THE SYSTEM FOR ESTIMATION OF VARIANCE DUE TO NONRESPONSE AND IMPUTATION (SEVANI)

ABSTRACT The System for Estimation of Variance due to Nonresponse and Imputation (SEVANI) is a SAS-based prototype system with a graphical user interface. Variance estimation is based on the quasi-multi-phase framework. In this framework, a nonresponse model is required and an imputation model can also be used. Two types of nonresponse treatment methods can be dealt with: nonresponse weighting adjustment and imputation. If imputation is chosen, SEVANI requires that one of the following four imputation methods be used: deterministic linear regression imputation, random linear regression imputation, auxiliary value imputation or nearest-neighbour imputation. In this paper, the methodology that SEVANI is based on will be described and an example using real data will be presented to illustrate the theory in practice. KEY WORDS: Quasi-randomization; Two-phase sampling; Nonresponse model; Imputation model. 1. INTRODUCTION Most surveys, if not all, have to deal with the problem of nonresponse. Different reasons might explain the presence of nonresponse, such as a refusal to provide the desired information for at least one question or an impossibility to contact a given unit. Nonresponse can also be produced at the editing step of the survey in an attempt to resolve problems of inconsistent or suspect responses. Therefore, nonresponse takes here its general meaning of missing values in the sample. Nonresponse leads inevitably to an observed sample of smaller size than the sample originally selected. This sample size reduction is most of the time accompanied by an increase in the variance of the estimates, no matter which method is chosen to treat nonresponse. This increase in variance is called the nonresponse variance. The imputation variance is defined here as a component of the nonresponse variance which is due to the use of a random imputation method. At the beginning of the 80's, most research efforts on nonresponse were focused on the evaluation and the reduction of nonresponse bias. Since that time, a lot of research work has been devoted to estimating the nonresponse variance, especially when imputation is used to replace the missing valu es (see Lee, Rancourt and Sarndal, 2001 for a review). The result of some of this research activity lead to the development of the System for Imputation Variance (SIMPVAR), which was presented at the Statistics Canada Symposium 1997 (Rancourt, Gagnon, Lee, Provost and Sarndal 1997). More recently, work has been done to allow more nonresponse treatment methods to be handled in a unified framework for variance estimation, called the quasi-multi-phase (or quasi-randomization in the terminology of Oh and Scheuren, 1983) framework. Sarndal and Swensson (1987), Sarndal (1992), Rao and Sitter (1995) and Beaumont (2000) are examples of papers that are based on the quasi-two-phase framework. As a result of the substantial modifications in SIMPVAR, the name was changed to the System for Estimation of Variance due to Nonresponse and Imputation (SEVANI). SEVANI is a prototype system developed using SAS v8. Therefore, SEVANI only supports SAS v8 files and libraries. It is a collection of macros that can be run separately or by using the graphical user interface. Version 1.0 of SEVANI requires that the population parameter to be estimated be a domain total or a domain mean and that the full response estimator be the Horvitz-Thompson estimator or in the family of calibration estimators. Two types of nonresponse treatment methods can be dealt with: nonresponse weighting adjustment and imputation. If imputation is