How to analyse three categorical variables 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.
 A: 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.
A: 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.
