Despite increases in the number of articles published in higher education journals using structural equation modelling (SEM), research addressing their statistical sufficiency, methodological appropriateness and quantitative rigour is sparse. In response, this article provides a census of all covariance-based SEM articles published up until 2013 (N = 143) across eight leading higher education journals: "The Review of Higher Education, Journal of Higher Education," "Research in Higher Education," "Higher Education," "Studies in Higher Education," "Assessment & Evaluation in Higher Education," Higher Education Research & Development" and Journal of College Student Development." Several areas for improvement are found regarding the statistical application of SEM in higher education research. Recommendations are to focus on: building theoretically supported models, data screening, missing data, estimation methods, sample size and power, fit indices, validity and reliability and the testing of alternative models. Best-practice statistical guidelines for higher education researchers wishing to apply SEM to their research are provided.