How to conduct factor analysis and how does it help simplify data?

Factor analysis is a multivariate statistical method that reduces data dimensionality by identifying latent constructs, called factors, underlying observed variables. It helps simplify complex datasets by explaining correlations among variables through a smaller number of these underlying dimensions. Successful application involves meeting key assumptions, primarily linear relationships between variables and factors, and sufficient correlation among variables (often assessed via the KMO test and Bartlett's test). Principal component analysis or maximum likelihood are common techniques for factor extraction. Determining the optimal number of factors relies on criteria like eigenvalues greater than one or the scree plot. Subsequently, factor rotation (e.g., Varimax) enhances interpretability by simplifying the factor structure. Implementation typically requires data screening, selecting appropriate variables, and choosing the factor extraction method. After rotation, factors are interpreted based on variables loading highly on them. This process significantly simplifies data interpretation by reducing numerous variables into a few meaningful, uncorrelated factors. It aids in data visualization, model building by reducing multicollinearity, identifying key underlying constructs, and providing more manageable variables for subsequent analysis.