This is the page associated with our chapter, Exploratory Factor Analysis, in Breakwell, Sutton & Wright (2011). We go through extra detail on some of the computations, showing them in both R, SPSS, and CEFA (a do-it-all comprehensive package for EFA).
Data sets: The data are in different formats because the different packages like them in different formats.
Spearman's data
Table for R (ASCII, so can be read in Notepad)
as a R data object
as an SPSS .sav file
as an SPSS .sps file (ASCII, so can be read in Notepad)
as a .inp file for CEFA (ASCII, so can be read in Notepad)
Social Anxiety data
Table (for read.table in R, an ASCII file)
as a R data object
as an SPSS .sav file
as an SPSS .sps file (ASCII, so can be read in Notepad)
as a .inp file for CEFA (ASCII, so can be read in Notepad)
Packages:
SPSS/PASW You have to buy this, but if you are at a university you may have a cite license.
R Go to mirror, and following the instructions to download for the appropriate platform. For an intro to R, go here. The code was written in TINN-R, available on a number of cites including here.
CEFA (Comprehensive EFA) Go here, tick CEFApak, and follow instructions. Get the manual when asked! A brief intro is here.
Example 1. Single Factor Model with small n (from Spearman data)
Spearman's data in R: code, output (which includes code)
Spearman's data in SPSS: output (which includes syntax in the log boxes above each bit of output)
Spearman's data in CEFA. See here.
Comparing the three programs for the single factor model here.
Example 2. Two Factor Model
Social anxiety in R: code, output (which includes code)
Social anxiety in SPSS: output.
Social anxiety in CEFA. See here.
If you want to add an example of your own, email us here
What is an eigenvalue and principal component analysis? here
Lecture slides
(these are part of Dan's first year graduate course so get updated annually)
Introduction to EFA here (these are the slides for the chapter)
Latent trait and latent class models here
Principal component analysis here
Multiple Choice Questions
(Instructors: contact publisher)
Useful links
Thurstone Psychometric Lab (UNC). (Thurstone on Thurstone here)
Lots of useful factor analysis/measurement papers here.
Classic References
Spearman, C. (1904). “General Intelligence”, Objectively determined and measured. American Journal of Psychology, 15, 201-93. Here
Thurstone, L. L. (1934). The vectors of mind. Psychological Review, 41, 1-32. here.
Introductions
Bartholomew, D. J., Steele, F., Moustaki, I., & Galbraith, J. I. (2002). The analysis and interpretation of multivariate data for social scientists. Chapman & Hall: CRC. Chapter 6. This book is particularly useful for latent variable models because it brings several latent variable techniques together within the same framework.
Everitt, B. S. (1999). Making sense of statistics in psychology. Oxford: OUP. Everitt has a 25 page chapter the describes EFA and PCA clearly and compactly, providing both examples and some of the maths. Everitt prints the correlation matrix. To run this from SPSS see here.
Hair, J. F. Jr., Anderson, R. E., Tatham, R. L. & Black, W. C. (1998). Multivariate data analysis (5th edition). Upper Saddle River: NJ: Prentice-Hall International. Chapter 3 covers factor analysis. This is a well written book at about the right level for this course.
Loehlin, J. C. (1998). Latent variable models: An introduction to factor, path, and structural analysis. London: Lawrence Erlbaum Associates. Many places have graduate courses just on latent variable models and many of these use this excellent textbook.
Stevens, J. (various editions). Applied multivariate statistics from the social sciences. New Jersey: LEA. Stevens describes principal component analysis (PCA) which as discussed in the lecture is related to EFA. He uses both SPSS and SAS.
More Advanced
Johnson, R. A. & Wichern, D. W. (2002). Applied multivariate statistical analysis (5th edition). New Jersey: Pearson Education. If you want to mathematics behind EFA and are okay with matrix algebra, this is a good source.
Mulaik, S. A. (2010). Foundations of Factor Analysis: Second Edition. Chapman & Hall/CRC: Boca Raton, FL. errata here. This is the long over-due second edition of a classic.
Niel Waller's course here
+ Lots of other statistics books.
On Item Response Modeling (also called latent trait modeling)
Embretson, S. E. & Reise, S. P. (2000). Item response theory for psychologists. Mahmah, NJ: Lawrence Erlbaum Associates.
Henard, D. H. (2000). Item response theory. In L. G. Grimm & P. R. Yarnold (Eds.) Reading and Understanding More Multivariate Statistics (pp. 67-97). Washington, DC: American Psychological Association. This is a good introductory chapter.
Reise, S.P., Ainsworth, A.T., Haviland, MG. (2005). Item response theory. CD in PS. Great intro available on psychologicalscience.org.
Rizipolous, D. (2009). http://cran.r-project.org/web/packages/ltm/ltm.pdf This is an R package that is used in the lectures.
Wright, D. B., & Skagerberg, E. M. (2006). A dialogue about MCQs, reliability, and item response modelling. Psychology Teaching Review, 12, 66-79. The link is to the whole issue, just print what you want.
Zickar, M.J. (1998). Modeling item-level data with item response theory. Current Directions in Psychology, 7, 104-109. This is a review article aimed at postgraduates. It is available from psychologicalscience.org.
On Taxometrics (which was discussed in an early draft of the chapter, but we ran out of words)
Ruscio, J., Haslam, N., and Ruscio, A. M. (2006). Introduction to the taxometric method: A practical guide. Mahwah, NJ: Lawrence Erlbaum Associates. here.
Waller, N.G., & Meehl, P. E. (1998). Multivariate taxometric procedures: Distinguishing types from continua. Thousand Oaks, CA : Sage Publications. Waller used to have a good page on taxometrics, but the link is down. This will be added when available.
Latent class modeling
Bartholomew et al. (2002, above) Chapter 10.
Seminar at UCLA here (using MPlus)
Brief introduction (but some math) here
Brief introduction (bit less math) here
Matrices
Gilbert Strange's MIT Linear Algebra Course
DRAFT in Word .docx (may not download), DRAFT in .doc (formatting may be off)
DRAFT in pdf