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## Nonresponse in Social Science Surveys: A Research Agenda (2013) Committee on National Statistics (CNSTAT)

### Citation Manager

. "3 Mitigating the Consequences of Nonresponse." Nonresponse in Social Science Surveys: A Research Agenda. Washington, DC: The National Academies Press, 2013.

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 Front Matter (R1-R16) Summary (1-4) 1 The Growing Problem of Nonresponse (5-31) 2 Nonresponse Bias (32-40) 3 Mitigating the Consequences of Nonresponse (41-48) 4 Approaches to Improving Survey Response (49-86) 5 Research Agenda (87-90) References (91-113) Appendix A: Nonresponse Research in Federal Statistical Agencies (114-118) Appendix B: Research Agenda Topics Suggested by the Literature (119-128) Appendix C: Biographical Sketches of Panel Members (129-131)

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Prepublication Copy — Uncorrected Proofs ˆ ∑yd i i Y0 = r . ∑d r i The bias can be expressed in two ways: (1) A deterministic framework assumes the population contains a stratum of respondents and a stratum of nonrespondents. Let the population means in the two strata be Yr and Ynr , respectively. The respondent stratum is R percent of N, and the bias of the unadjusted estimator ( ) ˆ  (1 − ( ) is bias Y = R) Y − Y . In the deterministic view the bias arises when the means of the 0 r nr respondents and of the nonrespondents differ. (2) A stochastic framework assumes every unit in the population has some nonzero probability of responding. The bias of the unadjusted estimator is ˆ ( ) 1 N ∑ (Yi − Y ) (ϕi − ϕ ) where � is the mean of the response propensities. Thus, in the stochastic view the bias arises 𝜑 bias Y0 ≈ Nϕ i when the characteristic and response propensity co-vary. A natural adjusted estimator is then ∑ di yiϕi−1 ˆ′ = r ˆ Y , ∑ diϕi−1 where ⏞ I is an estimate of the response propensity. 𝜑 ˆ r The selection of the weighting framework—deterministic or stochastic—depends then on the theoretical model of the response mechanism. In other words, the underlying model is the rationale for the selection of the adjustment scheme. Most models now in use assume that the missing data are missing completely at random (MCAR) or missing at random (MAR). The MCAR assumption holds if all the units in the population have the same probability of responding, that is, if the respondents are a smaller random sample. MCAR means that the distribution of the missingness (an indicator for whether the unit responds or not) is independent of the y-variable and all auxiliary (or x) variables. Missing at random is a more realistic assumption than MCAR. MAR implies that the probability of response does not depend on the y-variable once we control for a vector of known auxiliary variables, x. Weighting class adjustment schemes that define groups (sometimes called “response homogeneity groups”) – (h = 1,…, H ) using the auxiliary data such that the sample units within the groups have the same response propensity are consistent with the MAR assumption. These methods adjust the weights for respondents in the group with ϕhi = ϕh ∀ i ∈ h . ˆ ˆ This type of estimator is a weighting-class estimator or post-stratified estimator, depending on the type of data available for computing the adjustment. If the data are at the sample level (known for sampled units but not for the entire population), it is a weighting-class estimator; if the data are at the population level, then it is post-stratified estimator. The 3-2

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Prepublication Copy — Uncorrected Proofs adjustment requires that sample members can be divided into cells using the vector of observable characteristics. In the weighting-class approach, the adjusted weight is calculated in four stages: 1. Calculate a base weight that is the reciprocal of the probability of selection of the case under the sample design; 2. when there is nonresponse and the eligibility of the nonrespondents cannot be determined, distribute the base weights of the nonrespondents into the eligible nonresponse category based on the proportion of the weights that are eligible in the respondent set; 3. adjust these weights to compensate for eligible nonrespondents; and 4. compute a final weight for the eligible respondent cases as the product of the base weight, the eligibility adjustment factor, and the nonresponse adjustment factor (Yang and Wang, 2008). In choosing weighting classes for the adjustment in stage (c), bias is limited when the variables and classes are such that either: (1) ϕ= ϕh ∀ i or ˆhi (2) Yhi Yh ∀ i . = As noted in the stochastic model of nonresponse, nonresponse bias only exists when the response propensities and the outcomes are correlated. However, since most surveys have a multitude of survey outcomes, the idea of using classes that are related only to the response propensities is commonly adopted. Models constructed to meet (1) are called response propensity stratification, and those designed to meet (2) are referred to as predicted mean stratification. The classes themselves are sometimes formed by subject matter experts, based on information on the key survey outcomes. An empirical method that is used often with categorical data is to form weighting classes by using classification software such as CART, CHAID, or SEARCH. Often the dependent variable is the response (respondent or not), and sometimes the survey outcomes are used as dependent variables, depending on the criteria being used. In either case, this approach may result in a very large number of weighting classes. Eltinge and Yansaneh (1997) suggested methods to test whether appropriate classes are formed. There are many alternative methods of making these adjustments that are sometimes used. We describe several of these alternatives below. Propensity Model Approach The propensity model approach uses multiple regression analysis to examine the nonresponse mechanism and calculate a nonresponse adjustment. In this method a response indicator is regressed on a set of independent variables such as those used to define weighting class cells. A predicted value derived from the regression equation is called the propensity score, which is simply an estimated response probability (Rosenbaum and Rubin, 1983). Survey population members with the same observable characteristics are assigned the same propensity score. The response propensity can be used to adjust directly by using the inverse of the 3-3

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