In order to study that the marginal effect of some explanatory variables may depend on other covariates such as in the problem of income inequality on health，we propose a semi-parametric binary response model with random effects which can reduce both model specification and omitted variable bias． Its nonparametric specification can also be used to the exploratory data analysis． Then the estimation procedures are established，where the difficulties lies in the evaluation of the intractable integral caused by random effects，and the existence of nonparametric parts makes it even tougher． We solve it by using EM and MCMC algorithm together with non-parametric B spline method． The estimators are shown to be consistent． Simulation studies show the good properties of the estimators． A practical application of our model supports the weak version of income inequality hypothesis．