Random effects probit and logit: understanding predictions and marginal effects

Random effects probit and logit are nonlinear models, so we need predicted probabilities and marginal effects to communicate the economic significance of results. In these calculations, how one treats the individual-specific error term matters. Should one (i) set them equal to zero or (ii) integrate them out? We argue that (ii) is the quantity that most readers would expect to see. We discuss these in the context of the statistical package Stata, which changed its default predictions from (i) to (ii) in version 14. In Appendix 5, we illustrate how to calculate predictions and marginal effects using method (ii) in Stata 13 and earlier.