Markov chain Monte Carlo approach to the analysis of response patterns in data collection process

Survey research, such as telephone, mail, or online questionnaires, is one of the most widely used tools for collecting sample data. We are often interested in the total number of replies that would be received during a given time period. Many researchers have developed a wide variety of curve-fitting methods to predict the response rate of recipients over time. However, previous models are based on some assumptions that are hardly justified in practice. In this paper, a new response model is proposed that is based on meaningful parameters such as the ultimate response rate of questionnaire recipients, delay rate of respondents, and average delivery time of responses. To estimate those model parameters, we use the Markov chain Monte Carlo (MCMC) method, which is increasingly popular in the operational research community. With mail survey data in marketing research, we test our Bayesian response model and compare its performance with those of traditional curve-fitting models.