MCA graphs interpretation

[Zainab Ali]

How to interpret these two graphs I made for women empowerment index by using 4 binary variables (education, employment, health and decision making) by using indicator method as all variables are binary. Also what does sign mean in the coordination graph?

[George Ford]

https://www.youtube.com/watch?v=5TIq434eRKw

[Nick Cox]

I don't have a suggestion on the question because I have never used MCA and find what little I have sampled of its literature unconvincing, failures of mine which don't mean much at all!

But I do note that with 4 binary variables you're in territory in which the complete structure of the data is conveyed by an upset plot. See e.g. https://www.statalist.org/forums/for...lable-from-ssc in which fortuitously but fortunately the first example has 4 binary variables.

That work is now written up at https://journals.sagepub.com/doi/pdf...6867X241258010

[Zainab Ali]

Hey thank you for replying everyone, I got it. Now I just want to clear that as my mca coordinate plot is showing that negative pole has high level of women empowerment index while positive pole has low level of women empowerment index. As I got the range of my mca from -1.756 to 4.597. Does it mean that -1.756 is showing high level of empowerment index and 4.597 is showing low level of empowerment index?

[Nick Cox]

#4 I know that with PCA the sign of results is just conventional, so that negating the scores of any PC or the corresponding set of loadings gives a solution just as good. So, my wild guess -- trusting that others will correct me if this is wildly wrong -- that MCA is just the same in this respect.

On a different level: the success of a search for a single index is convincing when there is a simple interpretation of the construct and the desired result accounts for a massively large fraction of the total variability. With your kind of data that goal (Grail?) seems very elusive.

[Zainab Ali]

#5 Thank you Nick. I am interpreting it after running tsls; taking age at marriage as endogenous variable, menarche as a instrument and women empowerment index as dependent variable. My coefficient value is -0.245 which is highly significant so my interpretation for this coefficient is like a year delay in age at marriage is reducing the empowerment index by 24% which is representing low empowerment (positive empowerment index = low empowerment and vice versa), hence increasing the empowerment of women. Kindly correct me if I am wrong.

[Nick Cox]

It's absolutely your project and your choices to make. Like most other people, you're presumably working in a context of literature to follow and a set of common practices in your field or even instructions or a strong steer from someone in charge.

I'm just bemused by tribal habits here. In my own field -- essentially geography and related Earth and environmental sciences -- interest in multivariate analysis as a way to construct single indexes peaked around 1970. People are more likely to use regression or other modelling directly, even if they have multiple outcomes. Some other fields well represented here -- including econometrics and medical statistics -- seem similar in using multivariate analysis only occasionally.

A large question is whether this is just, as said, varying tribal habits.

[Zainab Ali]

How to interpret these two graphs I made for women empowerment index by using 4 binary variables (education, employment, health and decision making) by using indicator method as all variables are binary. Also what does sign mean in the coordination graph?

Can some one please help me out. As according to the graph my yes, yes, safe and 1 values are showing high empowerment for index (my 4 variables are binary and 1 shows the person is educated, employed, had safe pregnancies and chose the spouse by herself) and other 4 dots show the opposite i.e., 0 value. My MCA index got a range of -1.75 to 4.98 and after running tsls, the value of coefficient is -0.245. how to interpret the results? And what does the negative sign show both in index range and with the value of coefficient?