Principal component analysis on the covariance matrix for data reduction in large-scale assessments

Abstract The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix as a data reduction method for the contextual variables. This adjustment, compared to the conventional use of a correlation matrix, weights variables with respect to sample size. In a simulation study involving low test reliability for a subset of the sample, we found that PCA-covariance substantially reduces estimation bias and mean squared error. We demonstrate how a large-scale assessment can transition to using PCA-covariance without impacting primary trend inferences using data from the 2022 National Assessment of Educational Progress (NAEP). Our findings demonstrate that PCA-covariance accommodates a broader reporting scope with improved estimation.