I'm guessing this is a pretty basic question, but I am having a hard time wrapping my head around it.
So my understanding with linear regression, is that it shows how much a change in X, will cause a change in Y. And the same with multiple linear regression.
But can the same be said about logistic regression? What if both of the variables are nominal? Can you do logistic regression this way?
I am currently running an ordinal variable against a nominal one, and I get similar results when I alternate independent vs dependent.
So, my question is should logistic regression be viewed as explaining causal relationships as we do with linear regression? Or is it possible that causality is overwritten by multicollinearity? Leaving us with strictly correlational inferences?
Thanks
Best Answer
Causality has nothing to do with regression. You can regress any variables that are not causally linked. Better way of thinking of regression is "response of Y to X", or "relationship of Y and X". And in this regard it does not matter if the link function is identical (as in the normal regression) or logit function (as in the logistic regression). In logistic regression the response of Y to X will just have different shape due to the logit link function than it would have in normal regression.
So the answer is no, there are no differences in causality.