|The authors are grateful to Graham Kalton, Joseph Waksberg, Robert Moffitt, and the referees for their valuable comments and suggestions that led to improvements in this paper.
Partly as a consequence of the recent significant changes in welfare programs and policies, many states are conducting or sponsoring surveys to investigate the effect of changes in welfare policy on the well-being of people living at or below the poverty level. Under ideal circumstances, every low-income person (or family) in the state would have a chance of selection for such a survey, would be located and agree to participate in the survey, and would provide correct answers to all questions asked. In practice, these circumstances are not realized in any population survey. This paper focuses on the problems of missing data in surveys arising from a failure to give all members of the target population a chance of selection for the survey and a failure to obtain the survey data from some of those sampled. The following sections indicate how missing data can lead to biased survey estimates and describe some widely used methods to reduce this effect.
Missing data in surveys can be divided usefully into three classes:
Noncoverage. Noncoverage occurs when persons (or families) in the target population of interest are not included in the sampling frame from which the sample is selected. In the case of a survey of a state's low-income population, noncoverage could, for instance, occur if the list from which the sample was drawn was out of date, and hence failed to include those most recently enrolled.
Unit nonresponse. Unit nonresponse occurs when a sampled unit (person or family) fails to participate in the survey. Unit nonresponse can occur, for example, because the sampled person cannot be located, refuses to participate, is too ill to participate, cannot participate because of language or hearing problems, or is away from the area for the period of the survey fieldwork.
Item nonresponse. Item nonresponse occurs when a sampled unit participates in the survey but fails to provide responses to one or more of the survey questions. This failure may occur because the respondent refuses to answer a question on the grounds that it is too sensitive or personal, or because he or she does not know the answer to the question. Item nonresponse also occurs when an interviewer fails to ask a question or record the answer and when recorded responses are deleted in editing a questionnaire because the response is inconsistent with the answers recorded for other questions.
There is a potential for bias whenever sampled persons who did not participate in the survey have different characteristics than those who did. For some important characteristics, the respondents may be substantially different from those with missing data. In fact, if such differences exist and no attempt is made to adjust for them in the analyses, estimates or inferences for the target population may be misleading. The potential for bias is particularly great when nonresponse rates are high. Thus, for example, if those recently enrolled are not included on the sampling frame for enrollees in a state's welfare program, the survey clearly will produce biased estimates of the distribution of length of time on the program, and any other associated estimates. Similarly, in a survey of welfare leavers, it may be that those who participate in the survey have had appreciably different experiences than those who do not, and thus, estimates based on the respondents will be biased. Suppose that families with positive outcomes (those who successfully made the transition from welfare) are easier to locate and more willing to respond than families with negative outcomes. In fact, policy makers are concerned that this situation does exist and that nonresponding and nonlocatable families and those whose current status is no longer reflected in administrative data are worse off and at greater risk than families for whom data are available (U.S. General Accounting Office, 1999). This situation can result in estimates with large nonresponse bias.
The standard method of attempting to reduce the potentially biasing effect of noncoverage and of unit nonresponse is a ''weighting adjustment." Weighting adjustments for these two sources of missing data are described in this paper. Because some state surveys have experienced high nonresponse rates, non-
response weighting adjustments are likely to be particularly important.The intent of this paper is to describe how they may be applied.
All methods for handling missing data aim to reduce their potential biasing effects, but these methods cannot be expected to eliminate the effects of missing data. The best protection against potential nonresponse bias is to plan and implement field procedures that maintain a high level of cooperation. A wide variety of tools and strategies are available to improve survey response rates. Some examples include an advance letter to sampled cases, effective callback or followup strategies, reductions in the length of the questionnaire or the interview, improved interviewer training, and payment of incentives. The literature includes an extensive discussion on methods for obtaining high response rates in surveys. Cantor and Cunningham (this volume), Weiss and Bailar (this volume), and Singer and Kulka (this volume) describe such methods for low-income surveys. However, even with the best strategies, some nonresponse occurs.
The standard method of attempting to reduce the potentially biasing effect of noncoverage and of unit nonresponse is a ''weighting adjustment." Weighting adjustments for these two sources of missing data are described in this paper. Because some state surveys have experienced high nonresponse rates, nonresponse weighting adjustments are likely to be particularly important.(1) The intent of this paper is to describe how they may be applied.
The usual method for handling item nonresponse is some form of imputation, that is, assigning a value for the missing response based on the responses given to other questions in the survey and usually conducted within classes of sample persons with similar characteristics. If done well, imputation usually can reduce bias in survey estimates. It is nearly always preferable to impute missing items rather than treating them as randomly missing data at the analysis stage because confining analyses to nonmissing responses to questionnaire items may lead to biased estimates. But bias reduction depends on the suitability of the assumptions made in the imputation. When imputations are performed separately on different variables, the bias may be reduced for univariate statistics, but multivariate relationships among variables could become distorted. Also, researchers may treat the resulting data set as if it were complete, thus affecting the variances of the estimates. An extensive body of literature currently exists for compensating for item nonresponse in surveys. Readers are referred to Kalton and Kasprzyk (1986) and Brick and Kalton (1996).
This paper focuses on the standard weighting adjustment methods used to compensate for noncoverage and unit nonresponse in survey research. These methods are general-purpose strategies that automatically adjust all analyses of the survey data, at a low cost. Other available procedures are more complex and may produce somewhat better results when analysts have a specific model they plan to estimate. Because these procedures have only limited applicability in multipurpose surveys, they have not been included here. Refer to Little and Rubin (1987) for information about these methods.
Studies of low-income populations involve various methods of data gathering. We begin with a brief description of two alternative types of low-income studies. We then provide a brief discussion of noncoverage and unit nonresponse in low-income surveys. Sample weighting is then described, followed by a review of the most common general-purpose nonresponse adjustment procedures. Finally, we include a brief summary of the paper. The procedures are illustrated using examples that we carry throughout the paper.