Small-Area Estimates of School-Age Children in Poverty Evaluation of Current Methodology (2000) / Chapter Skim
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Appendix B: Regression Diagnostics on Alternative County Regression Models
Appendix B: Regression Diagnostics on Alternative County Regression Models
Pages 185-193
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log rate model (under 18~. This appendix summarizes the results of an internal evaluation for 13 county models, listed below (see Chapter 5 and Appendix A for the model specifications)
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NOTE: The years for which coefficients were fit are in parentheses; for the bivariate models, the year shown is for the CPS equation. REGRESSION DIAGNOSTICS METHODS Regression diagnostics is an analysis of the extent to which the various assumptions on which a regression model is based are supported by the data.
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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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, Fixed State Effects 1989 0.36 0.27 0.45 -0.56 0.51 (.13)
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aPredictor variables: (1) number of child exemptions reported by families in poverty on tax returns (1989 or 1993)
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ratio of child exemptions reported by families in poverty on tax returns to total child exemptions in 1989; (2) ratio of people receiving food stamps in 1989 to total population; (3)
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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) versus log CPS sample size.
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Homogeneous Variances All of the models exhibited nonconstant variances of the standardized residuals. 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.
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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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