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.