A Semiparametric Propensity Score Weighting Method To Adjust for Nonresponse Using Multivariate Auxiliary Information
Damiao N. da Silva1, Chris Skinner2
1Southampton Statistical Sciences Research Institute (S3RI) (and Departamento de Estatistica), University of Southampton (and Universidade Federal do Rio Grande do Norte), Southampton, Hampshire, United Kingdom; 2Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, Southampton, Hampshire, United Kingdom

Propensity score weighting is a useful technique that is often applied to adjust survey estimators to account for unit nonresponse. A key element to implement these types of procedures is the estimation of the propensity scores of response, i.e. the probabilities of response, for all respondents of the survey. To protect the estimation procedure against misspecification of parametric regression models, an issue that can lead to seriously biased adjusted estimators, the response probabilities can be estimated by employing techniques of nonparametric regression. Kernel smoothing, local polynomial regression and splines are examples of such techniques that can yield more robust adjusted estimators under misspecified regression curves. However, their usual implementation restricts the response mechanism to depend on a single univariate and quantitative auxiliary variable, which is often a rather unrealistic setting in many surveys. To overcome this limitation for multivariate auxiliary information settings, we discuss one approach based on the use of semiparametric regression to estimate the response probabilities using continuous and categorical auxiliary variables. Statistical properties of the adjusted estimators resulting from this proposed procedure are discussed.

Keywords: Survey sampling; Unit nonresponse; Response probability; Logistic regression

Biography: Dr. Da Silva is an adjoint professor in the Department of Statistics of the University of Rio Grande do Norte, Natal, Brazil. He is currently in a postdoctoral fellowship with Professor Chris Skinner, at the Southampton Statisical Sciences Research Institute (Univesity of Southampton). Dr. Da Silva's research interests are on nonresponse and other adjusments for nonsampling errors.