Introduction to Factor Analysis

Outline

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