I've a suggestion, but I'm not sure whether this is justifiable or not. I hope @technocrat or someone else on this community will explain that.

Suppose you have y as the Ginni coefficient values (in between and 1) and some predictors x_1, x_2, ..., x_p.

I say, model a linear regression of logit(y) on all the predictors, i.e. fit the model:

log(\frac{y}{1-y})=\alpha_0+\sum\limits_{j=1}^p\beta_j x_j

Then predict using this model, and suppose you have z_0 as the prediction for x_0 from this model. Reverse the transformation to get the predicted y value, i.e. predict the Ginni coefficient for x_0 as Y_0=\frac{e^{z_0}}{1+e^{z_0}}.

Can it be done?