1. The performance of polychoric correlation is not consistent and reliable. Though it was argued that the potential benefits of the poychoric correlations are expected for ordered polytomous variables, the serious non-convergence hamper the implicaiton of the polychoric correlations. Thus, it is suprising that the authors still recommended it in the paper.
2. What’s the real reason for the deterioration in performance with increasing sample size? The interpretation provided in the paper seemed to fail to explain the results.