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 ;)

Christopher, I am actually a frequentist :P

The fact that in SEM you identify your model a priori does not really imply it's a bayesian method. The point is that your model is defined a priori because you want to "test" if your theoretical model fits with the real world, which might sound like pure Bayesian (and only pure Bayesian, i.e. if you use non-informative prior distributions you're already out of that) but is not necessarily Bayesian. In fact, when I said there are some formal tests to use with SEM, I was referring to frequentist inferential tests (otherwise my footnote with the disclaimer about p-value would not have made sense...).

BTW, just for sake of clarity and completeness: you can use SEM (and also EFA) with categorical data. You just have to pay attention to the way you estimate your correlation or covariance matrix - if you choose an appropriate index you can deal with categorical data.

Moreover, MCA focuses on categories, not on "entire" variables, which is quite a difference.

In order to choose which method is better, you should look at first at the aim of your analysis. Do I have an already defined theoretical model which I want to confirm? In order to accomplish my goal, should I better look at variables, or categories instead?

First of all, if it's not a confirmatory purpose, then you're sure it's not a SEM. Then, it MIGHT be MCA if it's coherent with your research question to look individually (separately) at the categories of your variables. (Please note also that you can compute MCA with different mathematical approaches - Burt matrix, JCA, and so on - which are not the same and might give different results).

In the end, if you do an analysis focused on variables (e.g. EFA) and an analogous focused on categories (i.e. MCA with a Burt or JCA approach) you should expect yourself to get coherent and consistent results, but you're looking at your data from two different perspectives, thus you're not going to get the same information from one method or the other.