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The Schutz correlation matrix example from Shapiro and ten Berge

### Description

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.

### Usage

data("Schutz")

### Format

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" ...

### Details

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.

This example is used to show problems with different methods of factoring. Of the various factoring methods, fm = "minres", "uls", or "mle" produce a Heywood case. Minrank, alpha, and pa do not.

See the blant data set for another example of differences across methods.

### Source

Richard E. Schutz,(1958) Factorial Validity of the Holzinger-Crowdeer Uni-factor tests. Educational and Psychological Measurement, 48, 873-875.

### References

Alexander Shapiro and Jos M.F. ten Berge (2002) Statistical inference of minimum rank factor analysis. Psychometrika, 67. 70-94

### Examples

data(Schutz)
corPlot(Schutz,numbers=TRUE,upper=FALSE)
#f4min <- fa(Schutz,4,fm="minrank") #for an example of minimum rank factor Analysis
#compare to
#f4 <- fa(Schutz,4,fm="mle") #for the maximum likelihood solution which has a Heywood case