sciences, Columbia University, (2013).

Rasch, G., Probabilistic Models for Some Intelligence and Attainment Tests, Chicago: MESA, (1960).

Rizopoulos, D., “ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses”, Journal of Statistical Sofware, 17 (5), (2006).

Toribio, S. G., “Bayesian Model Checking Strategies for Dichotomous Item Response Theory Models”, Graduate College of Bowling Green State University, (2006).