The Comparison of Estimation Methods for the Four-Parameter Logistic Item Response Theory Model

ABSTRACT

The four-parameter logistic (4PL) Item Response Theory (IRT) model has recently been reconsidered in the literature due to the advances in the statistical modeling software and the recent developments in the estimation of the 4PL IRT model parameters. The current simulation study evaluated the performance of expectation-maximization (EM), Quasi-Monte Carlo EM (QMCEM), and Metropolis-Hastings Robbins-Monro (MH-RM) estimation methods for the item parameters in the 4PL IRT model under the manipulated study conditions, including the number of factors, the correlation between factors, and test length. The results indicated that there was no method to be recommended as the best one among the three estimation algorithms for the estimation of 4PL item parameters accurately across all study conditions. However, using the MH-RM algorithm for 4PL model item parameter estimation can be suggested when the number of factors is 2 or 3. In addition, it may be advised to prefer long test lengths rather than shorter test lengths (n = 24), as three algorithms provide better item parameter estimates at long test lengths (n = 48).

KEYWORDS:

• 4PL IRT model
• expectation-maximization
• Metropolis-Hastings Robbins-Monro
• Quasi-Monte Carlo EM
• upper asymptote

Acknowledgements

The author expresses his gratitude to İsmail Çuhadarr for valuable comments on earlier versions of this article and extends his thanks to R. Philip Chalmers for helpful communications and suggestions. The author thanks two anonymous reviewers for offering helpful comments that improved the quality of this manuscript and special thanks are due to the editor Randall Schumacker for superb editorial assistance.