Using American Community Survey Data to Expand Access to the School Meals Programs (2012) / Chapter Skim
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Appendix C: Model-Based Estimates for School Districts and School Attendance Areas
Appendix C: Model-Based Estimates for School Districts and School Attendance Areas
Pages 264-281
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From page 264... ...
, operated by the Census Bureau, has been releasing annual estimates for the number of related1 children aged 5-17 living in families with income below the poverty level since 1999.2 Title I of the No Child Left Behind Act of 2001 directed the U.S. Department of Education to allocate $14 billion to school districts based on SAIPE results.3 The SAIPE model estimates are produced for a given year with about a 1-year time lag.
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From page 265... ...
The dependent variable in the model is the ACS 1-year direct estimate.5 Independent variables include the poverty rate from the 2000 census, the tax return poverty rate, the tax return nonfiler rate, a Supplemental Nutrition Assistance Program (SNAP, formerly the Food Stamp Program) participation ratio, and the Supplemental Security Income (SSI)
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From page 266... ...
Margins of error are not currently provided for school district-level estimates, although the Census Bureau continues to conduct research on the estimation of standard errors for school district-level estimates. The 2008 school district estimates are based on the 2008 county estimates and tabulations of poverty from the 2000 census and income tax data for tax year 2007 from the Internal Revenue Service (IRS)
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From page 267... ...
In the case of the school meals programs, the universe contains children aged 0-19 attending pub lic school. The only source for public school attendance consistent with Census Bureau population and survey estimates is the ACS.
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From page 268... ...
eligibility rate; 7The SAIPE county model estimates one set of parameters across all counties. For the school meals programs, the Census Bureau addressed the issues of size variation by using the size partitions associated with 1-year, 3-year, and 5-year ACS estimates.
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From page 269... ...
; and · 2 k = the model variance associated with partition k. The independent variables that constitute the vector xi in the free eligibility model and reduced-price eligibility model are as follows: · Free eligibility model -- Tax income/poverty ratio -- the ratio of the number of child exemptions in households with income less than or equal to 130 percent of the poverty level to the total number of child exemptions in the county -- Child tax coverage ratio -- the ratio of the number of child exemptions on tax returns in the county divided by the total household population with age less than or equal to 19 -- Four-year average ACS rate -- the average of the free eligibility rates for the other 4 years of the ACS9 · Reduced-price eligibility model -- Tax income/poverty ratio -- the ratio of the number of child exemptions in households with income greater than 130 per cent of the poverty level but less than or equal to 185 percent of the poverty level to the total number of child exemptions in the county -- Four-year average ACS rate -- the average of the reduced-price eligibility rates for the other 4 years of the ACS Estimation of the parameters proceeds on the assumption that ACS sampling variances are known, using the GVF estimate, ^ i , described below and iterating the weighted least squares regression equations to the maximumlikelihood estimate of the model variance 2 k for each partition k.
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From page 270... ...
Values for the school district tax variables -- tax income/poverty ratio free, tax income/poverty ratio reduced-price, and child tax coverage level -- are calculated using minimum-change synthetic estimates.10 Then, shrinkage estimates (empirical best predictions) for school districts (i.e., predictions of Yj for school district j)
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From page 271... ...
The median free eligibility rate showed a slight upturn in 2009, while the reduced-price eligibility rate was relatively flat. Figure C-2 shows the average across districts of 5-year ACS eligibility rates for free and reduced-price meals by size of school district.
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From page 272... ...
Census Bureau.
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From page 273... ...
Census Bureau. FIGC-1.eps 30 Free Reduced price 25 20 Eligibility Rate 15 10 5 0 < 10k (8,086)
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> 65k (942) FIGURE C-3 Median of relative standard errors for percentages eligible for free meals estimated by the model and from the 5-year and 1-year ACS by size of FIGC-3.eps school district.
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From page 275... ...
Census Bureau. 12 Model results ACS 1-year 10 Percentage Eligible 8 6 4 2 0 < 10k (8,086)
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From page 276... ...
The Census Bureau provided the following observations about the choice of prediction methods for school districts and school attendance areas for this study, relative to the shares methodology used for current SAIPE school district production: 13Figures in this section cover only those districts with combined free and reduced-price eligibility rates over 70 percent, as measured by 5-year average empirical Bayes rate modeled estimates. 14For example, in many places there are elementary, middle, and secondary schools that serve the same geographic area.
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From page 277... ...
SE, 2009 13,753 0 0.2 0.3 0.4 0.6 0.9 1.6 2.3 5.1 Model RMSD, 05-09 13,753 0.1 0.4 0.7 1.8 2.7 3.9 6.2 8.5 26.7 ACS Est., 2009 13,347 0 0 0 0 6.0 13.8 36.5 68.3 100 ACS Rel. SE, 2009 13,347 0.1 0.2 0.3 0.6 1.1 1.6 2.7 3.8 14.4 ACS RMSD, 05-09 13,687 0 0 0 3.7 6.8 11.9 24.9 40.9 50 Free + Reduced Price Model Est., 2009 13,753 1.4 5.4 10.9 25.2 37.6 49.9 67.0 79.1 99.5 NOTE: ACS = American Community Survey; RMSD = root mean squared difference; SE = standard error.
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From page 278... ...
> 65k (26) FIGURE C-7 Median of relative standard errors for model-based and 1-year and 5-year ACS-based free eligibility percentages by size of school district.
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From page 279... ...
> 65k (26) FIGURE C-9 Median of relative standard errors for model-based and 1-year and 5-year ACS-based reduced-price FIGC-9.eps eligibility percentages by size of school district.
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From page 280... ...
· The shares methodology is a two-step process, adding estimation error at each step. PANEL'S SUGGESTIONS FOR MODELING ELIGIBILITY PERCENTAGES FOR THE SCHOOL MEALS PROGRAMS As noted previously, the models for the school meals programs were developed quickly as a proof of the concept that using SAIPE-like smallarea models for the school meals programs might provide accurate and timely estimates of eligibility.
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From page 281... ...
· While assuming that estimated eligibility percentages follow nor mal distributions may be reasonable in some instances, it is not a good assumption for small samples (as for the school attendance areas in a small or medium-sized district) or for small percentages (such as reduced-price percentages)
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