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Omega estimates

omega() function of psych package performs hierarchical factor analysis to produce omega as an estimate of general factor saturation. The plot produced shows the most significant relations: 

code:

> library(psych)
> omega(birthwt) 

Loading required namespace: GPArotation
Omega 
Call: omega(m = birthwt)
Alpha:                 0.54 
G.6:                   0.61 
Omega Hierarchical:    0.49 
Omega H asymptotic:    0.75 
Omega Total            0.65 

Schmid Leiman Factor loadings greater than  0.2 
           g   F1*   F2*   F3*   h2   u2   p2
low-    0.78 -0.63             1.00 0.00 0.60
age                            0.05 0.95 0.17
lwt                 0.20       0.07 0.93 0.46
race-               0.69       0.51 0.49 0.07
smoke-             -0.56       0.36 0.64 0.11
ptl-                           0.05 0.95 0.49
ht-                            0.03 0.97 0.78
ui-     0.29                   0.09 0.91 0.91
ftv                            0.02 0.98 0.20
bwt     0.99                   0.99 0.01 0.99

With eigenvalues of:
   g  F1*  F2*  F3* 
1.84 0.43 0.88 0.01 

general/max  2.08   max/min =   148.98
mean percent general =  0.48    with sd =  0.34 and cv of  0.71 
Explained Common Variance of the general factor =  0.58 

The degrees of freedom are 18  and the fit is  0.33 
The number of observations was  189  with Chi Square =  59.79  with prob <  0.0000022
The root mean square of the residuals is  0.08 
The df corrected root mean square of the residuals is  0.13
RMSEA index =  0.114  and the 90 % confidence intervals are  0.08 0.143
BIC =  -34.56

Compare this with the adequacy of just a general factor and no group factors
The degrees of freedom for just the general factor are 35  and the fit is  0.57 
The number of observations was  189  with Chi Square =  103.73  with prob <  0.00000001
The root mean square of the residuals is  0.1 
The df corrected root mean square of the residuals is  0.12 

RMSEA index =  0.104  and the 90 % confidence intervals are  0.08 0.125
BIC =  -79.73 

Measures of factor score adequacy             
                                                 g  F1*  F2*   F3*
Correlation of scores with factors            0.99 0.99 0.79  0.11
Multiple R square of scores with factors      0.99 0.97 0.62  0.01
Minimum correlation of factor score estimates 0.98 0.94 0.24 -0.98

 Total, General and Subset omega for each subset
                                                 g  F1*  F2*  F3*
Omega total for total scores and subscales    0.65 0.45 0.14 0.99
Omega general for total scores and subscales  0.49 0.35 0.08 0.99
Omega group for total scores and subscales    0.05 0.10 0.06 0.00

                         

These relations can be subjected to confirmatory factor analysis using structural equation modeling as discussed in a later section.


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