Assessment of school performance through a multilevel latent Markov Rasch model

TL;DR

This paper introduces a multilevel latent Markov Rasch model to analyze longitudinal binary data with covariates, accounting for clustering effects, and demonstrates its application in assessing middle-school students' math achievement development.

Contribution

It extends the latent Markov Rasch model to include cluster effects and provides an EM algorithm for maximum likelihood estimation, enabling better assessment of educational progress.

Findings

Model effectively captures student ability development over time.

Cluster effects significantly influence test scores.

Application demonstrates practical utility in educational assessment.

Abstract

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, e.g. students clustered in classes. For each subject, the latent process is used to represent the characteristic of interest (e.g. ability) conditional on the effect of the cluster to which he/she belongs. The latter effect is modeled by a discrete latent variable associated with each cluster. For the maximum likelihood estimation of the model parameters we outline an EM algorithm. We show how the proposed model may be used for assessing the development of cognitive Math achievement. This approach is applied to the analysis of a dataset collected in the Lombardy Region (Italy) and based on test scores over three years of middle-school students attending public and private schools.