Abstract
Parameters of the two-parameter logistic model are generally estimated via the expectation-maximization algorithm, which improves initial values for all parameters iteratively until convergence is reached. Effects of initial values are rarely discussed in item response theory (IRT), but initial values were recently found to affect item parameters when estimating the latent distribution with full non-parametric maximum likelihood. However, this method is rarely used in practice. Hence, the present study investigated effects of initial values on item parameter bias and on recovery of item characteristic curves in BILOG-MG 3, a widely used IRT software package. Results showed notable effects of initial values on item parameters. For tighter convergence criteria, effects of initial values decreased, but item parameter bias increased, and the recovery of the latent distribution worsened. For practical application, it is advised to use the BILOG default convergence criterion with appropriate initial values when estimating the latent distribution from data.
Highlights
The two-parameter logistic model (2PL; see [1]) is widely used, especially in medical settings and in health care applications (e.g., [2])
By means of a Monte Carlo simulation, the present study investigated effects of initial values and of the convergence criterion on parameters of the 2PL in BILOG-MG 3 [12], a widely used software package in item response theory (IRT) employing MML estimation as well as the empirical histogram (EH) method
Initial values for the latent distribution were (2a) uniform distribution, (2b) BILOG-MG 3 default values, (2c) weights estimated by means of classical test theory, and (2d) values generated by the shortrun procedure
Summary
The two-parameter logistic model (2PL; see [1]) is widely used, especially in medical settings and in health care applications (e.g., [2]). ; ð1Þ where ai and bi label the item discrimination and item difficulty parameter of item i, respectively, and zj denotes the latent ability of testee j These parameters are generally estimated by means of the maximum likelihood (ML) method. As the ML equations do not have simple algebraic solutions, the expectation-maximization (EM) algorithm [7] is usually used to obtain ML estimates for the parameters In this algorithm, assumed initial values for each estimated parameter are improved iteratively until some convergence criterion is met. By means of a Monte Carlo simulation, the present study investigated effects of initial values and of the convergence criterion on parameters of the 2PL in BILOG-MG 3 [12], a widely used software package in IRT employing MML estimation as well as the EH method
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