Computing interaction effects and standard error in logit and probit models

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Conclusion 
Interaction effects are complicated to compute and interpret in nonlinear models. Because of their widespread use, however, having a command to compute them is important for applied reseachers. The new command inteff allows users to compute the magnitude, sign, statistical significance of interaction effects in logit and probit models.

The results of two examples are typical of patterns we have found after computing interaction effects for a wide range of problems. The interaction effects has a wave shape when plotted against predicted values. Some interaction effects are positive, som nagative, no matter what the sign of coefficient on the interaction term. For predicted value equals to 0.5 the interaction effects is B12O'(u) for probit case. There is wide variation in the statistical significance of the interaction effect.

There are two limitations to the inteff command. One is that the code will only work for logit and probit models, even though the issue applies to all nonlinear models, such as tobit and count models. In addtion, the command will only work for the interaction between two variable that do not also have higer order terms. For example, the command would yield the wrong answer if, in the first example, age squared was also included as an independent variables. For other nonlinear models, interactions between more than two variables or interactions of variables with higher - order terms use the Stata command predictnl with great care