Adjusting nonresponse bias in small area estimation without covariates via a Bayesian spatial model

Abstract

Sometimes a survey sample is drawn from a large area even if the estimate of interest is at a smaller subdomain level. This strategy, however necessary, may cause small sample problems. The estimation problem is further complicated by survey nonresponse. We build a Bayesian hierarchical spatial model that takes into account both small sample size and nonresponse. This Bayesian model gives the estimates of marginal satisfaction rates at subdomains even when there is no covariate available via modeling the phasespecific response rates and conditional satisfaction rates given response status at subdomains. This method is illustrated using data from the 2001 Missouri Deer Hunter Attitude Survey. Satisfaction, in this survey, refers to whether respondents were satisfied with the Missouri Department of Conservation's deer management program. The estimated satisfaction rates are lower after adjusting for nonresponse bias compared to the satisfaction rates based only on responses.