Multivariate Statistics

We will begin our journey by exploring the multivariate approach to data analysis. Key topics will include the multivariate normal distribution, the variance-covariance matrix, and the Mahalanobis distance. As we progress, we will delve into Principal Components Analysis (PCA), discussing both its theoretical underpinnings and practical applications. This will set the stage for our exploration of latent variable models, starting with the common factor model. Here, we will introduce concepts such as Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA), examining various estimation methods, goodness-of-fit statistics, and issues related to model specification. Our discussions will also cover marked methods, both standardized and unstandardized solutions, modification indices, interpretation of results, higher-order factors, and analysis of invariance, all integral to understanding and implementing factor analysis.

The culmination of our course will be an in-depth look at Structural Equation Modeling (SEM), a powerful statistical technique that allows for the analysis of complex relationships between observed and latent variables. Throughout the course, we will conduct practical tutorials using the R programming language, focusing on essential libraries such as 'psych' and 'lavaan'. These sessions are designed to enhance your analytical skills and provide hands-on experience. Read Less