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I have 4 categorical variables in a dataset let $X_1$, $X_2$, $X_3$ and $Y$. Where $X_1$,$X_2$ and $Y$ is a binary random variable and $X_3$ have 3 categories.

How can I study the association of $X_1$ and $Y$ fixing/controlling $X_2$ and $X_3$?

How can I study the association of $X_2$ and $Y$ considering the four variables?

What's the better way to do that? Boxplots? Using wald.test?

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Log-linear models are one approach. Fortunately, the literature on this class of models is extensive. One of the earliest contributions is Bishop, Fienberg and Holland's Discrete Multivariate Analysis: Theory and Practice, out in a 2007 edition. Another excellent resource is Thomas Wickens' Multiway Contingency Tables Analysis for the Social Sciences. Stat packages and freeware modules handle them easily.

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  • $\begingroup$ Sorry if I don't was clear enough. What I want to know is if exists a way to show that exists association between two categorical variables with graphs. $\endgroup$
    – user72621
    Commented Jul 10, 2016 at 20:57
  • $\begingroup$ There are many possibilities for displaying such a small amount of data. Have you tried conditional bar charts, perhaps side-by-side? $\endgroup$
    – user78229
    Commented Jul 10, 2016 at 21:13
  • $\begingroup$ My data following this form stats.stackexchange.com/questions/223028/…, and I want to study the relationsheep between severity of accident and helmet , severity of accident and speed. Conditional bar charts can be useful in this case? $\endgroup$
    – user72621
    Commented Jul 10, 2016 at 21:31
  • $\begingroup$ Ok...this is more like a consultant's powerpoint slide question. Assuming you have some software like Excel, Tableau or ppt, this could be a grouped bar chart. The first thing you might do would be to create two groups of bars for the y/n helmet question. Within each of those two groups, you could have three bars -- one for each level of speed. Within each of the these bars, you could have the percent of y/n severity. If you build a log-linear model testing for significance of the association, you could substitute the repercentaged Wald chi-square results from the model. $\endgroup$
    – user78229
    Commented Jul 10, 2016 at 21:41
  • $\begingroup$ Beyond graphs I can make some hypothesis test to investigate if exists a association between "Severity of aciddent" and "Helmet" without the variable "Speed" ,and after that make some test with the "Speed" together? $\endgroup$
    – user72621
    Commented Jul 10, 2016 at 21:53

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