Examining the robustness of a model selection procedure in the binary latent block model through a language placement test data set

TL;DR

This paper evaluates a model selection method for binary latent block models applied to French university placement test data, focusing on stability and robustness of student grouping.

Contribution

It introduces a procedure to select the number of groups in latent block models and assesses its robustness using simulated and real placement test data.

Findings

The model selection procedure effectively identifies the number of groups.

The stability of student groupings remains consistent despite variations in student numbers.

Simulation studies validate the robustness of the proposed method.

Abstract

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.