Hierarchical Bayesian Modeling in Dichotomous Processes in the Presence of Nonresponse

Abstract

Sampling units that do not answer a survey may dramatically affect the estimation results of interest. The response may even be conditional on the outcome of interest in the survey. If estimates are found using only those who responded, the estimate may be biased, known as nonresponse bias. We are interested in finding estimates of success rates from a survey. We begin by looking at two current Bayesian approaches to treating nonresponse in a hierarchical model. However, these approaches do not consider possible spatial correlations between domains for either success rate or response rate. We build a Bayesian hierarchical spatial model to explicitly estimate the success rate, response rate given success, and response rate given failure. The success rates in the domains of the survey are allowed to be spatially correlated. We also allow spatial dependence between domains in both response rate given success and response rate given failure. Spatial dependence is induced by a common latent spatial structure between the two conditional response rates. We use the 1998 Missouri Turkey Hunting Survey to illustrate this methodology. We find significant spatial correlation in the success rates and incorporating nonrespondents has an impact on the success rate estimates.

Adjusting Nonresponse Bias at Subdomain Levels using Multiple Response Phases

“…One approach is to condition on success or failure. Response rate given success or failure is then calculated as done by Stasny (1991), Nandrum and Choi (2002) and Oleson and He (2004). In this approach, there is partial data in estimating all the parameters of interest.…”

“…How should this additional data from multiple response phases be treated? Methods by Basu and de B. Pereira (1982), Stasny, (1991) and Oleson and He (2004) account for nonresponse rates but do not account for multiple response phases. Lessler and Kalsbeek (1992) review many methods for dealing with the problem of survey nonresponse.…”

“…The application presented here is the spring 1998 Missouri Turkey Hunting Survey (MTHS). There were 110,691 hunting permit holders and we use a sample of 6412 hunters (See Oleson and He, 2004). To better regulate hunting activities, MDC needs to study the relationship between success rate and public opinion at the county level.…”

“…In order to determine this relationship, estimates of success rate at the hunters county of residency are required. These county level hunter success rates are spatially dependent since most hunters tend to hunt locally and turkey habitat is spatially correlated (Oleson and He, 2004).…”

“…The proposed model in this paper estimates conditional success rates by separating the respondents into different response phases. In contrast, Oleson and He (2004) analyzed the same MTHS data using the conditional approach of response rate given success and response rate given failure. Their model also combined all respondents together.…”