factoranalysis

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. The primary goal is to reduce the number of variables while retaining as much information from the original variables as possible. It is often used in the social sciences, market research, and product and market analysis.

The underlying assumption of factor analysis is that the observed variables are linear combinations of underlying, unobserved latent factors, plus error terms. These factors represent common underlying causes or constructs that influence multiple observed variables. For example, a set of survey questions about satisfaction with different aspects of a product might be explained by a single underlying factor of "overall satisfaction."

There are two main types of factor analysis: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA is used when the researcher has no specific hypothesis about the factor structure and aims to discover the underlying factors. CFA is used when the researcher has a predefined hypothesis about the number and nature of the factors and tests whether the observed data fit this hypothesized structure.

The process typically involves calculating a correlation matrix of the observed variables, extracting factors that explain a significant portion of the variance, and then rotating the factor solution to improve interpretability. Factor analysis helps in understanding complex relationships between variables and can be a precursor to other statistical analyses.