At the population level, parallel data have equal inter-item covariances (i.e., non-diagonal elements of the covariance matrix) and equal variances (i.e., diagonal elements of the covariance matrix). For example, the following data satisfy the parallel condition. In parallel data, even if a correlation matrix is used instead of a covariance matrix, there is no loss of information. All parallel data are also tau-equivalent, but the reverse is not true. That is, among the three conditions, the parallel condition is most difficult to meet.