Help understanding separate- and joint- factor analyses in CFA and ESEM


I am reading an article that tested 2 models--one with an hypothesized separate-factor relationship between five pairs of personality dimensions as measured by two personality assessments, the other with a hypothesized joint-factor relationship between the dimensions--using CFA and ESEM with both models (4 analyses).

The authors claim that the ESEM test of the joint-factor relationship showed that one set the two assessments measure the same five constructs and that one set of constructs is really the same as the other set.

Can someone please explain how to interpret the results of each model analysis (separate and joint) for each type of factor analysis (CFA and ESEM)? What the article says does not make sense to me.




Can't make spagetti
I feel we need quite a bit of context here before we can say anything about it. If you could post the citation (or a link) to the article you're referring to it would be a lot easier.

Thanks for your interest in helping me. Below is what you requested. If you dont want to read all this stuff, you could help me simply by explaining in general the difference between separate and joint factor models and possible, plausible interpretation of what a fit of the latter model means when dealing with two assessments that on their face measure similar constructs.



Here is the link:

This describes the 2 models: [p.3]

The Present Study
Two hypothesized models tested the hypothesis that openness
facets and their corresponding OEs represent the same
latent constructs. In the separate-factor model, indicators of
OEs and indicators of openness facets were modeled as two
separate constructs expected to show a very strong correlation.
Openness facets and their corresponding OEs are as follows:
O1 Fantasy and imaginational OE, O2 Aesthetics and
sensual OE, O3 Feelings and emotional OE, O4 Actions and
psychomotor OE, O5 Ideas and intellectual OE, and O6
Values on its own. The joint-factor model made this hypothesized
relationship more explicit by having all openness and
OE items belonging to each combination load into one single
latent variable.

Key result:
Model 2, in which openness facets and their corresponding
OEs were specified as joint factors, fit the data well
with the exception of CFI, and results were interpretable.

One Interpretation of this result:
Based on the results, openness to experience and OEs seem
to represent largely the same construct.

Another interpretation:

the joint-factor model had acceptable fit and interpretable loadings; thus,
openness seems to encompass OEs.