Lecture Overview

Welcome to Multivariate Statistical Modelling!

In our technology-driven world, we are surrounded by vast amounts of data. In psychology and cognitive neuroscience, our measurement techniques are becoming increasingly powerful, providing us with highly valuable but complex data. With this comes the need to understand and make sense of this data. For example, to understand patterns of gene expression and their relationship to brain function and complex human cognition, emotion and behaviour, and even the vast networks of social interactions, we cannot simply eyeball the data provided by our technology-driven measurement tools. Even simple questionnaire data cannot be understood just by looking at it. All of this data contains many variables that correlate and interact with each other. This is where multivariate statistics comes in. Without multivariate statistical modelling, we cannot make sense of these important sources of data that have the potential to improve human brain and mental health and, ultimately, well-being.

This course will provide you with powerful tools and techniques for understanding linear and non-linear associations in multivariate data. We will discuss methods that allow us to analyse multiple variables of different types simultaneously, revealing patterns of relationships and insights that would otherwise remain hidden. More specifically, we begin the lecture by ensuring that all students have a firm grounding in the General Multivariate Linear Model, a powerful framework that extends the familiar concepts of simple linear regression to include multiple quantitative predictors of a quantitative outcome. From there, in the second lecture we will explore how to deal with situations where our independent variable is not continuous. Categorical regression provides the means to analyse relationships between a categorical predictor and a quantitative outcome variable. We will then change the type of outcome variable to categorical and learn about logistic regression and its applications in predicting binary events. We will uncover more nuanced relationships between variables in the fourth lecture session: Moderated regression will allow us to understand how the relationship between two variables can change depending on a third, moderator variable, providing insights into interaction effects. We then move on to understanding simultaneous equations with path modelling, a technique that uses visual diagrams and parameter estimation across multiple regression equations to represent and test hypothesised (causal) relationships between multiple variables - even multiple outcomes. In addition, these models allow the study of so-called mediation effects. Multivariate analysis would not be complete without techniques helping to uncover hidden structures within the data. Exploratory factor analysis (EFA) allows the identification of underlying latent factors that explain the relationships between observed variables, such as personality traits, cognitive abilities, etc. Taking this further and combining factor analysis and path modelling, Structural Equation Modelling (SEM) is introduced as a powerful and highly flexible tool for testing complex relationships involving both observed and latent variables. Our exploration will also extend beyond linear relationships. Polynomial regression will enable us to model curvilinear patterns of association, allowing to capture phenomena where relationships are not simply linear. We will also explore more advanced methods such as spline and local regression, which offer even greater flexibility in modelling non-linear relationships. Recognizing that data often exhibits hierarchical structures, we will finally delve into multilevel regression, a technique designed to analyze nested data, such as students within classrooms within schools or measurement occasions within individuals. Finally, we will summarize procedures of multivariate statistical inference, ensuring that we can understand parameter estimation and hypotheses tests to draw meaningful conclusions from our multivariate data analyses.

I hope the above motivates you to get started. Please note that some topics in high school mathematics and basic statistics are necessary to follow this course. If you do not feel equipped, please make sure you update your knowledge with the material provided in the bridging module “Introduction to Statistics” held during the orientation week. A great reference to look at is Heumann & Schomaker Shalabh (2023) [HSShalabh24].