Sample-based nonresponse adjustments make use of information that is available for the sample, and thus do not require any external population counts. In effect, sample-based nonresponse adjustments distribute the base weights of the nonresponding units to the responding sampled units so that the sum of the adjusted weights over the responding units equals the sum of the base weights for the entire sample.
The basic form of the sample-based nonresponse adjustments is a ratio of sums of base weights where the sums extend over specified subsets of the sample defined by response status. The particular form of the adjustment depends on whether the eligibility status of the nonresponding units can be ascertained. First, we describe the nonresponse adjustment under the assumption that every sampled unit can be assigned to one of the following three response status groups:
Group 1: Respondents. This group consists of all eligible sample units that participated in the survey (i.e., provided usable survey data).
Group 2: Nonrespondents. This group consists of all eligible sample units that did not provide usable survey data.
Group 3: Ineligible or out of scope. This group consists of all sample units that were ineligible or out of scope for the survey.
In this particular case, it is assumed that all of the nonrespondents (Group 2) in the sample have been determined to be eligible for the survey and that all of those in Group 3 have been determined to be ineligible for the survey. If eligibility is unknown for some of the selected cases, the usual approach is to distribute proportionally the weights of those with unknown eligibility to those for which eligibility was determined. In the FIS example, let's assume that 850 families originally were selected from an administrative file. However, it was determined later that 30 families were ineligible because the administrative frame was outdated, for example. The total number of eligible families is 820, and 648 responded to the survey. In this case, Group 1 = 648, Group 2 = 172, and Group 3 = 30. The corresponding sample-based nonresponse adjustment factoris defined to be the ratio of sums:
where Wiis the base weight for the sampled unit i, R represents survey respondents (Group 1), and N represents nonrespondents (Group 2). The adjustment factor is applied only to the base weights of the respondents (Group 1) in the sample; that is, the nonresponse-adjusted weight is computed as
= 0, if unit i is nonrespondent (Group 2).
= Wi, if unit i is out of scope (Group 3).
if unit i is an eligible respondent (Group 1).
In practice, the nonresponse adjustment,, is calculated within specified weighting or adjustment classes. The procedures for forming appropriate weighting classes for this purpose were discussed earlier.
Table 5-5 shows the nonresponse adjustment factors and adjusted weights for the FIS example. Because the base weights are equal to N/n (=50) for each sampled family (as shown in an earlier section on base weights), the nonresponse adjustment factors in column 4 are simply equal to the ratio of column 2 to column 3. The base weights would be adjusted by multiplying the base weights by the nonresponse adjustment factors i.e., column 1 multiplied by column 4. That is, the adjusted weight for each of the respondents in the four cells created by gender and race is equal to the weight given in column (5).
|Head of Family's
Gender and Race
|Nonresponse Adjustment Factor
* Family Income Survey
** For presentation purposes, we have rounded up the adjustment factors (to two decimals) and the adjusted weights (to whole numbers). The calculations, however, carry all the decimals.
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