Harman's Eight Physical Variables

Unrotated factor loading matrix extracted by the centroid method for Harman's 8 physical variables, a classic dataset in factor analysis.

Usage

data(Harman)

Details

Harman8 is a \(8 \times 2\) matrix of unrotated factor loadings extracted by the centroid method (Table 14.3 in Harman, 1976) from the correlation matrix of 8 physical measurements taken on 305 girls (Table 2.3 in Harman, 1976). The centroid method was a standard extraction procedure before iterative methods became computationally feasible. The two columns represent unrotated centroid factors (CF1 and CF2). Row names are the 8 variable names.

The covariance matrix for these 8 physical variables is available in base R (see Harman23.cor).

Format

Harman8: a \(8 \times 2\) numeric matrix of unrotated centroid factor loadings. Row names are variable names; column names are CF1 and CF2.

Source

Harman, H.H. (1976). Modern Factor Analysis (3rd ed.). University of Chicago Press.

See also

Harman23.cor, GPForth, rotations, Thurstone, WansbeekMeijer, CCAI

Examples

  data(Harman, package = "GPArotation")

  # Centroid unrotated loadings from Harman (1976) Table 14.3
  print(Harman8)
#>                  CF1    CF2
#> height         0.830 -0.396
#> arm.span       0.818 -0.469
#> forearm        0.777 -0.470
#> lower.leg      0.798 -0.401
#> weight         0.786  0.500
#> bitro.diameter 0.672  0.458
#> chest.girth    0.594  0.444
#> chest.width    0.647  0.333

  # Rotate the centroid solution
  quartimax(Harman8)
#> Orthogonal rotation method Quartimax converged.
#> Loadings:
#>                  CF1   CF2
#> height         0.899 0.195
#> arm.span       0.934 0.130
#> forearm        0.902 0.104
#> lower.leg      0.877 0.171
#> weight         0.316 0.876
#> bitro.diameter 0.251 0.773
#> chest.girth    0.198 0.715
#> chest.width    0.308 0.659
#> 
#>                  CF1   CF2
#> SS loadings    3.559 2.407
#> Proportion Var 0.445 0.301
#> Cumulative Var 0.445 0.746
  oblimin(Harman8, randomStarts = 100)
#> Oblique rotation method Oblimin Quartimin converged at lowest minimum.
#> Of 100 random starts 100% converged, 100% at the same lowest minimum.
#> Loadings at lowest minimum:
#>                   CF1    CF2
#> height          0.892  0.056
#> arm.span        0.954 -0.023
#> forearm         0.929 -0.047
#> lower.leg       0.877  0.034
#> weight          0.014  0.925
#> bitro.diameter -0.017  0.821
#> chest.girth    -0.052  0.765
#> chest.width     0.086  0.683
#> 
#>                  CF1   CF2
#> SS loadings    3.362 2.604
#> Proportion Var 0.420 0.325
#> Cumulative Var 0.420 0.746
#> 
#> Phi:
#>       CF1   CF2
#> CF1 1.000 0.473
#> CF2 0.473 1.000