To assess the accuracy associated with estimating \(\mathbf{Q}\) we employ both matrix- and element-wise recovery rates across replication \(r\). As the estimation is valid up to a permutation, we present the accuracy rates after permutating the estimated Q matrix across all trait (column) orderings. Once the Q matrix has been permutated, we then compute and show the respective metric.
Matrix-wise recovery rate is defined as: \[ \frac{1}{R}\sum _{r=1}^R\mathcal I(\widehat{{Q}}^{(r)}=\widehat{Q}) \]
Element-wise recovery rate is defined as: \[ \frac{1}{R}\sum _{r=1}^R\frac{1}{JK}\sum _{j=1}^J\sum _{k=1}^K\mathcal I(\hat{q}_{jk}^{(r)}=q_{jk}) \]