Analysing survey data with incomplete responses by using a method based on empirical likelihood

Summary.  In many surveys, missing response is a common problem. As an example, Zahner, Jacobs, Freeman and Trainor analysed data from a study of child psychopathology in the State of Connecticut, USA. In that study, the response variable, psychopathology, was inferred from questions that were addressed to teachers of the children and was subject to a high level of missingness. However, the missing responses were supplemented by surrogate information that was provided by the parents and/or the primary care providers of the children. In such a situation, it is conceivable that the supplemental information can be used to recover some of the information that has been lost in the cases with missing response. This paper considers a method using empirical likelihood. Empirical likelihood is well known in providing nonparametric inference. But its application has largely been confined to complete-data situations. The method proposed exploits the semiparametric nature of empirical likelihood. The method gives consistent estimates if the cases with non-missing responses form a random sample of the population. In large samples, the method behaves similarly to a regression estimate that is applied to estimating equations. The method is easy to implement with standard statistical packages. In a small sample study, the method was found to give favourable results, when compared with existing methods.