Statistics and Its Interface

Volume 6 (2013)

Number 3

Likelihood estimate of treatment effects under selection bias

Pages: 349 – 359



Md. Moudud Alam (School of Technology and Business Studies, Dalarna University, Falun, Sweden)

Maengseok Noh (Department of Statistics, Pukyong National University, Busan, Korea)

Youngjo Lee (Department of Statistics, Seoul National University, Seoul, Korea)


We consider methods for estimating the 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, a simple comparison of treated and control outcomes will not generally yield valid estimates of casual effect. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based on some strong assumptions, which are not directly testable. In this paper, we present an alternative modelling approach to draw causal inferences by using a shared 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 also is less sensitive to model mis-specifications, which we consider, than existing methods.


causal inference, likelihood, propensity score, random-effect model

2010 Mathematics Subject Classification

Primary 60K35, 62P20. Secondary 62J12.

Published 22 August 2013