Value added in hierarchical linear mixed models with error in variables

Abstract

In this paper, we propose a methodology to evaluate the effects on the value-added estimators when there is a measurement error in variables. These errors lead to biased estimators; in most cases, these estimators have a large variance. The proposed methodology is illustrated under two scenarios: First, simulation studies for discussing the effects on value-added estimates for some values of reliability. Second, an application for real data using a Colombian database that contains the scores of two standardized tests: Saber 11 and Saber Pro. In the first test, the students are evaluated in the 11th grade of high school. In the second test, the students are evaluated in the last two years of the undergraduate program. We also implement the estimation method taking into account measurement error and adapt the Bootstrap procedure to Hierarchical Linear Mixed Model with error in variables. The results show that measurement error affects the higher-education value-added and the estimator variance. This implies universities can be incorrectly classified. Therefore, we may assert that any given university is contributing to students’ progress when, in reality, this is not so.