I only have idea of PCA here sir.Thanks

Hi Christopher,

MCA (and PCA and EFA) and SEM are quite different from various standpoints.

Before starting, just a quick prelude: SEM techniques can be used, with slight differences, for different purposes, including causal inference; in this answer, I will refer only to its uses as a counterpart of MCA/PCA/EFA.

First of all, MCA & co. are explorative methods (I mean: the results are driven only on your data) while SEM is more a confirmative method (i.e. you apply lots of constraints to your model). In other words, the former group of methods is intended to be used when you have no clue about what to expect (e.g. if you want to explore the presence of latent traits in "behind" your data), or at best when you have little clues but you want your analysis to be fully data-driven. On the contrary, in SEM you identify your model a priori and you "only" wish to see if your data support the model (i.e. if your model fits the data): in fact, SEM gives you the opportunity to do formal tests* of you model and its coefficients.

MCA, in particular, was born as an explorative method in sociology & communication science; it is suitable only for purely categorical data and it mainly allows you to look for archetipical profiles defined, in N dimensions (typically, you hope no more than 2 because otherwise interpretation becomes a bit tough), by the categories of your variables. More explicitly: you look at categories individually, not at the "entire" variable from which those categories are taken.

Moreover: what I described is variable-centric MCA (you look at your dataset "by column") but you can actually do a MCA also if you want your description of the data to be subject-centric (you look at your dataset "by row"), i.e. look at similarities and differences between the profiles of categories of your subjects (or, generally speaking, statistical units).

I won't talk about PCA and EFA, but we can also discuss about those if you want :-)

* Please note that I am against the centrality of the role of p-value in research.

Thanks for the detailed response. I also tend to disagree with the frequentists and understand the value of bayesian statistics.

since I have a large dataset consisting solely of categoical data that I need to better understand, it appears that the MCA will be a practical approach.

Plus nobody likes restraints ;)