Pennsylvania State University, PA, USA.
Br J Math Stat Psychol. 2010 Nov;63(Pt 3):509-25. doi: 10.1348/000711009X474502. Epub 2009 Dec 23.
We explore the justification and formulation of a four-parameter item response theory model (4PM) and employ a Bayesian approach to recover successfully parameter estimates for items and respondents. For data generated using a 4PM item response model, overall fit is improved when using the 4PM rather than the 3PM or the 2PM. Furthermore, although estimated trait scores under the various models correlate almost perfectly, inferences at the high and low ends of the trait continuum are compromised, with poorer coverage of the confidence intervals when the wrong model is used. We also show in an empirical example that the 4PM can yield new insights into the properties of a widely used delinquency scale. We discuss the implications for building appropriate measurement models in education and psychology to model more accurately the underlying response process.
我们探讨了四参数项目反应理论模型（4PM）的合理性和构建，并采用贝叶斯方法成功地恢复了项目和被试的参数估计。对于使用 4PM 项目反应模型生成的数据，与使用 3PM 或 2PM 相比，使用 4PM 可提高整体拟合度。此外，尽管在各种模型下估计的特质得分几乎完全相关，但在特质连续体的高低端进行推断时，使用错误的模型会导致置信区间的覆盖范围较差。我们还在一个实证示例中表明，4PM 可以深入了解广泛使用的犯罪行为量表的特性。我们讨论了在教育和心理学中构建适当的测量模型以更准确地模拟潜在反应过程的意义。
