Dear Maksim Sokolovskii,

SEM, CFA and Path are extensions of multiple linear regression analysis, and it is why they are in the same program (I never used AMOS, I use Lavaan, but they are in the same umbrella with similar functions).

CFA is a specific type of SEM that deals with measurement models.

SEMs are represented using a Path diagram.

Those books may help you:

Everitt, B., & Howell, D. (2005). Encyclopedia of Statistics in Behavioral Science - Vol. 1 (1st ed.). Wiley.

Brown, T. A. (2006). Methodology in the Social Sciences: Confirmatory Factor Analysis for Applied Research (D. A. Kenny (ed.)). Guilford Press.

I hope the answer has helped you.

Regards,

Amalia

Thank you very much, Dear Amalia Raquel Pérez Nebra.

Hi Maksim, I don't think there is any real difference in these techniques when you look under the bonnet. There are all regression based and the parameters, although they are called different things (loadings, paths etc), are the same. The only reason why we use these different names is to provide a shorthand description of the model. For example, if someone says 'I've done a CFA' I know the model only have latent variables and observed variables that are indicators of the latent variables. Similarly, if someone says 'I've done a path analysis', I know that they have tested a model about the relationships among a set of observed variables. So I agree with you when you say that "....but statistically, they look equal", but the names are also helpful for people to describe what they have and haven't done.

Best wishes

Mark

SEM is a combination of CFA and Path analysis. On the one hand, CFA creates measures of latent variables. On the other hand, Path analysis sets up a series of causal connections among variables. So, SEM sets up a series of causal connections among latent variables.

CFA (also measurement model) is done to check "how better measurable indicators explain their respective constructs". Path Analysis causal explanation between the latent variables. SEM estimates the latent variables from their measurable indicators and also estimates the association between the latent variables.

I agreed with the response of Mark Shevlin.

Structural Equation Modeling (SEM), Confirmatory Factor Analysis (CFA), and Path Analysis are all statistical techniques used in the field of data analysis. While they share some similarities, they have distinct purposes and applications.

CFA is a subset of SEM and focuses specifically on the measurement model, which involves assessing the relationships between observed variables and their latent constructs or factors. It aims to determine the extent to which the observed variables adequately reflect the underlying constructs. CFA allows researchers to confirm or test a predefined factor structure and evaluate the convergent and discriminant validity of the measurement model.

Path Analysis, on the other hand, is a more simplified form of SEM that primarily focuses on testing the direct relationships between variables. It allows researchers to examine causal relationships among variables and provides estimates of the strength and significance of those relationships. Path Analysis assumes that there are no mediating variables between the independent and dependent variables.

SEM is a broader framework that encompasses both CFA and Path Analysis. It allows researchers to test complex structural models that include both measurement and structural components. In addition to examining the direct relationships between variables, SEM also allows for the evaluation of indirect relationships and mediating effects. It provides a comprehensive analysis of the relationships between observed and latent variables, offering insights into both measurement and structural aspects of the model.

Although these techniques can be implemented in software like AMOS, it is important to note that they differ in their focus and the type of analysis they provide. While they may appear similar from a statistical standpoint, their applications and interpretations vary. Therefore, it is crucial to select the appropriate technique based on the research questions and objectives at hand, rather than assuming they are interchangeable.