Canonical correlation analysis in education: associations between student evaluations of courses and instructors

At the Technical University of Denmark (DTU) course evaluations are performed by the students on a questionnaire. On one form the students are asked specific questions regarding the course. On a second form they are asked specific questions about the teacher. We propose to apply canonical correlation analysis (CCA) to investigate the association between how students evaluate the course and how students evaluate the teacher and to reveal the structure of this association. Student’s evaluation data is characterized by high correlation between the variables (questions) and insufficient sample size, which can lead to inaccurate estimates of parameters, non-generalizable and hardly interpretable results of CCA. Newly developed regularized CCA and sparse CCA methods are used to address weaknesses of CCA. Regularized CCA is uses an $L_2$ penalization to shrink the weights by imposing penalty on their size; highly correlated variables get similar weights, resulting in a grouping effect. Sparse CCA incorporates variable selection in both sets of variables by introducing Lasso penalization.