Modeling and estimation methods for household size in the presence of nonignorable nonresponse applied to the Norwegian Consumer Expenditure Survey

This paper considers the problem of estimating, in the presence of considerable nonignorable nonresponse, the number of private households of various sizes and the total number of households in Norway. The approach is model-based with a population model for household size given registered family size. We account for possible nonresponse biases by modeling the response mechanism conditional on household size. Various models are evaluated together with a maximum likelihood estimator and imputation-based poststratification. Comparisons are made with pure poststratification using registered family size as stratifier and estimation methods used in official statistics for The Norwegian Consumer Expenditure Survey. The study indicates that a modeling approach, including response modeling, poststratification and imputation are important ingredients for a satisfactory approach.