AN EVALUATION OF THE TWO PARAMETER (2-PL) IRT MODELS THROUGH A SIMULATION STUDY

Year 2017, Volume: 30 Issue: 1, 235 - 249, 14.03.2017

Hülya Olmuş , Ezgi Nazman Semra Erbaş

Abstract

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. 

Keywords

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

References

• 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).