Introduction to Factor Analysis

Michael Friendly
Psychology 6140


  1. Basic Ideas of Factor Analysis
    1. Goal of factor analysis: Parsimony-- account for a set of observed variables in terms of a small number of latent, underlying constructs.
    2. Correlation and covariance matrices summarize (linear) relationships among a set of variables.
    3. To what extent do a set of observed variables measure the same underlying construct? How many different underlying constructs are needed to account for correlations among a set of observed variables?
    4. Rank of a correlation/covariance matrix = number of linearly independent variables.
    5. Factors of a matrix
  2. Principal components analysis
    1. Least squares fit to a data matrix
    2. Eigenvalues and eigenvectors
  3. The Common Factor Model
    1. common vs. specific variance
    2. FA vs. PCA
    3. Factoring methods: Principal factors, Unweighted Least Squares, Maximum likelihood
  4. Factor Rotation
    1. The idea of simple structure
    2. Analytic rotation methods - orthogonal, oblique, target
  5. Confirmatory Factor Analysis
    1. Development of CFA models
      • Restricted maximum likelihood FA (RIMLFA)
      • Analysis of covariance structures (ACOVS)
      • LISREL/EQS structural equations + latent variable models
    2. Applications of CFA
      • Test theory models of "equivalence
      • Sets of congeneric tests
      • Inter-rater reliability
      • Multi-trait, multi-method data
      • Simplex models for ordered latent variables
      • Factorial invariance