Exploratory and Confirmatory Factor Analysis

SCS Short Course

February - March, 2008

 Michael Friendly








Part 1: PCA

  PCA and Factor analysis: Overview

  Principal components analysis

  PCA details



US crime rates by state [pca2a.sas]

Plotting principal component scores [pca2g.sas]

Biplot of US crime data [biplcrime.sas]

Part 2: EFA

  Basic ideas of factor analysis

  Factor estimation methods

  Factor and component rotation


Demo: Partial linear independence


Factor analysis: estimation methods [twofact.sas]

Spearman’s “two-factor” theory [spear5.sas]

Holzinger & Swineford 9 ability measures


H & S rotation methods [psych9r.sas]  

Part 3: CFA

  Restricted ML factor analysis

  ACOVS model

  LISREL model: CFA and SEM

  Factorial invariance

  Power & sample size for EFA & CFA


Ability & aspiration: [calis13.sas] [lisrel1.ls8]

Holzinger & Swineford 9 ability measures [calis16t.sas]

  Output: [calis16t.pdf]

  LISREL: [lisrel4a.ls8] [lisrel4.dat]

Lord’s vocabulary data [calis1c.sas]

Factorial invariance [lisrel12.ls8] [lisrel12.dat]

Power analysis: Lord’s vocabulary data [calis1pow.sas]


Further readings:


Free book manuscript: L.R. Tucker & R. MacCallum, Exploratory Factor Analysis, http://www.unc.edu/~rcm/book/factornew.htm.


Bollen, K. A. (1989). Structural equations with latent variables, New York: Wiley. [A comprehensive introduction to LISREL/SEM models, including path analysis, structural equations, and confirmatory factor analysis, with many worked examples using the LISREL and EQS programs. This is a moderately difficult, graduate level text, but it is among the most complete treatment of LISREL models available. The discussion of rules and methods for identifying parameters of structural equation and factor analysis models is excellent.]

Byrne, B.M. (1998). Structural equation modeling with LISREL, PRELIS, and SIMPLIS. Hillsdale, NJ: Lawrence Erlbaum. [A ‘how-to’ book, with detailed examples of syntax and output. The emphasis is on psychological applications. Mainly covers LISREL 8, but also PRELIS 2, and SIMPLIS.]

Similar books also by Byrne: Structural equation modeling with Amos; Structural equation modeling with EQS.


Comrey, A. L. & Lee, H. B.  (1991). A first course in factor analysis. New York: Academic Press. [A relatively elementary text, mainly on EFA, at the graduate or advanced undergraduate level. The last few chapters contain a good discussion of designing a factor analytic study, with a case study of Comrey's personality scales.


Everitt, B. S. (1984). An Introduction to Latent Variable Models. New York: Chapman and Hall. [If brevity is the soul of wit, Everitt gets the prize for this compact, readable treatment of exploratory and confirmatory factor analysis in under 70 pages, of which half is devoted to a variety of LISREL/SEM models. Numerical examples are provided for most of the methods discussed and an additional chapter describes latent variable models for categorical data.]

Hoyle, Rick H., ed. (1995). Structural equation modeling: Concepts, issues, and applications. Thousand Oaks, CA: Sage Publications. [An edited volume of quite good chapters covering most aspects of CFA and SEM, with many applied examples (no code is presented, however).  A chapter by Hoyle & Panter describes how to write up CFA/SEM studies.]


Loehlin, J. C. (2004). Latent variable models: An introduction to factor, path and structural equation analysis. 4th Ed, Hillsdale, NJ: Lawrence Erlbaum. [A useful introduction to structural modeling, including EFA and CFA for practitioners. A large number of diagrams are presented, and the models are discussed meaningfully]