Stop or Continue Data Collection: A Nonignorable Missing Data Approach for Continuous Variables

We present an approach to inform decisions about nonresponse follow-up sampling. The basic idea is (i) to create completed samples by imputing nonrespondents’ data under various assumptions about the nonresponse mechanisms, (ii) take hypothetical samples of varying sizes from the completed samples, and (iii) compute and compare measures of accuracy and cost for different proposed sample sizes. As part of the methodology, we present a new approach for generating imputations for multivariate continuous data with nonignorable unit nonresponse. We fit mixtures of multivariate normal distributions to the respondents’ data, and adjust the probabilities of the mixture components to generate nonrespondents’ distributions with desired features. We illustrate the approaches using data from the 2007 U.S. Census of Manufactures.