Likelihood estimate of treatment effects under selection bias

We consider methods for estimating causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, simple comparison of treated and control outcomes will not generally yield valid estimates of casual effects. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based onsome strong assumptions, which are not directly testable. In this paper, we present an alternative modeling approachto draw causal inference by using share random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but it is also less sensitive to model misspecifications, which we consider, than the existing methods.