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I need some help identifying a test to use for three categorical variables: Subject (maths, business etc), Big 5, and Learning style. I am carrying out research on whether there is a relationship among the above three variables. There are no scores, only categories.

I looked at the chi-squared test, but it doesn't appear to be helpful if I have more than two variables. Participants are all one gender.

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    $\begingroup$ Chi-square can be done with more than two variables; but it's not clear that that is what you want. Is one of your variables (or more than one) a dependent variable? (That is, something you are trying to predict)? $\endgroup$ – Peter Flom - Reinstate Monica Apr 6 '13 at 19:04
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    $\begingroup$ Hi yes, my dependent variable was subjects, I wanted to find whether learning style or big 5 would predict subject choice. I ended up doing a standard multiple regression. Did I get it right? $\endgroup$ – user23997 Apr 6 '13 at 20:48
  • $\begingroup$ You should have tried logistic regression. Search this site. $\endgroup$ – kjetil b halvorsen Aug 10 '19 at 10:44
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No, a "standard multiple regression" is not appropriate here, assuming by this you mean a regression with a single continuous variable as the response. Regression of this sort can only makes any sense if the different levels of the response can be seen as different values on a continuous variable. There is no way this can be the case with Subject. Even if it were you would have a lot of problems with dealing with the usual assumptions in fitting such a model.

I don't know how your stats package let you do this - probably it converted Subject into a continuous variable based on its internal coding eg 1=Maths, 2=business, etc probably in alphabetical order - but it will certainly have given meaningless results.

A chi-square test would tell you if there is a relationship between the variables, but if you want to understand whether Big 5 and Learning style are related specifically to Subject, you will probably be best off with a multinomial regression.

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You can fit a three way contingency table. See Section 4 (Loglinear Models) of this paper: http://cran.r-project.org/web/packages/vcdExtra/vignettes/vcd-tutorial.pdf

Also, for visualizing the relationship, refer to Section 6 on Mosaic Plots. Figure 6, for instance, is one method of showing a relationship between three categorical variables.

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