<p>When entering a French university, the students’ foreign language level is assessed through a placement test. In this work, we model the placement test results using binary latent block models which allow us to simultaneously form homogeneous groups of students and of items. However, a major difficulty in latent block models is to correctly select the number of rows and the number of columns. The first purpose of this paper is to tune the number of initializations needed to limit the initial values problem in the estimation algorithm to propose a model selection procedure in the placement test context. Computational studies are investigated based on simulated data sets and on two placement test data sets. The second purpose is to investigate the robustness of the proposed model selection procedure in terms of stability of the groups of students when the number of students varies.</p>