Hello Kamakshalah. Different approaches to regression include different estimation methods. Whilst ordinary least square (OLS) may produce regression parameters, so may maximum likelihood (ML). However,their estimation methods also provide the basis for various other statistics (as you rightly refer to with fit indices so common to SEM). Different estimation methods often produce some similar statistics (r-square, say), while other resultant statistics are specific to the estimation method.

Chi^2 is not obtained from f or z statistics, but rather from the comparison of the variance/covariance matrices of the data and your model. A very different approach and mathematical computation (estimation method) than OLS. 

I feel your frustration on the various software tools. However, some are better suited to different purposes. I made the leap over to a SEM-specific program (to add to the more traditional stat programs) when I started dealing with latent variables. As they often say, "If the only tool you have is a hammer, you tend to treat everything like a nail."

Wishing you happy hunting on the various approaches to your research questions.

Hello Kamakshalah! In response to your question, while regression analysis and CFA share some features, for example loadings, as you mention, regression and CFA are not the same, meaning that these methods are not different approaches to do the same analysis. We need to go over the particularities of each method, depending on what our research questions are, as Tim Edwards Powers points out. When doing statistical analyses, the use of  specific statistical software is attached and I completely agree that the different software options can be daunting. In my case, it has helped that I mostly use one statistical software (SAS) and over time, one becomes more skilled at using all the tools that the software offers and applying the software for different statistical methodology, regression or CFA becomes less problematic.

Hello Kamakshalah

As noted in the previous answers, there are differences between the direct application of regression analysis and CFA-methods. CFA is basically a measurement model. Sure, it uses regression, namely using the latent variable(s) as independent variable(s) and the observed variable (like an item in a questionnaire) as the dependent. By having several observed variables (usually at least 3 for each latent variable) it is possible from the three regression equations to estimate the latent variable and the regression parameters. As mentioned by Dr. Powers, there are several estimation methods for this purpose (basically derived from OLS, ML or Bayesian estimation methods). When you have performed a CFA, you will have one or more latent variables, which then in turn can be used in a regression analysis in order to explore the relation between several latent variables (each estimated by its own CFA), and/or other observed variables. This is the structural part of the SEM-model. In practice, however, you do not need to separate the CFA-part and the structural part, but you can perform them as one model - which is some of the beauty of using SEM-methods.

This is explained in paedagocial detail by Drs. Muthén in a series of videos which can be reached at www.statmodel.com.

Also Bengt and Linda Muthén has constructed the Mplus program, which is a general purpose program for such analyses, and which is able to use a lot of data types and perform many different types of analysis, including regression analysis with observed data (meaning without involving latent variables). The program is because of well-chosen defaults very easy to use. A demo version is to be found on the mentioned web site.

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Dear Ivanouw, thanks for your reply, but in your message you mentioned  

"........namely using the latent variable(s) as independent variable(s) and the observed variable (like an item in a questionnaire) as the dependent. "  

Are you sure? 

CFA and FA are not projections of regression analysis in my view. It will be appreciated if you clarify your question.