Researchers frequently use Rasch models to analyze survey responses because these models provide accurate parameter estimates for items and examinees when there are missing data. However, researchers have not fully considered how missing data affect the accuracy of dimensionality assessment in Rasch analyses such as principal components analysis (PCA) of standardized residuals. Because adherence to unidimensionality is a prerequisite for the appropriate interpretation and use of Rasch model results, insight into the impact of missing data on the accuracy of this approach is critical. We used a simulation study to examine the accuracy of standardized residual PCA with various proportions of missing data and multidimensionality. We also explored an adaptation of modified parallel analysis in combination with standardized residual PCA as a source of additional information about dimensionality when missing data are present. Our results suggested that missing data impact the accuracy of PCA on standardized residuals, and that the adaptation of modified parallel analysis provides useful supplementary information about dimensionality when there are missing data.

研究人员经常使用 Rasch 模型来分析调查响应，因为这些模型在缺少数据时可以为项目和受试者提供准确的参数估计。然而，研究人员尚未充分考虑缺失数据如何影响标准化残差的主成分分析 (PCA) 等 Rasch 分析中维度评估的准确性。由于遵守一维性是正确解释和使用 Rasch 模型结果的先决条件，因此了解缺失数据对该方法准确性的影响至关重要。我们使用模拟研究来检验具有不同比例的缺失数据和多维性的标准化残差 PCA 的准确性。我们还探索了改进的并行分析与标准化残差 PCA 的结合，作为存在缺失数据时有关维度的附加信息的来源。我们的结果表明，缺失数据会影响 PCA 对标准化残差的准确性，并且当存在缺失数据时，修改后的并行分析的适应性提供了有关维度的有用补充信息。