Small-Area Estimates of School-Age Children in Poverty Evaluation of Current Methodology (2000) / Chapter Skim
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Appendix A: Models for County and State Poverty Estimates
Appendix A: Models for County and State Poverty Estimates
Pages 169-184
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Appendices
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From page 171... ...
The same model forms can be used for poverty statistics for other age groups, with appropriately defined dependent and regression variables. NOTATION The following notation is used in the estimation program: · Yin = CPS 5-17 poverty estimate for county i in year t; · Ceni = previous census estimate for county i (where necessary, a specific census is distinguished by writing Cen90i or Cen80i)
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enter SAIPE models as regression variables in the equation for the 1990 census data but are not themselves the dependent variable in any model (because the corresponding regression variables Xi 79 are not available.) Note that Yin = Ye + en and Ceni = Zi + Hi.
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and (2) are thus the regression parameters A, A, 71, and y; the common model error variance (S2; and the sampling error variance parameter vet Decennial census sampling error variances for estimates of number of poor are available from published formulas (generalized variances)
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The CPS poverty universe, and the number of poor related children aged 5-17, are estimated from CPS data for each year using CPS weights modified to make each county "self-representing." For counties with a CPS sample in only 1 or 2 of the 3 years, the values for only that year, or for the 2-year average corresponding to (6) , are used.
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and (10) to be estimated are thus the regression parameter vectors ~ and A; the common model error variance (SU2; the model error correlation p; and the sampling error variance parameter vet Note that the bivariate model form differs from the SAIPE model form in that it does not include the previous census data as a regression variable, and it also allows the model errors to be correlated.
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From page 176... ...
are provided as part of the regression diagnostics for the fitted bivariate models. Because the bivariate model uses previous census data Ceni by jointly modeling it with the CPS data Nit, it could not be applied for t = 1989 because the regression variables Xi 79 needed for modeling the 1980 census data are not available.
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are needed to convert smoothed poverty rate estimates to estimates of the number of poor children. For some counties with very small CPS sample sizes there may be no related children aged 5-17 observed in the sample.
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To assume that the CPS sampling errors of direct poverty rate estimates have variance of the form ve I nit is inconsistent with making the same assumption for CPS direct estimates of log number poor or log poverty rate. Simple Taylor series approximations suggest that if ve I nit is the appropriate variance for poverty rate estimates, then the sampling error variance for log poverty rates will depend on the underlying true poverty rate p, and vice versa.
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From page 179... ...
and (2~: the census data appearing on the right-hand side of the equations are analogous to the other regression variables defined as log number poor children 5-17, whereas Cen90i appearing on the left-hand side is the log census poverty rate. With the data thus defined, the model fitting proceeds in the same fashion as for the other models discussed.
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be vectors containing the county CPS and census data to be used for model fitting, and let X~ and X~g be the corresponding matrices of regression variables for their respective equations. The SAIPE model form given by (1)
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, one also needs to allow for the correlations between ut and z when estimating the regression parameters (p, 71~- This can be done by applying generalized least squares to (18~. In fact, it is simpler to structure the equations for the bivariate model so that the CPS and census data are paired off (for those counties with CPS data available for model fitting)
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From page 182... ...
In the Splus bivariate model software, all the census data are used in the model fitting, along with as much CPS data as are available for the year and the poverty statistic being modeled. This approach assumes that the model applies equally well to counties with and without a CPS sample.
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For the comparisons that have been made, the differences in results appear to be small. SMOOTHED ESTIMATES Smoothed estimates from an estimated 1993 SAIPE model form are determined from the CPS equation (1)
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Prediction error variances in these cases could be taken to be those for the smoothed poverty rates multiplied by the square of the population estimates, though this ignores error in the 5-17 population estimates. Formal measures (variances)
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