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I have a data set with one binary response variable $Y$, and three categorical covariates $X_1$, $X_2$ and $X_3$. I want to find out what effect $X_1$ has on $Y$ (and if the effect is significant). Naturally, I solve this by fitting a logistic regression model (using all three covariates), and analyse the table of deviance.

Are there any alternative methods to solve this problem?

I'm aware of the classification methods mentioned here Alternatives to logistic regression in R, but my problem doesn't concern prediction.

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    $\begingroup$ What kind of alternative are you looking for AND/OR What kind of information other than odds ratios and p-values for significance are you looking for? $\endgroup$ – IWS Apr 13 '17 at 9:25
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    $\begingroup$ You can use a binomial glm with some other link function, to say more than this we need detail of your application. $\endgroup$ – kjetil b halvorsen Apr 13 '17 at 9:34
  • $\begingroup$ Essentially, I would like to know if there is a relation between $Y$ and $X_1$, given $X_2$ and $X_3$. This is a homework assignment, and I don't think I can be any more specific. So far, I've done some basic plotting as part of the EDA, and looked at pairwise correlations. $\endgroup$ – harisf Apr 13 '17 at 9:56
  • $\begingroup$ Have you considered interactions? $\endgroup$ – Scortchi Apr 13 '17 at 10:11
  • $\begingroup$ Do you mean interaction terms in the logistic regression model, such as $X_1 * X_2$? If so, yes. I understand my question lacks details, which makes it hard to answer, but to be clear; I would like to know if there's any other method than regression I could use in assessing the relation between two categorical variables $Y$ and $X_1$. $\endgroup$ – harisf Apr 13 '17 at 10:16

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