Reliability in R I'm having trouble understanding the difference between omega 1 and omega 3 in reliability function in the semTools package in R, when calculating the reliability of my factors in a bifactor model.
Are the omegas hierarchical?
 A: If you are referring to the reliability function in the semTools package, there is a nice explanation of the difference in the documentation.
Omega1 assumes that all covariance is accounted for by the common factor model, with no residual covariances between observed variables. This assumption is the basis for computing total variance (the denominator) using only the loadings and the covariances among factors.
Omega2 relaxes the "no residual covariance" assumption, and so the denominator is simply the model-implied covariance matrix of the observed variables.
Omega3, which is intended for models with constraints on relations between factors, replaces omega2's model-implied covariance matrix with the observed covariance matrix. If relations between factors are saturated, then there is no room for the structural model to be inconsistent with the data--this is what omega2 assumes. But if relations between factors are structured, then there may be misfit between model and data, which may have implications for estimated reliability. Omega3 allows for this possibility. 
