McDonald's Omega for ESEM

Calculates McDonald's omega using the data inside the Lavaan object of a fitted model. The formula is the following: $$ \omega = |\sum{\lambda_i}|^2 / |\sum{\lambda_i}|^2 + \delta_i_i $$ Where \(\lambda_i\) are the factor loadings and \(\delta_i_i\), the error variances.

Usage

omega_esem(esem_model_fit, target_matrix)

Arguments

esem_model_fit

Lavaan object with an ESEM fitted model.

target_matrix

Target rotation matrix. Usually, the same used to run esem_efa(). The names of the factors in the matrix must be exactly the same as the names in the fitted lavaan model.

Value

McDonald's Omega values for each factor.

Examples

#use Tucker 9 cognitive variables cov matrix
tucker <- psych::Tucker

# esem with oblique target rotation
target_mat <- make_target(9, list(f1 = c(1,2,5:7), f2 = c(3,4,8,9)))
tucker_esem_efa <- esem_efa(tucker,2,target_mat)

# fit lavaan model
referents_list <- find_referents(tucker_esem_efa, c("f2", "f1"))
model_syntax <- syntax_composer(tucker_esem_efa, referents_list)
fit <- lavaan::cfa(model_syntax, sample.cov = as.matrix(tucker), sample.nobs = 710)

# McDonald's Omega
omega_esem(fit, target_mat)
#>    f1    f2 
#> 0.824 0.907