Using the American Community Survey Benefits and Challenges (2007) / Chapter Skim
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Appendix C Alternatives to the Multiyear Period Estimation Strategy for the American Community Survey
Appendix C Alternatives to the Multiyear Period Estimation Strategy for the American Community Survey
Pages 290-312
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From page 290... ...
The weighting scheme currently proposed by the Census Bureau involves pooling the survey data across the 3 or 5 years. The weights will be developed starting with the inverse selection probabilities of sampled households.
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From page 291... ...
Details of the weighting procedures are given in Chapters 5 and 6 of the panel's report. The multiyear estimates produced by the Census Bureau's weighting scheme can be viewed as period estimates: they represent averages that reflect both changing characteristics and changes in the area's populations across the years.
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From page 292... ...
APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD BENEFITS AND CHALLENGES USING THE ACS: ESTIMATION 293 estimates for a given year within the period, this paper examines a strategy that assigns differential weights to the 1-year estimates, with largest weight given to the year in question and the next larger weights to the neighboring years. Each year the ACS will update the 3- and 5-year estimates by replacing the earliest year by the latest year.
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APPENDIX C 294 USING THE ACS: BENEFITS AND CHALLENGES with e t ∼ (0, σe 2 I ) , where I is the m × m identity matrix.
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USING THE ACS: BENEFITS AND CHALLENGES APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD ESTIMATION 295 More formally, strategies may be based on temporal models, either stochastic or deterministic. If the temporal model is stochastic, then optimal filters can be computed using well-known principles; for example, the Kalman filter does these computations recursively for large classes of linear state-space models.
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I use the class of I(1) strategies as formulated by William Bell in a presentation at a 1998 Committee on National Statistics workshop on the ACS (National Research Council, 2001)
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This is the estimator produced by the Census Bureau for areas of more than 65,000 persons. Between these two extremes lies a continuum of smoothing possibilities.
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APPENDIX C 298 USING THE ACS: BENEFITS AND CHALLENGES This value varies continuously between 1 and m. One df represents maximum smoothing; it corresponds to the simple moving average, or fitting of a common mean over the m-year window.
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APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD BENEFITS AND CHALLENGES USING THE ACS: ESTIMATION 299 A and on the true model through ψM . Also, observe that the term depending on ψM is the squared bias under model (C.2)
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APPENDIX C 300 USING THE ACS: BENEFITS AND CHALLENGES C–3.2 Results for the I(1) Strategy Under the I(1)
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00 APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD BENEFITS AND CHALLENGES USING THE ACS: ESTIMATION 301 Risk for I(1) Level Risk for Midpoint 16 4 16 8 32 2 64 8 4 2 1 1 16 4 true SNR 1 1 1 1/4 0.5 0.25 0.5 0.25 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current)
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0 APPENDIX C 302 USING THE ACS: BENEFITS AND CHALLENGES Gamma(0.2, 1) Prior for SNR Risk for Level Under I(1)
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0 USING THE ACS: BENEFITS AND CHALLENGES APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD ESTIMATION 303 In fact, it is easy to find the Bayes strategy analytically under the I(1) model and to show that this same strategy is Bayes for estimation of any linear function.
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304 USING THE ACS: BENEFITS AND CHALLENGES 0 APPENDIX C Change 1.5 1.0 Level Midpoint 0.5 Average 1 2 3 4 5 Degrees of freedom used FIGURE C.3 Bayes risk of I(1) strategy for various linear functions under I(1)
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0 APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD BENEFITS AND CHALLENGES USING THE ACS: ESTIMATION 305 Risk for I(2) Level Risk for Midpoint 8 12864 32 16 8 4 2 1 16 4 2 1 16 True SNR 4 1 1 1 1/4 0.25 0.5 0.5 0.25 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current)
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0 APPENDIX C 306 USING THE ACS: BENEFITS AND CHALLENGES Risk for Line Level Risk for Midpoint 12864 32 16 8 4 2 1 16 True SNR 4 1 1 1 1/4 0.25 0.5 0.5 0.25 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current) 1-Year Change Risk (Final)
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0 USING THE ACS: BENEFITS AND CHALLENGES APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD ESTIMATION 307 Risk for S2 Level Risk for Midpoint 2 2 1 0.5 1 16 True SNR 4 1 1 1 1/4 0.25 0.5 0.25 0.5 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current) 1-Year Change Risk (Final)
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0 APPENDIX C 308 USING THE ACS: BENEFITS AND CHALLENGES Risk for S3 Level Risk for Midpoint 8 8 42 1 4 2 1 16 True SNR 4 1 1 1 1/4 0.25 0.5 0.25 0.5 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current) 1-Year Change Risk (Final)
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0 APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD BENEFITS AND CHALLENGES USING THE ACS: ESTIMATION 309 Risk for S4 Level Risk for Midpoint 8 4 16 8 4 2 2 1 1 16 True SNR 4 1 1 1 1/4 0.25 0.5 0.25 0.5 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current) 1-Year Change Risk (Final)
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0 APPENDIX C 310 USING THE ACS: BENEFITS AND CHALLENGES Risk for S5 Level Risk for Midpoint 8 16 32 2 2 1 4 1 16 True SNR 4 1 1 1 1/4 0.25 0.5 0.25 0.5 0 1 2 3 4 5 1 2 3 4 5 1-Year Change Risk (Current) 1-Year Change Risk (Final)
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0 USING THE ACS: BENEFITS AND CHALLENGES APPENDIX C: ALTERNATIVES TO MULTIYEAR PERIOD ESTIMATION 311 N = 225 Median = 0.2008032 Quartiles = 0.04122658, 0.548866 Decimal point is 1 place to the left of the colon 0 : 00000000000000000001111111111111111112222223333333334444444555556666677778888889 1 : 0000000011122222233556677788999 2 : 0001111123344445666789 3 : 0011223334455557789 4 : 012345566789 5 : 123456899 6 : 0024478 7 : 1226899 8 : 0578 9 : 0 10 : 2346 11 : 26 12 : 13 13 : 069 14 : 2 15 : 6 High: 1.699346 2.000000 2.027793 2.226016 2.321182 2.380952 2.434674 2.565172 2.659353 High: 2.804506 3.336079 3.555556 3.742215 3.830619 4.089362 4.339465 5.979310 5.980068 High: 9.161348 13.35308 FIGURE C.10 Stem-and-leaf plot of estimated signal-to-noise ratios in the line model fitted to four years of ACS data on demographic, social, economic, and housing characteristics in Multnomah County, Oregon. With this empirical prior for SNR, the Bayes risk for various linear functions can be computed.
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312 USING THE ACS: BENEFITS AND CHALLENGES APPENDIX C 2.0 Change 1.5 1.0 Level Midpoint 0.5 Average 1 2 3 4 5 Degrees of freedom used FIGURE C.11 Bayes risk for various linear functions using empirical prior fitted from Multnomah County ACS data. NOTE: See Figure C.10 for derivation of the empirical prior using the "line" model as the true model.
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Journal of the American Statistical Association, 69, 674–678.
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