I am reading some material about structural equation modeling. I found it to be extremely similar to confirmatory factor analysis - modeling a construct as the linear combination of several other measures or constructs plus an error term. And the software package that can perform CFA can also perform SEM.
So I am wondering what is the difference between these two models?
SEM is an umbrella term. CFA is the measurement part of SEM, which shows relationships between latent variables and their indicators. The other part is the structural component, or the path model, which shows how the variables of interest (often latent variables) are related.
You can run CFA alone, path analysis alone, or a full SEM. Path analysis is SEM without latent variables.
I agree with @Hotaka's answer and would like to add to it. CFA (Confirmatory factor analysis) actually tests a measurement model. This means that you have some data collected using a questionnaire. The questions of the questionnaire are called items or indicator variables. Using EFA (or similar process) you come to derive the constructs for the groups of these items. CFA is used to confirm and trim these constructs and items (measurement model). SEM is used to find if relationships exist between these items and constructs (structural model). Collectively they are known as CFA-SEM, where SEM is an umbrella term, and CFA is a subset. But we use the term SEM specifically for hypothesis testing part (testing relationships among indicators and constructs).
I've taken this from Wikipedia:
"CFA is distinguished from structural equation modeling by the fact that in CFA, there are no directed arrows between latent factors. In other words, while in CFA factors are not presumed to directly cause one another, SEM often does specify particular factors and variables to be causal in nature. In the context of SEM, the CFA is often called 'the measurement model', while the relations between the latent variables (with directed arrows) are called 'the structural model'."
Bollen and Pearl (2013) in "Handbook of Causal Analysis for Social Research" treat factor analysis models (like CFA) as part of SEM.
Excerpt:
In the path diagram, the ovals or circles represent the latent variables. As stated above, these are variables that are part of our theory, but not in our data set. As in the previous path diagrams, the observed variables are in boxes, single-headed arrows stand for direct causal effects, and two-headed arrows (often curved) signify sources of associations between the connected variables, though the reasons for their associations are not specified in the model. It could be that they have direct causal influence on each other, that some third set of variables not part of the model influence both, or there could be some other unspecified mechanism (preferential selection) leading them to be associated. The model only says that they are associated and not why. [...]
To my mind, CFA is a SEM model where you don't take any position on why or how the latent variables are correlated.
