Share of total score variance due to the single general factor

Cronbach alpha is routinely read as evidence that a scale measures one thing, and it is not: alpha is high whenever the items intercorrelate at all. Omega hierarchical answers the question alpha is mistaken for, putting only the general-factor loadings in the numerator.

Usage

Omegah(X, loadings_g, loadings_specific = NULL)

Arguments

X

Item scores; used only for the reported observed variance.

loadings_g

General-factor loadings.

loadings_specific

Group-factor loadings, optional.

Value

List with estimate, omega_total, var_total, uniqueness, p.

Details

Formula: omega_h = (sum lambda_g)^2 / Var(T), Var(T) = (sum lambda_g)^2 + (sum lambda_s)^2 + sum psi.

References

Zinbarg, Revelle, Yovel & Li (2005) Psychometrika 70:123-133; McDonald, R. P. (1999), Test Theory, ch 6.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Omegah(V, V)
#> $estimate
#> [1] 1.178182
#> 
#> $omega_total
#> [1] 1.178182
#> 
#> $var_total
#> [1] 1100
#> 
#> $uniqueness
#> [1]   0  -3  -8 -15 -24 -35 -48 -63
#> 
#> $p
#> [1] 8
#> 
#> $method
#> [1] "McDonald omega hierarchical"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"