To all the statisticians out there:
I'm running an exploratory data analysis to understand the relationship between my dependent variable (binary categorical) and all my independent variables. So I am conducting a simple logistic regression for each independent variable to interpret the log-odds and how much effect that each independent variable has on my dependent variable.
The problem I'm not quite understanding is the assumption that the log-odds should have a linear relationship to the independent variable. If this assumption is violated, are the results of my logistic regression model useless?
Based on internet research, to meet this assumption, I have created a new variable for each independent variable that multiplies the value to the log of the value (x*log(x)) and determined its significance when incorporated into the model (currently using GLM in python). If the p-value is < alpha, we can consider that variable to not be linearly related to the log-odds. And if that is the case, adding a squared polynomial term will give it linearity.
The polynomial term seemed to work for a couple variables but others, it did not.
So overall, if this assumption is violated, is it a serious issue when drawing inferences? And if it absolutely needs to be met, how can I meet it? Or perhaps if it can't be met, I should torch logistic regression completely and try something else?
Note: This is for exploratory analysis and not predictive analytics.