Average partial effects I need to explain what average partial effects (APEs) are to a very general non-statistical audience (i.e. the APEs derived from a probit model). I have tried to define APEs using layman's terms but I find it hard, can somebody please help me with this?
 A: It helps to make things concrete, so I will assume we are analyzing the effect of credit score on loan default, controlling for other stuff, like income.  You will have to search and replace to put in your example.  I recommend against trying to explain it in general.  Laymen are pretty much never interested in that.  How about (maybe too long?):
The partial effect of credit score on default probability is the amount that default probability goes up (or down) when credit score rises by one point and all other factors stay the same.  Think about two people, one with a credit score of 650 and one with a credit score of 651.  In all other respects (income, time on job, loan-to-value ratio, etc), they are identical.  The one with the higher credit score will have a lower probability of default.  The probability may only be a tiny, tiny bit lower since this is such a small difference in credit scores, but, because everything else is the same, it will be lower.  This difference in default probabilities between a person with a credit score of 650 and a credit score of 651 but with everything else identical is the partial effect of credit score on default probability.
There are two complications, though.  First, the difference in default probability between a person with a 650 score and a 651 credit score will not be the same as the difference in default probability between someone with a 750 and 751 credit score.   Second, the 650 vs 651 difference in default probability will depend on their other characteristics.  Two low income people, one with a 650 and one with a 651, may have a larger difference in default probability than two high income people, one with a 650 score and one with a 651.
To deal with these complications, we first calculate a personalized partial effect, the difference in default probabilities due to a one point increase in credit score, for each person in the sample.  Then, we average over these personalized partial effects to give the average partial effect.  This is called the "average partial effect" of credit scores on default probabilities.
