How to make prediction models more interpretable? It seems to me as if the go-to technique that is used to make any prediction model more "interpretable" is to reduce the number of input variables that are used in the model. 
I'm wondering if there are any other big picture approaches that one can take to make these models more interpretable? 
By a model that is interpretable, I mean a model that is easier to use and understand.
 A: We deliver a "verbal.txt" file which explains in a narrative form precisely what the prediction equation is all about. We also deliver a breakout table to detail how much of the forecast is due to each and every variable in the model. Additionally we present the equation in such a way that one can then use arithmetic (multiplication/addition) to compute the forecast. Finally we allow a "what-if" to enable the user to set different values of the cause variables in the model to determine sensitivity and to actually deliver elasticities. 
A: Interpretation (or explanation) and prediction are different missions. Asking for a model that does both well, might sometimes be impossible. This will depend on the data generating process. 
 1. Convert continuous variables to intuitive categories (height-> {tall, short}). While this might bear a cost on goodness of fit, it is much more interpretable. In particular, when allowing for interactions. 
 2. Stick to interpretable classes of models. A linear predictors, or a CART is much more interpretable than a neural network of random forest. As I previously mentioned, this might (but not necessarily) bear a cost on the goodness of fit and predictions. 
 3. As you mentioned in the question- a dimension reduction stage before the model fitting could improve interpretability, but not necessarily. Say, PCA could suggest rather weird factors, which are both impossible to interpret and might not improve the prediction (since the dimension reduction was done while disregarding the dependent variable). 
