Sharon L. Lohr
Abstract In a dual frame survey, independent samples are drawn from two frames whose union covers the population. Most estimators, however, have been developed under the assumption that there is no nonresponse or measurement error. We review estimators for dual frame surveys and examine their properties in the presence ofnonsampling errors. We also discuss implications of nonsampling errors for survey design. Key words: Combining Data from Different Sources, Misclassiﬁcation, Multiple Frame Survey, Mode Effects, Nonresponse, Sampling for Rare Events
In an ideal sampling world, we have a ﬁnite population U with N units, with yi a measurement on unit i in the population. A probability sample S istaken from the ˆ frame, and the ﬁnite population total Y = ∑N yi is estimated by Y = ∑i∈S wi yi , i=1 ˆ where wi = 1/πi is the sampling weight. The estimator Y is unbiased for Y if the sampling frame includes everyone in the target population, if all sampled units respond, and if there is no measurement error. In practice, of course, these assumptions are rarely met. Nonresponse rates areincreasing, which means that survey estimates rely more on models and often have nonresponse bias. While sampling frames may be improving, undercoverage of speciﬁc subpopulations continues to be a problem. With populations having increasingly diverse languages and technological access, multiple modes may be needed to sample the entire population; this may result in measurement error if there are modeeffects. Typically, nonresponse and undercoverage are dealt with through weight adjustments—increasing weights of selected
Sharon L. Lohr School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287-1804 USA, e-mail: firstname.lastname@example.org
Sharon L. Lohr
respondents in an attempt to reduce bias. Attempts are made to reduce measurement error through carefulsurvey and questionnaire design and through modeling. Multiple frame surveys can help address some of these problems. The potential advantages of using a multiple frame survey include: 1. Use of multiple list frames from administrative records, to make more efﬁcient use of administrative data. 2. Multiple mode sampling (for example, using independent samples from a mobile telephone frame and alandline telephone frame). 3. Future use of the internet for data collection. Although the internet presents many coverage and domain speciﬁcation challenges, it is worthy of consideration because of the potential cost savings and ease of data collection and processing. 4. Improved small area estimation. A national survey could be supplemented with smaller, localized surveys to obtain more precision inthose areas. 5. Improved estimation for rare populations. A general population survey may be supplemented by a survey from a frame with a high concentration of members of the rare population. 6. Modular survey design. A multiple frame approach can give more ﬂexibility for design of continuing surveys. As particular frames become less expensive to sample from, the relative allocation of samplesize to the different frames can be modiﬁed. The modular approach also allows more ﬂexibility in responding to changing needs for data. At the same time, however, multiple frame surveys are also sensitive to nonsampling errors, and are subject to more types of nonsampling errors than their single frame counterparts. In this paper, we summarize estimators that have been proposed for multiple framesurveys, and discuss some of the research that is completed and research that may be needed for their practical implementation. We consider multiple frame surveys in which a unit may belong more than one frame; screening multiple frame surveys, in which units belonging to multiple frames are removed from all except one of the frames, are a special case. Fig. 1 depicts two frames that are both...