# MCA vs Multinomial Logistic Regression

Lets say I have made survey using a sample of a given number of people, containing a set of 25 questions that have 6 possible answers (Fully agree/ Partially Agree/ Neutral/ Partially Disagree/ Fully disagree/ Don't know), and a few other questions concerning variables I'll be using to qualify them (such as gender, average income, region of residence, age, color, and so on).

Now lets say I want to try and find correlations between gender/race/age/etc and the specific answers given to the set of the 25 questions. Lets say I also want to see if there might be correlations between answers. In other words, I want to find all possible correlations among these variables and the questions, and among the questions themselves.

Should I be thinking about using a Multiple Correspondence Analysis for this objective, or a Multinomial Logistic Regression, or maybe both, or some other specific technique?

I've been studying statistics by myself and I'm confronted with this problem and unsure of what path to follow. Both ways seem to want to find similar answers, but there seem to be nuances in choosing which one to use that I am missing.

• By "MCA" & "Multiple Correlation Analysis", did you mean multiple correspondence analysis (b/c you include the [correspondence-analysis] tag)? You certainly wouldn't want Multinomial LR, b/c your response is ordered; you'd want ordinal LR. Most likely, what you ultimately want is to use item response theory; however, it is pretty advanced & requires a lot of data. You may need to work w/ a consultant or settle for simpler analyses. – gung Apr 8 '14 at 16:56
• Yes, indeed I meant correspondence there. Sorry. I've edited and fixed it. – user135206 Apr 8 '14 at 17:10
• The true reason for me asking this question is that there has been a study published recently where I live, following this format, where they seem to have used a logit regression to find their results. In order to do so, they took all 25 or so questions with 6 possible answers, made up a dichotomy by saying that "Fully Agree" and "Partially agree" with both count as "Yes", and all the rest would count as "No". They did similar things for color, region and several "non-binary" variables. It felt like they're "cheating". Is their method valid? Would MCA be better suited for this? – user135206 Apr 8 '14 at 17:12
• Moreover, since they made their raw data available, I was thinking about how far I could go in applying some of these techniques myself to try and compare to their results, should they be questionable, since this was an important survey. Hence my doubt. – user135206 Apr 8 '14 at 17:15

Your 25 questions are ordinal; you can look at correlations among them using rank correlation. Similarly for their correlation with age. Gender and race are nominal variables (depending on how you code gender) and therefore, you can't use correlations with them. Do you mean association?

Or, perhaps you want to somehow combine the 25 questions into one or more scales and then see if those scale scores relate to demographics? That would be regression. Or, if you want to see how each individual question among your 25 relates to the demographics, you probably want ordinal logistic regression.

Dichotomizing any of the variables is not recommended, it leads to loss of power and information and increases both type I and type II error.

• Regarding age and comparing questions among one another, I think I understand the general outline of what to do, from what you pointed out. But indeed, one of the important questions I would like to answer is. "Does race/gender have an influence on what answers a person will give to these questions?". So I might be lacking the exact word here, but I am indeed looking for an association, or correspondence between these nominal variables and the given answers, as well. How should I proceed? – user135206 Apr 8 '14 at 17:38
• It sounds like you want regression, not correlation. – Peter Flom Apr 8 '14 at 17:59