Suppose a logistic regression model is used to predict whether an online shopper will purchase a product (outcome: purchase), after he clicked a set of online adverts (predictors: Ad1, Ad2, and Ad3).
The outcome is a binary variable: 1 (purchased) or 0 (not purcahsed). The predictors are also binary variables: 1 (clicked) or 0 (not clicked). So all variables are on the same scale.
If the resulting coefficients of Ad1, Ad2, and Ad3 are 0.1, 0.2, and 03, we can conclude that Ad3 is more important than Ad2, and Ad2 is more important than Ad1. Furthermore, since all variables are on the same scale, the standardized and un-standardized coefficients should be same, and we can further conclude that Ad2 is twice important than Ad1 in terms of its influence on the logit (log-odds) level.
But in practice we care more about how to compare and interpret the relative importance of the variables in terms of p(probability of the purchase) level, not the logit(log-odds).
Thus the question is: Is there any approach to quantify the relative importance of these variables in terms of p?