Course Catalogue

This course gives an introduction to the basic elements of linear algebra and mathematical calculus that are relevant for statistical modeling and hypothesis testing in psychological research and in related areas of the social sciences. We will go through essential concepts and operations of matrix and vector algebra, differential equations and integral calculus, and we will discuss implications for parameter estimation and measures of statistical uncertainty in multivariate models. Beyond these formal foundations, an advanced overview of applied statistical models will be provided, including linear and generalized linear models, machine learning-based regularization procedures, structural equation models, and multilevel analysis with a particular focus on modeling longitudinal data. The statistical models and procedures will be illustrated with simulated and empirical data. In addition, model specification, parameter estimation and hypothesis testing will be demonstrated and practiced in R. The combination of mathematical foundations and applied statistical analysis enhances the understanding of key concepts of statistical modeling, and it enables students and young researchers to tailor statistical models and tests according to their specific research questions. The course will be conducted using meetings, videos and exercises; meetings are on-site meetings on 12 September, 17 October, 21 November 09:00-12:30 CET each, with an option of digital attendance for remote participants from partner universities. Literature: Dunn, P. K., & Smyth, G. K. (2018). Generalized linear models with examples in R. New York: Springer; Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. New York: Routledge; James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An intro¬duction to statistical learning with applications in R. New York: Springer; Kline, R. B. (2023). Principles and practice of structural equation modeling. New York: Guilford; Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel analysis: An introduction to basic and advanced multilevel modeling. London: Sage