I am relatively new in statistics and I would like to prove the value of the method to my superiors, instead of relying on heuristics.
I would like to know what would be the best approach for the following case I have:
-A single dependent binary variable,
-Many independent nominal unordered categorical variables (with two discrete variables (number of previous events) and another discrete (or continuous) variables (age, that I can turn into a ordered categorical variable by creating bins of age groups)
I would like to find out which independent variables are important and how important are they, so I'm thinking "variance explained". I'm dealing with the population (every single event) and descriptive statistics, not inference.
I was thinking of treating everything as nominal categorical variables (even if there a two variables that are numerical), because from my understanding using the "lowest-common denominator" (like using a Chi-Square on a continuous variable) is doable (while sacrificing some statistical power, but without sacrificing significance which I don't want to do, I prefer to not reject the null hypothesis if I'm not 95% sure or more, way more if necessary).
I have read that Principal-component analysis (PCA) could be "problematic" with nominal variables so I would prefer to stay on the safe side and keep anyway from it.
Multiple correspondence analysis (MCA) seems more what I need, but my comprehension is limited (it talks of inertia more than variance explained) and I would prefer confidence intervals (to give a range of the variance explained) and p-values (to give a measure of how likely the variance explained falls in that interval) which I have trouble understanding with MCA or if that is even possible.
Cramér's V sounds interesting, but it looks like it's more a "one on one thing."
Is there a tool or approach that could give me what I'm looking for?
Also, I'd prefer a means that is relatively easy to understand as Excel and SQL are the only tool I can use, so I will have to do most of the calculations in code and loops.
Thank you for your time.