Estimating the Incidence of Rape and Sexual Assault (2014) / Chapter Skim
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Appendix E: Statistical Rationale Behind Some Initial Findings on the Relative Statistical Plausibility of a Multiple-Frame Approach to Estimating the Victimization Rate of Rape and Sexual Assault
Appendix E: Statistical Rationale Behind Some Initial Findings on the Relative Statistical Plausibility of a Multiple-Frame Approach to Estimating the Victimization Rate of Rape and Sexual Assault
Pages 247-256
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From page 247... ...
It explores the statistical rationale behind some initial findings on the relative statistical plausibility of a multiple-frame approach.2 BACKGROUND AND ASSUMPTIONS 1. The primary analysis objective is to estimate the proportion (P)
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design but uses a standard area household frame as currently used in the NCVS. While more complex forms of strati fied cluster sampling would be used with DF and SF designs, one assumes SRSWR sampling is applied to each frame, with the pre sumption that effects of greater sampling complexity would cancel, thus sustaining a comparison between the two design alternatives.
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If one defines Ch, the average cost of adding another survey respondent in the h-th stratum, then we can use the simple linear variable cost model, H C* = ∑ Ch nh and the Cauchy-Schwartz inequality to establish the sample h =1 { } { } allocation that minimizes V ( pW )
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Ratio of Average Unit Costs for the Two Dual-Frame Strata -- This ratio depicts the ratio of the average cost of adding another respon dent to the administrative stratum compared to the comparable average cost for the nonadministrative household stratum. This indicator is computed as
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PHH 3. Extent of Oversampling Members of the Administrative Frame in the Dual-Frame Design -- This is a descriptive indicator of the relatively greater sampling intensity in the administrative stratum compared to the household stratum in the DF design.
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estimates from a household SF design as currently used in the NCVS. To determine the relative utility of DF and SF designs one might pose this question.
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CA + WHH PHH (1 − PHH ) CHH CHH Thus, the total sample size for the DF design in this case would be
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The variance of the weighted estimate of P from the DF design based on this most cost-efficient sample allocation between strata will be WA PA (1 − PA )
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Nonetheless, I believe that these preliminary findings strongly suggest that it would be worthwhile for BJS to more closely investigate the feasibility of using a dual-frame approach for estimating rates of RSA, particularly if these estimates are obtained from an independent RSA victimization survey as recommended by the panel. Finally, the panel's suggestions accompanying a further investigation of the dual-frame might be to incorporate more realistic elements overlooked by my simplifying assumptions above.
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