I have a zero-inflated and extremely positively-skewed outcome variable - lottery wins in dollars. Thus, I use two-part analysis, since adjusting is also needed: one for positive values (lognormal regression) and the second for non-zero probability (logistic regression/bernoulli).
I have found that presenting the results of these two regressions in one plot makes the interpretation really simple: you can see the probability of winning (x-axis) together with the received amount of money (in case you won).
The plot looks like this:
y-axis outcome variable values come from a lognormal model
x-axis outcome variable values come from a logistic regression/bernoulli model (I report them as probabilities, not odds-ratios).
It's well known practice that crude non-normal data should be reported as median (IQR/min-max/quantiles/percentiles). However, if these values come from regression analysis, should I report them as means or medians in this graph? Does regression "convert" these variables to "normally distributed" variables?