On this Picostat.com statistics page, you will find information about the Schutz data set which pertains to The Schutz correlation matrix example from Shapiro and ten Berge. The Schutz data set is found in the psych R package. You can load the Schutz data set in R by issuing the following command at the console data("Schutz"). This will load the data into a variable called Schutz. If R says the Schutz data set is not found, you can try installing the package by issuing this command install.packages("psych") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Schutz R data set. The size of this file is about 513 bytes.
The Schutz correlation matrix example from Shapiro and ten Berge
Shapiro and ten Berge use the Schutz correlation matrix as an example for Minimum Rank Factor Analysis. The Schutz data set is also a nice example of how normal minres or maximum likelihood will lead to a Heywood case, but minrank factoring will not.
The format is:
num [1:9, 1:9] 1 0.8 0.28 0.29 0.41 0.38 0.44 0.4 0.41 0.8 ...
- attr(*, "dimnames")=List of 2
..$ :1] "Word meaning" "Odd Words" "Boots" "Hatchets" ...
..$ : chr [1:9] "V1" "V2" "V3" "V4" ...
These are 9 cognitive variables of importance mainly because they are used as an example by Shapiro and ten Berge for their paper on Minimum Rank Factor Analysis.
The solution from the
fa function with the fm='minrank' option is very close (but not exactly equal) to their solution.
Richard E. Schutz,(1958) Factorial Validity of the Holzinger-Crowdeer Uni-factor tests. Educational and Psychological Measurement, 48, 873-875.
Alexander Shapiro and Jos M.F. ten Berge (2002) Statistical inference of minimum rank factor analysis. Psychometrika, 67. 70-94
#f4min <- fa(Schutz,4,fm="minrank") #for an example of minimum rank factor Analysis
#f4 <- fa(Schutz,4,fm="mle") #for the maximum likelihood solution which has a Heywood case
Dataset imported from https://www.r-project.org.