When entering 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 to simultaneously form homogeneous groups of students and of items. However, a major difficulty in latent block models is to select correctly the number of groups of rows and the number of groups 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 in order to propose a model selection procedure in the placement test context. Computational studies based on simulated data sets and on two placement test data sets are investigated. The second purpose is to investigate the robustness of the proposed model selection procedure in terms of stability of the students groups when the number of students varies.

翻译：进入法国大学时，学生的外语水平通过水平测试进行评估。本研究使用二元潜在分块模型对测试结果进行建模，该模型能够同时将学生和题目划分为同质组别。然而，潜在分块模型的主要难点在于正确选择行组数和列组数。本文的首要目的是调整初始值数量，以限制估计算法中的初始值问题，从而提出适用于水平测试场景的模型选择程序。基于模拟数据集和两个水平测试数据集的数值研究被开展。第二个目的是探究所提出的模型选择程序的鲁棒性，重点关注学生组别在人数变化时的稳定性。