Bayesian spatial models for adjusting nonresponse in small area estimation

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] There are two kinds of nonresponse: item nonresponse and unit nonresponse. Inferences made from respondents about the population of interest will be subject to nonresponse bias in both situations. When the population of interest is binary and nonresponse has a degree of nonignorability, there are special difficulties in the data analysis. One common practice in mail surveys is to resend the survey questionnaire to nonrespondents multiple times in an effort to increase the number of respondents. In addition, sometimes a sample is drawn from a large area although the estimate of interest is at a smaller sub-domain level. The sample sizes may be sufficient for inference at the large area, but too small to obtain accurate estimates at sub-areas. Analysis with multiple mailings and the small area estimation problems are pertinent to the 2001 Missouri Deer Hunter Attitude Survey (MDHAS). The 2001 MDHAS is used to illustrate our approaches. We build generalized linear mixed models in a Bayesian hierarchical spatial modeling framework to estimate response rates and conditional satisfaction rates given response or nonresponse simultaneously at sub-domain level. One model also includes auxiliary information such as hunter age and number of deer harvested. We confirm that nonresponse is nonignorable in our example. The estimates of satisfaction rates after adjusting for nonresponse are lower than those without consideration of nonresponse.