Small-Area Estimates of School-Age Children in Poverty Interim Report 2, Evaluation of Revised 1993 County Estimates for Title I Allocations (1998) / Chapter Skim
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APPENDIX C. REGRESSION DIAGNOSTICS ON ALTERNATIVE COUNTY REGRESSION MODELS
APPENDIX C. REGRESSION DIAGNOSTICS ON ALTERNATIVE COUNTY REGRESSION MODELS
Pages 124-132
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From page 124... ...
The other 6 county models are bivariate models in which two equations are jointly estimated to develop estimates of poor school-age children in 1993. In one equation, the dependent variable is a weighted average of data from the 124
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From page 125... ...
The regression coefficients for all the CPS models are presented in Table C1; Table C-2 shows the regression coefficients for the 1990 census equation for the 6 bivariate models (see pages 128-130~. Single-Equation Models Bivariate Models Log number under 21 (1989, 1993)
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From page 126... ...
Linearity Linearity of the relationships between the dependent variable and the predictor variables was assessed graphically, by observing whether there was evidence of curvature in the plots of standardized residuals against predictor variables in the model. In addition, plots of residuals against CPS sample size and against the predicted values from the regression model were examined for curvature.
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From page 127... ...
The statistics included: Spearman's rank correlation coefficient of absolute standardized residuals with the predicted values and also with the CPS sample size, and a robust regression of the log absolute standardized residuals on CPS sample size. The graphical displays included: scatterplots of absolute standardized residuals versus model predictor variables; box plots of absolute standardized residuals for categories of counties; plots of the median absolute deviation of the standardized residuals in a category by categories; plots of absolute standardized residuals versus log CPS sample size; and plots of standardized residuals to the two-thirds power (the Wilson-Hilferty transformation)
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From page 128... ...
, Fixed State Effects 1989 0.36 0.27 0.45 -0.56 0.51 (.13)
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From page 129... ...
aPredictor variables: (1) number of child exemptions reported by families in poverty on tax returns (1989 or 1993)
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From page 130... ...
ratio of total child exemptions on tax returns in 1989 to population under age 21. Inclusion or Exclusion of Predictor Variables All of the models with fixed state effects have a large fraction of state effects that are not significant at the 5 percent level.
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From page 131... ...
One would expect the standardized residual variance to remain constant over the distribution of CPS sample size; however, for these models, it increased with increasing sample size. Most of the models also had some variance heterogeneity as a function of the predicted value (number or proportion of poor school-age children)
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From page 132... ...
The bivariate approach appears promising due to the heterogeneity in the regression coefficient mentioned above, the lack of patterns in the analysis of the standardized residuals, and the correlation observed by corresponding residuals in the CPS and census regression equations. Finally, according to the internal evaluation, none of the alternative models is clearly superior to the log number model, and the use of the predictor variable for the population under age 18 instead of under age 21 is supported for the log number model.
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