This research proposes a new statistic for testing latent variable distribution fit for unidimensional item response theory (IRT) models. If the typical assumption of normality is violated, then item parameter estimates will be biased, and dependent quantities such as IRT score estimates will be adversely affected. The proposed statistic compares the specified latent variable distribution to the sample average of latent variable posterior distributions commonly used in IRT scoring. Formally, the statistic is an instantiation of a generalized residual and is thus asymptotically distributed as standard normal. Also, the statistic naturally complements residual-based item-fit statistics, as both are conditional on the latent trait, and can be presented with graphical plots. In addition, a corresponding unconditional statistic, which controls for multiple comparisons, is proposed. The statistics are evaluated using a simulation study, and empirical analyses are provided.

这项研究提出了一种新的统计数据，用于测试适合一维项目响应理论（IRT）模型的潜在变量分布。如果违反了正常性的典型假设，则项目参数估计值将产生偏差，并且诸如IRT得分估计值等相关数量将受到不利影响。拟议的统计数据将指定的潜在变量分布与IRT评分中常用的潜在变量后验分布的样本平均值进行比较。正式地，统计量是广义残差的实例，因此作为标准正态渐近分布。同样，该统计数据自然补充了基于残差的项目拟合统计数据，因为两者均以潜在特征为条件，并且可以用图形表示。此外，还有相应的无条件统计信息，提出了用于多重比较的控件。使用模拟研究评估统计数据，并提供经验分析。