Campbell sparkspaa12

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This is a presentation that we gave at the 2012 Population Association of America meeting in San Francisco, CA. In it, we describe a comparison between Bayesian county level poverty rate estimates and those of the SAIPE program of the US Census Bureau

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Campbell sparkspaa12

  1. 1. AN APPLICATION OF BAYESIAN METHODS TOSMALL AREA ESTIMATES OF POVERTY RATESJoey CampbellCorey SparksThe University of Texas at San AntonioDepartment of Demography
  2. 2. INTRODUCTION Estimates of various socio-demographic variables for small geographical areas are proving difficult with the replacement of the Census long form with the American Community Survey (ACS). Sub-national demographic processes have generally relied on Census 2000 long form data products in order to answer research questions.
  3. 3. INTRODUCTION ACS data products promise to begin providing up-to-date profiles of the nations population and economy Unit and item level non-response in the ACS have left gaps in sub-national coverage The result is unstable estimates for basic demographic measures.
  4. 4. PURPOSE Borrowing information from neighboring areas with a spatial smoothing process based on Bayesian statistical methods Generate more stable estimates of rates for geographic areas not initially represented in the ACS. A spatial smoothing process grounded in Bayesian statistics, is used to derive estimates of poverty rates at the county level for the United States.
  5. 5.  Data come from two sources US Census 2000 Summary File 3 American Community Survey  2001 – 2005 1-year estimates  2005 – 2007, 2006 – 2008 3-year estimates  2005 – 2009 5-year estimates U.S. Counties  N=3,141 (Continental)  2000 Census is missing poverty rates for 0 counties  ACS is missing poverty rates for up to 3,123 counties for some years  Primarily due to small population sizes of counties
  6. 6. ESTIMATING COUNTY-LEVEL RATES
  7. 7. METHODS: BAYESIAN HIERARCHICAL MODEL Bayesian Statistics  Uses Prior information for estimation of parameters of interest  Allows for posterior estimation of these parameters using the combination of the information in the likelihood and the prior Hierarchical Modeling  Bayesian Hierarchical Model  Allows for a spatially and temporally smoothed estimate of rates  Draws “strength” from neighboring observations  Estimated with WinBUGS via Markov–Chain Monte Carlo methods  100,000 simulations with 20,000 burn in period
  8. 8. THE MODELS yi~ bin(pi, ni) logit(pi) = μ0+Ai+Bj+ Cij
  9. 9. THE MODELS yi~ bin(pi, ni) logit(pi) = μ0+Ai+Bj+ Cij Overal l rate
  10. 10. THE MODELS yi~ bin(pi, ni) logit(pi) = μ0+Ai+Bj+ Cij Overal l rate The spatial group
  11. 11. THE MODELS yi~ bin(pi, ni) logit(pi) = μ0+Ai+Bj+ Cij Overal l rate The spatial group The time group
  12. 12. THE MODELS yi~ bin(pi, ni) logit(pi) = μ0+Ai+Bj+ Cij Overal l rate The spatial group The time group The space -time group
  13. 13. THE MODELS yi~ bin(pi, ni) logit(pi) = μ0+Ai+Bj+ Cij Summary of Model Specification Spatial Temporal Space-time Terms Terms Terms Model Ai Bj Cij 1 vi+ui βtj 0 2 vi+ui tj 0 3 vi+ui tj+ξj 0 4 vi+ui tj ψij 5 vi+ui tj+ξj ψij 6 vi+ui tj ψijEach model was evaluated with respect to how itrecreated the overall poverty rate, the known time trend,and the known spatial distribution
  14. 14. RESULTS: OVERALL POVERTY RATE The overall estimate of U.S. poverty in 2001 according to  SAIPE = 13.74 percent.  Model 1 = 13.97 percent  Model 2 = Model 3 =13.96 percent  Model 4 = Model 5 = 14.15 percent, and  Model 6 = 14.17 percent. Overall, the Bayesian models produce similar rates of those estimated by more traditional methods.
  15. 15. RESULTS: ERROR RATESMean Absolute Percent Error (MAPE) Rates for Bayesian Estimates of US CountyPoverty Rates compared to SAIPEModel 2001 2002 2003 2004 2005 2006 2007 2008 2009 Total 10.6 1 11% 10.8% 11.2% 8.8% 9.3% 9.8% 10.9% 13.1% 11.5% % 2 10.5% 10% 10.4% 11.1% 8.2% 9.1% 9.8% 11% 13% 10.3% 3 10.5% 10.4% 10.4% 11.1% 8.2% 9.1% 9.8% 11.0% 13.0% 10.3% 4 10.6% 11.8% 12.0% 13.1% 10.3% 11.0% 10.6% 11.1% 11.7% 11.3% 5 10.6% 11.8% 12.0% 13.1% 10.3% 11.0% 10.6% 11.1% 11.7% 11.3% 6 10.7% 11.9% 12.2% 13.2% 10.3% 11.0% 10.5% 10.8% 11.8% 11.3%
  16. 16. DISCUSSION Although the estimates of various socio- demographic variables in the ACS have improved over time, progress is not as fast as expected Local level efforts have been advocated to help combat various outcomes associated with poverty. Consequently, reliable estimates for small areas are necessary for these efforts to move forward
  17. 17. DISCUSSION The Bayesian approach has been demonstrated to produce reliable and dependable estimates by borrowing information both across time and from neighboring counties Hopefully these estimates (and this method) can be employed to effectively understand how socio-demographic variables vary at the local level Additionally, models may be formulated that incorporate ACS errors directly (Bayesian SEM)

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