I had a question regarding the calculations behind omega hierarchical using the 'reliability' command in semTools.
I have a bifactor model with a general and two specific factors being estimated across 7 time points, so I have autoregressive paths connecting each respective factor over time (e.g., general factor at first time point predicting itself at the next time point). My confusion is that when I calculate McDonald's OmegaH using the reliability function for this model, the estimates for 'omega3' in the output don't match my hand calculations. However, if I estimate the bifactor model cross-sectionally at each time point, the estimates from semTools do match my hand calculations.
I'm assuming then that the autoregressives are impacting my reliability estimates somehow, but I'm not sure how exactly this is playing out...The estimate for omegaH that semTools gives me for my general factor at the first time point is ~.655, but my hand calculations show that the value should be around ~.58.
If anyone has any thoughts on what could be happening, that would be very much appreciated! Ideally, I was planning on using the estimates from the model with all time-points modeled simultaneously, but now I'm wondering if it would be more appropriate to use the cross-sectional estimates instead? Again, any insight or comments would be very much appreciated!