A Bayesian spatial model with auxiliary covariates to assess and adjust nonignorable nonresponse

Nonresponse is a persistent problem in surveys because results from respondents only are subject to nonresponse bias. Many methods have been developed to deal with ignorable (missing at random) nonresponse data. In this paper, we provide a method to assess and adjust nonignorable (not missing at random) nonresponse bias in a small area estimation problem. We propose a bivariate Bayesian hierarchical linear mixed model to estimate both satisfaction rate and response rate. This model uses spatial dependencies among subdomains and auxiliary information from sample units to assess and adjust nonresponse bias. In addition, it explicitly includes a parameter that indicates whether the nonresponse is ignorable or not. The method is used to analyze the 2001 Missouri Deer Hunter Attitude Survey (MDHAS). The result shows that the nonresponse in MDHAS is nonignorable. Hunter age and the number of deer harvested have strong effects on satisfaction and response rates, and spatial dependencies are strong amongst counties of hunters’ residences. The estimated satisfaction rates are lower after adjusting for nonresponse bias.