Sample Size Requirements for Parameter Recovery in the 4-Parameter Logistic Model

ABSTRACT

In practice, some test items may display misfit at the upper-asymptote of item characteristic curve due to distraction, anxiety, or carelessness by the test takers (i.e., the slipping effect). The conventional item response theory (IRT) models do not take the slipping effect into consideration, which may violate the model fit assumption in IRT. The 4-parameter logistic model (4PLM) includes a parameter for the misfit at the upper-asymptote. Although the 4PLM took more attention by researchers in recent years, there are a few studies on the sample size requirements for the 4PLM in the literature. The current study investigated the sample size requirements for the parameter recovery in the 4PLM with a systematic simulation study design. Results indicated that the item parameters in the 4PLM can be estimated accurately when the sample size is at least 4000, and the person parameters, excluding the extreme ends of the ability scale, can be estimated accurately for the conditions with a sample size of at least 750.

KEYWORDS:

• 4-parameter logistic model
• sample size
• parameter recovery
• item response theory