Students' proficiency evaluation: a non-parametric multilevel latent variable model approach

In higher education, students' assessment has a two-fold aim: (i) evaluate students' proficiency level concerning the topics of a specific course; (ii) identify students' weaknesses throughout the whole learning activity and, if any, relate them to a set of socio-demographic and psychological covariates/predictors. In this vein, this manuscript proposes a multilevel latent class model as an analytic strategy to detect homogeneous groups of students based on their abilities, operationalized according to the following dimensions: Knowledge, Applying knowledge, and Judgment. As a novelty, the proposed model associates each dimension with a first-level latent class variable, which contributes to the identification of a second-level latent class variable that summarizes students' abilities according to the whole learning activity. The presented empirical results are based on Statistics tests covering three different topics and survey instruments administered to students of an introductory Statistics course. The main results show that the model identifies distinct overall patterns of learning and differences according to ability dimensions and topics. Moreover, the study of the relationships between the second-level latent class variable and socio-demographic and psychological covariates helps to characterize and deeply understand the students' profiles, fostering the development of tailored recommendations.