I am running binary logistic regression and all my independent variables are categorical (mostly binary). How do I check for multicollinearity? Using SPSS, Regression >linear> should I put my DV and all my IV's and check collinearity diagnostics or it is only applicable in case of continous variables.
Am I also right to say that I will not be producing a correlation matrix as all my variables (DV and IV) are categorical, and instead I should preform chi-square test for independence to explore the relationship between my DV and IV's and consider p value and effect size?
There is nothing wrong with using correlations between predictors to see if they are collinear. For collinearity diagnostics I would just run a multiple linear regression to get tolerance, VIF etc. in SPSS. Collinearity is about the linear relationship between predictors which is captured by these procedures.
If you are using binary logistic regression then the chi-square tests aren't really helpful. Mathematically logistic regression is essentially equivalent to chi-square tests of independence in the 2x2 case (with the slight change that the test statistic is usually the Likelihood chi-square rather than the Pearson chi-square).
I agree with what Thom Baguley already said.
To add to that: why are you worried about multicollinearity in the first place? Unless you are in the situation where the correlation (better word here is dependence because we are talking about binary predictors) are extremely high, your logistic regression will work just fine. One thing you might see with extreme collinear variables is very large standard errors and accompanying confidence intervals for the coefficients of these variables. If you are truly in that setting and you still want to make use of two highly collinear predictors, you may think of using a Ridge logistic regression. See: https://stats.stackexchange.com/questions/104779/why-does-ridge-regression-work-well-in-the-presence-of-multicollinearity
I agree with the previous answers, but I am a bit puzzled with your statement " categorical (mostly binary)". Are the non-binary predictors continous or multicategorical? If the latter, how did you enter them in the regression?
It is a tricky question, because it depends on what do you expect from your regression. If you want to select features, such as risk factors, the best features for a simpler multiple regression, then a correlation matrix can be useful. Simpler models are less prone to overfitting and perform close to full models in new cases. Remember that, for your model to be used in practice, complexity is a cost (related to cognitive effort, most often). On the other hand, if you are developing for an autonomous system, complexity costs are very low.
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