Mixed-effects location scale models for joint modelling school value-added effects on the mean and variance of student achievement

TL;DR

This paper extends traditional school value-added models by incorporating analysis of achievement variability across schools using mixed-effects location scale models, providing deeper insights into school performance beyond average effects.

Contribution

It introduces mixed-effects location scale models to jointly analyze mean and variance of student achievement, enhancing understanding of school performance variability.

Findings

Identifies schools with unusually high or low achievement variability

Demonstrates the application of location scale models in educational data

Discusses implications for school accountability systems

Abstract

School value-added models are widely applied to study, monitor, and hold schools to account for school differences in student learning. The traditional model is a mixed-effects linear regression of student current achievement on student prior achievement, background characteristics, and a school random intercept effect. The latter is referred to as the school value-added score and measures the mean student covariate-adjusted achievement in each school. In this article, we argue that further insights may be gained by additionally studying the variance in this quantity in each school. These include the ability to identify both individual schools and school types that exhibit unusually high or low variability in student achievement, even after accounting for differences in student intakes. We explore and illustrate how this can be done via fitting mixed-effects location scale versions of the traditional school value-added model. We discuss the implications of our work for research and school accountability systems.