Schmid.Leiman: 12 variables created by Schmid and Leiman to show the...

Description Usage Details Source References Examples

Description

John Schmid and John M. Leiman (1957) discuss how to transform a hierarchical factor structure to a bifactor structure. Schmid contains the example 12 x 12 correlation matrix. schmid.leiman is a 12 x 12 correlation matrix with communalities on the diagonal. This can be used to show the effect of correcting for attenuation. Two additional data sets are taken from Chen et al. (2006).

Usage

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Details

Two artificial correlation matrices from Schmid and Leiman (1957). One real and one artificial covariance matrices from Chen et al. (2006).

Source

John Schmid Jr. and John. M. Leiman (1957), The development of hierarchical factor solutions.Psychometrika, 22, 83-90.

F.F. Chen, S.G. West, and K.H. Sousa.(2006) A comparison of bifactor and second-order models of quality of life. Multivariate Behavioral Research, 41(2):189-225, 2006.

References

Y.-F. Yung, D.Thissen, and L.D. McLeod. (1999) On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64(2):113-128, 1999.

Examples

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data(Schmid)
cor.plot(Schmid,TRUE)
print(fa(Schmid,6,rotate="oblimin"),cut=0)  #shows an oblique solution
round(cov2cor(schmid.leiman),2)
cor.plot(cov2cor(West),TRUE)

Example output

Loading required namespace: GPArotation
Factor Analysis using method =  minres
Call: fa(r = Schmid, nfactors = 6, rotate = "oblimin")
Standardized loadings (pattern matrix) based upon correlation matrix
      MR1  MR4   MR6   MR2   MR3   MR5    h2   u2 com
V1   0.80 0.00  0.00  0.00  0.00  0.00 0.637 0.36   1
V2   0.90 0.00  0.00  0.00  0.00  0.00 0.814 0.19   1
V3   0.00 0.00  0.70  0.00  0.00  0.00 0.485 0.52   1
V4   0.00 0.00  0.61  0.00  0.00  0.00 0.364 0.64   1
V5   0.00 0.00  0.00  0.00  0.77  0.00 0.599 0.40   1
V6   0.00 0.00  0.00  0.00  0.42 -0.01 0.171 0.83   1
V7   0.00 0.00  0.00  0.00  0.00  0.77 0.589 0.41   1
V8   0.00 0.00  0.00  0.00  0.01  0.18 0.033 0.97   1
V9   0.02 0.78  0.01  0.02  0.00  0.01 0.635 0.36   1
V10 -0.04 0.60 -0.02 -0.03 -0.01 -0.01 0.326 0.67   1
V11  0.00 0.00  0.00  0.60  0.00  0.00 0.363 0.64   1
V12  0.00 0.00  0.00  0.70  0.00  0.00 0.486 0.51   1

                       MR1  MR4  MR6  MR2  MR3  MR5
SS loadings           1.45 0.96 0.85 0.85 0.77 0.62
Proportion Var        0.12 0.08 0.07 0.07 0.06 0.05
Cumulative Var        0.12 0.20 0.27 0.34 0.41 0.46
Proportion Explained  0.26 0.17 0.15 0.15 0.14 0.11
Cumulative Proportion 0.26 0.44 0.59 0.75 0.89 1.00

 With factor correlations of 
     MR1  MR4  MR6  MR2  MR3  MR5
MR1 1.00 0.43 0.56 0.14 0.16 0.21
MR4 0.43 1.00 0.38 0.29 0.17 0.22
MR6 0.56 0.38 1.00 0.12 0.14 0.19
MR2 0.14 0.29 0.12 1.00 0.05 0.07
MR3 0.16 0.17 0.14 0.05 1.00 0.23
MR5 0.21 0.22 0.19 0.07 0.23 1.00

Mean item complexity =  1
Test of the hypothesis that 6 factors are sufficient.

The degrees of freedom for the null model are  66  and the objective function was  1.9
The degrees of freedom for the model are 9  and the objective function was  0 

The root mean square of the residuals (RMSR) is  0 
The df corrected root mean square of the residuals is  0 

Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   MR1  MR4  MR6  MR2  MR3  MR5
Correlation of (regression) scores with factors   0.93 0.84 0.81 0.78 0.80 0.78
Multiple R square of scores with factors          0.87 0.71 0.66 0.61 0.64 0.61
Minimum correlation of possible factor scores     0.73 0.43 0.32 0.23 0.27 0.22
      V1   V2   V3   V4   V5   V6   V7   V8   V9  V10  V11  V12
V1  1.00 1.00 0.56 0.56 0.15 0.15 0.23 0.23 0.40 0.40 0.13 0.13
V2  1.00 1.00 0.56 0.56 0.15 0.15 0.23 0.23 0.40 0.40 0.13 0.13
V3  0.56 0.56 1.00 1.00 0.13 0.13 0.20 0.20 0.35 0.35 0.12 0.12
V4  0.56 0.56 1.00 1.00 0.13 0.13 0.20 0.20 0.35 0.35 0.12 0.12
V5  0.15 0.15 0.13 0.13 1.00 1.00 0.24 0.24 0.15 0.15 0.05 0.05
V6  0.15 0.15 0.13 0.13 1.00 1.00 0.24 0.24 0.15 0.15 0.05 0.05
V7  0.23 0.23 0.20 0.20 0.24 0.24 1.00 1.00 0.23 0.23 0.08 0.08
V8  0.23 0.23 0.20 0.20 0.24 0.24 1.00 1.00 0.23 0.23 0.08 0.08
V9  0.40 0.40 0.35 0.35 0.15 0.15 0.23 0.23 1.00 1.00 0.27 0.27
V10 0.40 0.40 0.35 0.35 0.15 0.15 0.23 0.23 1.00 1.00 0.27 0.27
V11 0.13 0.13 0.12 0.12 0.05 0.05 0.08 0.08 0.27 0.27 1.00 1.00
V12 0.13 0.13 0.12 0.12 0.05 0.05 0.08 0.08 0.27 0.27 1.00 1.00

psych documentation built on Sept. 22, 2021, 5:07 p.m.