1. The four steps in Rasch trees seemed to be similar to iterative procedure in DIF analysis, but in semi-parametric approach.
2. It was assumed that all important/interested covariates were provided in the study. What will be if an important covariate was not provided. In mixture approach, the covariates/groups were found during estimation. In this sense, the proposed approach is not likely to perform better when the membership was unobserved.
3. The most interesting about the proposed method is that under the same covariate (e.g., male), different groups (e.g., group <= 35 & group > 35) still can be found (see Figure 1). How can it be modeled by LR?