Five classic data sets reported by Harman (1967) are 9 psychological (cognitive) variables taken from Holzinger and 8 emotional variables taken from Burt. Two others are socioeconomic and political data sets. Additionally, 8 physical variables. All five of these are used for tests and demonstrations of various factoring algortithms.
data(Harman)
data(Harman.5)
data(Harman.political)
data(Harman.8)Harman.Holzinger: 9 x 9 correlation matrix of ability tests, N = 696.
Harman.Burt: a 8 x 8 correlation matrix of ``emotional" items. N = 172
Harman.5: 12 census tracts for 5 socioeconomic data (Harman p 14)
Harman.political: p 166.
Harman.8 8 physical measures
Harman.Holzinger. The nine psychological variables from Harman (1967, p 244) are taken from unpublished class notes of K.J. Holzinger with 696 participants. This is a subset of 12 tests with 4 factors. It is yet another nice example of a bifactor solution. Bentler (2007) uses this data set to discuss reliablity analysis. The data show a clear bifactor structure and are a nice example of the various estimates of reliability included in the omega function. Should not be confused with the Holzinger or Holzinger.9 data sets in bifactor.
Harman.Burt. Eight ``emotional" variables are taken from Harman (1967, p 164) who in turn adapted them from Burt (1939). They are said be from 172 normal children aged nine to twelve. As pointed out by Harman, this correlation matrix is singular and has squared multiple correlations > 1. Because of this problem, it is a nice test case for various factoring algorithms. (For instance, omega will issue warning messages for fm="minres" or fm="pa" but will fail for fm="ml".)
The Eight Physical Variables problem is taken from Harman (1976) and represents the correlations between eight physical variables for 305 girls. The two correlated clusters represent four measures of "lankiness" and then four measures of "stockiness". The original data were selected from 17 variables reported in an unpublished dissertation by Mullen (1939).
Variable 6 ("Bitrochanteric diamter") is the distance between the outer points of the hips.
The row names match the original Harman paper, the column names have been abbreviated.
The fa solution for principal axes (fm="pa") matches the reported minres solution, as does the fm="minres".
For those interested in teaching examples using various body measurements, see the body data set in the gclus package.
The Burt data set probably has a typo in the original correlation matrix. Changing the Sorrow- Tenderness correlation from .87 to .81 makes the correlation positive definite.
As pointed out by Jan DeLeeuw, the Burt data set is a subset of 8 variables from the original 11 reported by Burt in 1915. That matrix has the same problem. See burt.
Other example data sets that are useful demonstrations of factor analysis are the seven bifactor examples in Bechtoldt and the 24 ability measures in Harman74.cor
There are several other Harman examples in the psych package (i.e., Harman.8) as well as in the dataseta and GPArotation packages. The Harman 24 mental tests problem is in the basic datasets package at Harman74.cor.
Other Harman data sets are 5 socioeconomic variables for 12 census tracts Harman.5 used by John Loehlin as an example for EFA. Another one of the many Harman (1967) data sets is Harman.political. This contains 8 political variables taken over 147 election areas. The principal factor method with SMCs as communalities match those of table 8.18. The data are used by Dziubian and Shirkey as an example of the Kaiser-Meyer-Olkin test of factor adequacy.
Harman, Harry Horace (1967), Modern factor analysis. Chicago, University of Chicago Press.
P.Bentler. Covariance structure models for maximal reliability of unit-weighted composites. In Handbook of latent variable and related models, pages 1--17. North Holland, 2007.
Burt, C.General and Specific Factors underlying the Primary Emotions. Reports of the British Association for the Advancement of Science, 85th meeting, held in Manchester, September 7-11, 1915. London, John Murray, 1916, p. 694-696 (retrieved from the web at https://www.biodiversitylibrary.org/item/95822#790
See also the original burt data set, the Harman.5 and Harman.political data sets.
# NOT RUN {
data(Harman)
cor.plot(Harman.Holzinger)
cor.plot(Harman.Burt)
smc(Harman.Burt) #note how this produces impossible results
f2 <- fa(Harman.8,2, rotate="none") #minres matches Harman and Jones
# }
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