Psychology 6140

- Basic Ideas of Factor Analysis
- Goal of factor analysis: Parsimony-- account for a set of observed variables in terms of a small number of latent, underlying constructs.
- Correlation and covariance matrices summarize (linear) relationships among a set of variables.
- 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?
- Rank of a correlation/covariance matrix = number of
*linearly independent*variables. - Factors of a matrix

- Principal components analysis
- Least squares fit to a data matrix
- Eigenvalues and eigenvectors

- The Common Factor Model
- common vs. specific variance
- FA vs. PCA
- Factoring methods: Principal factors, Unweighted Least Squares, Maximum likelihood

- Factor Rotation
- The idea of simple structure
- Analytic rotation methods - orthogonal, oblique, target

- Confirmatory Factor Analysis
- Development of CFA models
- Restricted maximum likelihood FA (RIMLFA)
- Analysis of covariance structures (ACOVS)
- LISREL/EQS structural equations + latent variable models

- 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

- Development of CFA models