Four-parameter models have received increasing psychometric attention in recent years, as a reduced upper asymptote for item characteristic curves can be appealing for measurement applications such as adaptive testing and person-fit assessment. However, applications can be challenging due to the large number of parameters in the model. In this article, we demonstrate in the context of mathematics assessments how the slip and guess parameters of a four-parameter model may often be empirically related. This observation also has a psychological explanation to the extent that both asymptote parameters may be manifestations of a single item complexity characteristic. The relationship between lower and upper asymptotes motivates the consideration of an asymmetric item response theory model as a three-parameter alternative to the four-parameter model. Using actual response data from mathematics multiple-choice tests, we demonstrate the empirical superiority of a three-parameter asymmetric model in several standardized tests of mathematics. To the extent that a model of asymmetry ultimately portrays slips and guesses not as purely random but rather as proficiency-related phenomena, we argue that the asymmetric approach may also have greater psychological plausibility.

近年来，四参数模型受到越来越多的心理学关注，因为减少项特征曲线的上渐近线对于诸如自适应测试和人体适应性评估之类的测量应用可能具有吸引力。但是，由于模型中有大量参数，应用程序可能会面临挑战。在本文中，我们在数学评估的背景下演示了四参数模型的滑移和猜测参数通常如何在经验上相关。这种观察还具有心理上的解释，即两个渐近线参数都可能是单个项目复杂性特征的体现。下渐近线和上渐近线之间的关系促使人们考虑将不对称项目响应理论模型作为四参数模型的三参数替代方案。使用来自数学选择题测试的实际响应数据，我们在几个标准化的数学测试中证明了三参数不对称模型的经验优势。在一定程度上，不对称模型最终描绘了滑移，并猜测其不像纯粹是随机的，而是像与熟练程度有关的现象那样，我们认为非对称方法也可能具有更大的心理似然性。