The Linear Logistic Test Model (LLTM) is a valuable statistical tool for the development of psychological tests which allows for the demonstrably fair assessment of traits in the educational context. One crucial feature of the LLTM is that model fit can be assessed by means of a Likelihood Ratio Test (LRT), given that a Rasch Model (RM) could be established for a data set. The theoretic appeal of this procedure suffers somewhat from the fact that in many practical applications the LRT rejects the LLTM. This raises the question whether the LRT is a robust procedure, i.e. whether it maintains the chosen nominal alpha niveau. By means of a simulation study (using the R-language) the robustness properties of the test were investigated. We were able to identify conditions, where the LRT in fact shows non-robust behavior and therefore provides misleading results. Our results provide means to identify problematic conditions and hence protect us from drawing artificial conclusions. This is of eminent importance for educational research, as a psychological test actually complying with the model would erroneously be rejected.