Sinharay Sandip
McGraw-Hill Education CTB, Monterey, USA.
Psychometrika. 2016 Dec;81(4):992-1013. doi: 10.1007/s11336-015-9465-x. Epub 2015 May 8.
The [Formula: see text] statistic (Drasgow et al. in Br J Math Stat Psychol 38:67-86, 1985) is one of the most popular person-fit statistics (Armstrong et al. in Pract Assess Res Eval 12(16):1-10, 2007). Snijders (Psychometrika 66:331-342, 2001) derived the asymptotic null distribution of [Formula: see text] when the examinee ability parameter is estimated. He also suggested the [Formula: see text] statistic, which is the asymptotically correct standardized version of [Formula: see text]. However, Snijders (Psychometrika 66:331-342, 2001) only considered tests with dichotomous items. In this paper, the asymptotic null distribution of [Formula: see text] is derived for mixed-format tests (those that include both dichotomous and polytomous items). The asymptotically correct standardized version of [Formula: see text], which can be considered as the extension of [Formula: see text] to such tests, is suggested. The Type I error rate and power of the suggested statistic are examined from several simulated datasets. The suggested statistic is computed using a real dataset. The suggested statistic appears to be a satisfactory tool for assessing person fit for mixed-format tests.
[公式：见正文]统计量（Drasgow等人，《英国数学与统计心理学杂志》38:67 - 86，1985年）是最常用的个体拟合统计量之一（Armstrong等人，《实践评估、研究与评价》12(16):1 - 10，2007年）。Snijders（《心理测量学》66:331 - 342，2001年）推导了在估计考生能力参数时[公式：见正文]的渐近零分布。他还提出了[公式：见正文]统计量，它是[公式：见正文]的渐近正确标准化版本。然而，Snijders（《心理测量学》66:331 - 342，2001年）仅考虑了具有二分项目的测试。在本文中，推导了混合格式测试（包括二分项目和多分项目的测试）中[公式：见正文]的渐近零分布。提出了[公式：见正文]的渐近正确标准化版本，可将其视为[公式：见正文]对此类测试的扩展。从几个模拟数据集检验了所提出统计量的I型错误率和功效。使用一个真实数据集计算了所提出的统计量。所提出的统计量似乎是评估混合格式测试中个体拟合度的一个令人满意的工具。
