Factor analysis Definition & Meaning

Factor analysis is a statistical technique used in the field of multivariate statistics to identify underlying relationships between observed variables. The primary goal of factor analysis is to explain the observed variability among correlated variables in terms of a potentially lower number of unobserved variables called factors. These factors are considered to represent the common underlying dimensions that are responsible for the observed correlations among variables.

Here are the key components and steps involved in factor analysis:

• Variables: Factor analysis begins with a set of observed variables, which are often correlated. These variables could be measurements or responses collected from a sample or dataset.

• Factor Structure: The analysis assumes that there are underlying factors that influence the observed variables. The goal is to identify these factors and understand their relationships with the observed variables.

• Loadings: Each observed variable is associated with one or more factors, and these associations are represented by "loadings." Loadings indicate the strength and direction of the relationship between a variable and a factor. High loadings suggest a strong relationship.

• Eigenvalues: Eigenvalues are used to determine the number of factors to retain in the analysis. An eigenvalue represents the amount of variance explained by a factor. Factors with eigenvalues greater than 1 are typically retained.

• Factor Rotation: After identifying the initial factor structure, rotation techniques (e.g., Varimax, Promax) may be applied to make the factors more interpretable and easier to understand.

Factor analysis is commonly used in psychology, economics, marketing, and other fields to explore the underlying structure of observed variables. It can help researchers identify common patterns, reduce data complexity, and gain insights into the latent constructs influencing the observed data.