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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology
APPENDIX
C
County Model Comparisons with 1990 Census Estimates
An external evaluation of alternative models for producing county estimates of poor school-age children can be carried out by comparing the county estimates obtained from each model for 1989 with 1900 census estimates of related children 5-17 who were poor in 1989. Although this evaluation is not ideal, it serves as a valuable tool for model assessment.
Chapter 6 reports the results of such an evaluation for four candidate models and four procedures that rely more heavily on estimates from the 1980 census. This appendix supplements the material in Chapter 6 in two ways. First, it provides additional results for the four models and four procedures examined in Chapter 6. Second, it provides evaluation results for the six single-equation models that were considered in the first round of evaluations.
EVALUATION MEASURES
Four measures are used for the evaluations in Chapter 6 and in this appendix. Two are overall measures of the differences between the county estimates from a model (or procedure) and the census, and two are measures for categories of counties. The four measures are defined as follows:
Average absolute difference: the sum over all counties of the absolute (unsigned) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the number of counties (3,141), or
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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology
APPENDIX
C
County Model Comparisons with 1990 Census Estimates
An external evaluation of alternative models for producing county estimates of poor school-age children can be carried out by comparing the county estimates obtained from each model for 1989 with 1900 census estimates of related children 5-17 who were poor in 1989. Although this evaluation is not ideal, it serves as a valuable tool for model assessment.
Chapter 6 reports the results of such an evaluation for four candidate models and four procedures that rely more heavily on estimates from the 1980 census. This appendix supplements the material in Chapter 6 in two ways. First, it provides additional results for the four models and four procedures examined in Chapter 6. Second, it provides evaluation results for the six single-equation models that were considered in the first round of evaluations.
EVALUATION MEASURES
Four measures are used for the evaluations in Chapter 6 and in this appendix. Two are overall measures of the differences between the county estimates from a model (or procedure) and the census, and two are measures for categories of counties. The four measures are defined as follows:
Average absolute difference: the sum over all counties of the absolute (unsigned) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the number of counties (3,141), or
∑(|Ymodel i − Ycensus i|) / n .
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Average proportional absolute difference: the sum over all counties of the absolute difference between the model estimate of poor school-age children and the 1990 census estimate as a proportion of the census estimate for each county, divided by the number of counties,1 or
∑[(|Ymodel i − Ycensus i |) / Ycensus i ] / n.
Category algebraic difference: the sum for all counties (i) in a category (j) of the algebraic (signed) difference between the model estimate of poor school-age children and the 1990 census estimate for each county in the category, divided by the sum of the census estimates for the counties in the category, or
∑i (Ymodel ij −Ycensus ij) / ∑i Ycensus ij .
Category average proportional algebraic difference: the sum for all counties (i) in a category (j) of the algebraic difference between the model estimate of poor school-age children and the 1990 census estimate as a proportion of the census estimate for each county in the category, divided by the number of counties in the category, or
∑i [(Ymodel ij − Ycensus ij) / Ycensus ij ] / nj .
Measure (1) expresses overall absolute model-census differences in terms of numbers of poor school-age children; measure (2) expresses overall absolute model-census differences in terms of percentage errors for counties. Similarly, for categories of counties, measure (3) expresses model-census differences in terms of numbers of poor school-age children, while measure (4) expresses model-census differences in terms of percentage errors for counties. The two kinds of category differences are algebraic (not absolute) measures, in which positive differences offset negative differences.
For measures (3) and (4), the counties are grouped into categories of the following characteristics: census geographic division; metropolitan status of county; population size in 1990; population growth from 1980 to 1990; percentage of poor school-age children in the 1980 census; percentage of Hispanic population in 1990; percentage of black population in 1990; persistent poverty from 1960 to 1990 for rural counties; economic type for rural counties; percentage of group quarters residents in 1990; whether the county had households in the CPS sample; and percentage change from 1980 to 1990 in the proportion of poor school-age children.2 Table C-1 and Table C-2 show the number of counties in each category.
1
An analogous measure, shown in Table 6-3, is the average proportional absolute difference in estimated proportions of poor school-age children.
2
The characteristic of percentage change in the proportion of poor school-age children from 1980 to 1990 was not included in the first round of evaluations.
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TABLE C-1 Comparison of Model Estimates and Other Procedures with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Algebraic Difference by Category of County (in percent)
Model
Other Procedures
Log No. Under 21
Log No. Under 18
Log Rate Under 21
Log Rate Under 18
Stable Shares
Stable Shares in State
Stable Rates in State
Average of Census and (a)
Category
Countiesa (Number)
(a)
(b)
(c)
(d)
(i)
(ii)
(iii)
(iv)
Census Divisionb
New England
67
−2.9
−2.9
−2.9
−2.9
35.9
−2.9
−2.9
7.8
Middle Atlantic
150
−2.8
−2.8
−2.8
−2.8
27.1
−2.8
−2.8
4.4
East North Central
437
−0.2
−0.2
−0.2
−0.2
−2.8
−0.2
−0.2
−5.6
West North Central
618
1.7
1.7
1.7
1.7
−1.8
1.7
1.7
−2.1
South Atlantic
591
0.5
0.5
0.5
0.5
14.8
0.5
0.5
8.1
East South Central
364
−4.5
−4.5
−4.5
−4.5
14.1
−4.5
−4.5
2.1
West South Central
470
−2.7
−2.7
−2.7
−2.7
−18.1
−2.7
−2.7
−6.3
Mountain
281
4.3
4.3
4.3
4.3
−23.2
4.3
4.3
−3.1
Pacific
163
6.5
6.5
6.5
6.5
−21.3
6.5
6.5
0.2
Metropolitan Status
Central county of metropolitan area
493
2.4
1.6
−0.1
−0.5
−1.6
−0.6
−0.4
0.4
Other metropolitan
254
−6.6
−5.0
5.1
6.3
3.2
−6.1
10.1
3.4
Nonmetropolitan
2,394
−4.2
−2.8
−0.3
0.4
3.3
1.8
−0.5
−1.4
1990 Population Size
under 7,500
525
−9.0
−2.3
−1.9
2.3
16.5
23.0
9.4
1.3
7,500-14,999
630
−4.4
0.5
2.5
5.5
10.9
10.7
4.4
2.2
15,000-24,999
524
−5.1
−2.6
0.3
1.9
6.2
3.4
0.0
−0.6
25,000-49,999
620
−4.2
−2.9
0.6
1.3
2.4
−0.2
−0.3
−1.3
50,000-99,999
384
−3.5
−5.1
−1.2
−2.3
−2.5
−4.8
−2.5
−3.3
100,000-249,999
259
−1.8
−4.4
−1.8
−3.5
−4.9
−5.9
−2.9
−3.3
250,000 or more
199
3.3
3.2
0.5
0.5
−0.6
0.8
0.8
1.8
1980 to 1990 Population Growth
Decrease of more than 10.0%
444
−1.9
0.6
−3.4
−1.9
9.1
9.9
−3.1
−3.4
Decrease 0.1-10.0%
972
−0.6
−0.5
−1.9
−1.8
7.5
0.7
−4.6
−2.7
0.0-4.9%
547
−2.8
−2.8
−3.2
−3.1
11.0
−2.3
−3.3
−0.2
5.0-14.9%
620
0.0
−1.0
0.2
−0.6
6.1
0.2
1.7
2.1
15.0-24.9%
260
7.7
5.8
5.5
4.6
−12.8
4.4
3.5
2.4
25.0% or more
292
−4.0
−1.4
1.7
3.1
−21.2
−6.8
7.2
1.0
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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology
Model
Other Procedures
Log No. Under 21
Log No. Under 18
Log Rate Under 21
Log Rate Under 18
Stable Shares
Stable Shares in State
Stable Rates in State
Average of Census and (a)
Category
Countiesa (Number)
(a)
(b)
(c)
(d)
(i)
(ii)
(iii)
(iv)
Percent Group Quarters Residents, 1990
Less than 1.0%
545
−6.7
−2.7
2.0
4.7
−1.4
−0.9
3.7
0.3
1.0-4.9%
2,187
0.3
0.7
−0.3
0.1
−0.4
0.3
−0.1
0.1
5.0-9.9%
299
2.3
−4.4
0.5
−5.2
7.8
−1.4
−2.8
−0.8
10.0-41.0%
110
14.2
−3.2
7.4
−7.5
1.8
−0.9
−1.4
−2.2
Status in CPS, 1989-1991
In CPS sample
1,028
1.4
1.0
−0.2
−0.5
−0.6
−0.7
−0.4
0.5
In CPS, no poor children 5-17
246
−2.6
−1.9
7.3
7.8
10.0
3.7
12.0
5.9
Not in CPS sample
1,867
−4.1
−2.8
−0.1
0.6
0.6
2.3
−0.3
−2.3
Change in Poverty Rate for School-Age Children, 1980-1990
Decrease of more than 3.0%
536
7.5
10.4
16.2
18.1
51.6
30.1
32.8
30.0
Decrease 0.1-3.0%
649
2.1
1.9
3.1
2.9
29.2
8.0
9.8
12.1
0.0-0.9%
272
−2.6
−0.8
−0.4
0.5
4.3
−0.9
3.3
3.1
1.0-3.4%
621
3.8
2.2
3.4
2.6
−5.1
3.7
3.4
0.2
3.5-6.4%
532
−1.2
−2.4
−3.8
−4.3
−14.3
−7.7
−9.5
−8.3
6.5-38.0%
523
−7.2
−5.2
−8.7
−7.8
−25.2
−14.2
−16.5
−14.5
NOTES: The census estimates are controlled to the CPS national estimate for 1989. The algebraic difference by category is the sum for all counties in a category of the algebraic (signed) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the sum of the census estimates for all counties in the category. See Chapter 6 text for definitions of models.
a3,141 counties are assigned to a category for most characteristics; 3,135 counties are assigned to a category for 1980-1990 population growth and 1980 percentage poor school-age children; 3,133 counties are assigned to a category for 1980-1990 percentage change in poverty rate for school-age children.
bCensus division states: New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut Middle Atlantic: New York, New Jersey, Pennsylvania East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin West North Central: Missouri, Minnesota, Iowa, North Dakota, South Dakota, Nebraska, Kansas South Atlantic: Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada Pacific: Washington, Oregon, California, Alaska, Hawaii
cThe Economic Research Service, U.S. Department of Agriculture, classifies rural counties by 1960-1990 poverty status and economic type. Counties not classified are urban counties and rural counties for which a classification could not be made.
SOURCE: Data from U.S. Census Bureau.
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TABLE C-2 Comparison of Model Estimates and Other Procedurees with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Average Proportional Algebraic Difference for Counties in Each Category (in percent)
Model
Other Procedures
Log No. Under 21
Log No. Under 18
Log Rate Under 21
Log Rate Under 18
Stable Shares
Stable Shares in State
Stable Rates in State
Average of Census and (a)
Category
Counties (Number)
(a)
(b)
(c)
(d)
(i)
(ii)
(iii)
(iv)
Census Division
New England
67
4.1
4.5
6.6
7.1
45.6
7.0
8.6
20.2
Middle Atlantic
150
−5.9
−8.4
0.7
−1.0
28.8
−0.2
3.1
3.6
East North Central
437
−3.6
−3.0
2.5
3.0
0.6
3.5
5.8
−4.6
West North Central
618
−3.1
−0.6
0.5
2.3
18.7
21.0
15.9
3.7
South Atlantic
591
1.2
2.5
8.9
9.8
28.6
10.2
11.9
14.5
East South Central
364
−4.6
−3.0
0.5
1.3
19.5
0.4
0.3
5.0
West South Central
470
−7.6
−4.6
−4.0
−2.3
−6.4
8.8
−0.2
−5.5
Mountain
281
0.6
5.4
7.2
10.4
−3.4
30.5
22.6
2.6
Pacific
163
10.2
13.6
17.8
20.2
−9.6
23.9
20.6
7.5
Metropolitan Status
Central county of metropolitan area
493
0.6
−2.0
1.0
−0.6
4.2
−0.2
2.2
0.8
Other metropolitan
254
−3.6
−0.8
11.6
13.7
16.2
7.0
20.9
11.7
Nonmetropolitan
2,394
−2.6
0.2
2.9
4.7
13.2
15.0
9.9
3.6
1990 Population Size
under 7,500
525
−5.9
1.6
2.6
7.6
30.3
42.0
25.9
9.2
7,500-14,999
630
−1.0
3.0
5.7
8.4
16.3
17.5
12.2
6.1
15,000-24,999
524
−3.2
−1.8
2.1
3.2
9.0
6.8
4.5
1.1
25,000-49,999
620
−1.5
−0.7
4.2
4.6
6.0
3.1
5.3
2.2
50,000-99,999
384
−1.4
−3.3
2.5
1.2
3.1
−1.7
3.3
0.8
100,000-249,999
259
−0.7
−3.4
1.5
−0.3
2.4
−2.5
2.8
0.8
250,000 or more
199
1.0
0.4
1.3
1.1
7.9
2.9
6.5
4.5
1980 to 1990 Population Growth
Decrease of more than 10.0%
444
−5.2
−1.0
−1.2
2.0
29.0
36.9
17.5
3.7
Decrease 0.1-10.0%
972
−3.3
−2.2
0.1
0.9
11.6
10.1
3.0
−0.8
0.0-4.9%
547
−1.3
0.4
4.0
5.0
11.7
7.5
5.2
3.3
5.0-14.9%
620
−0.7
0.0
4.7
5.0
9.9
6.1
8.7
4.8
15.0-24.9%
260
4.0
3.8
10.6
10.1
8.7
8.7
16.0
10.4
25.0% or more
292
−4.1
2.3
9.8
14.0
−4.0
4.3
23.8
12.6
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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology
Model
Log Number Under 21
Log Number Under 18
Log Number Under 21, Fixed State Effects
Log Rate Under 21
Rate Under 21
Log Hybrid Rate-Number Under 21
Category
C.1
C.2
C.3
C.4
C.4a
C.5
C.5a
C.6
C.6a
Percent Group Quarters Residents, 1990
Less than 1.0%
−2.1
2.1
−0.5
7.0
4.9
8.9
6.7
2.7
0.6
1.0-4.9%
5.2
5.7
5.4
4.6
4.6
4.7
4.7
5.7
5.7
5.0-9.9%
7.4
0.3
5.0
5.5
7.3
4.0
5.8
0.3
2.0
10.0-41.0%
19.9
1.6
11.9
12.7
17.4
5.0
9.3
0.6
4.7
Status in CPS, 1989-1991
In CPS sample
6.4
5.9
5.8
4.7
4.4
5.3
5.0
6.8
6.6
In CPS, no poor children 5-17
2.2
3.0
0.8
12.6
10.2
−1.0
−2.9
5.3
3.0
Not in CPS sample
0.6
2.0
2.8
4.8
6.2
5.0
6.3
−1.4
−0.1
NOTES: See text for definitions of models and measures. 3,141 counties are assigned to a category for most characteristics; 3,135 counties are assigned to a category for 1980-1990 population growth and 1980 percentage of poor school-age children; 3,133 counties are assigned to a category for 1980-1990 percentage change in poverty rate for school-age children; see Table C-1 for number of counties in each category.
aCensus division states:
New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut
Middle Atlantic: New York, New Jersey, Pennsylvania
East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin
West North Central: Missouri, Minnesota, Iowa, North Dakota, South Dakota, Nebraska, Kansas
South Atlantic: Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida
East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas
Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada
Pacific: Washington, Oregon, California, Alaska, Hawaii
bThe Economic Research Service, U.S. Department of Agriculture, classifies rural counties by 1960-1990 poverty status and economic type. Counties not classified are urban counties and rural counties for which a classification could not be made.
SOURCE: Data from U.S. Census Bureau.
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TABLE C-5 Comparison of First-Round Model Estimates with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Average Proportional Algebraic Difference for Counties in Each Category (in percent)
Model
Log Number Under 21
Log Number Under 18
Log Number Under 21, Fixed State Effects
Log Rate Under 21
Rate Under 21
Log Hybrid Rate-Number Under 21
Category
C.1
C.2
C.3
C.4
C.4a
C.5
C.5a
C.6
C.6a
Census Division
New England
9.3
9.7
8.1
11.9
13.1
10.9
12.2
8.3
9.4
Middle Atlantic
−1.2
−3.9
−3.5
5.7
4.1
4.2
2.8
−1.2
−2.6
East North Central
1.2
1.8
2.2
7.5
8.5
6.4
7.4
−0.1
0.7
West North Central
1.7
4.4
7.4
5.4
7.3
6.1
8.0
−0.2
1.6
South Atlantic
6.2
7.6
8.1
14.3
12.6
14.5
12.8
7.7
6.1
East South Central
0.1
1.8
0.9
5.4
4.8
5.3
4.6
0.7
0.0
West South Central
−3.0
0.1
0.2
0.7
3.3
1.8
4.3
−6.7
−4.4
Mountain
5.6
10.6
12.2
12.5
14.6
17.0
19.3
3.9
5.7
Pacific
15.6
19.2
19.2
23.7
23.8
25.6
25.8
15.6
15.7
Metropolitan Status
Central county of metropolitan area
5.6
2.9
3.5
6.0
4.9
5.0
4.0
6.1
4.9
Other metropolitan
1.1
4.1
−0.1
17.1
13.3
16.1
12.4
6.8
3.4
Nonmetropolitan
2.2
5.1
6.5
7.9
9.4
9.0
10.5
0.3
1.6
1990 Population Size
under 7,500
−1.3
6.6
9.9
7.7
9.2
12.7
14.2
−3.5
−2.3
7,500-14,999
3.9
8.1
9.3
10.9
12.3
11.5
12.8
2.2
3.4
15,000-24,999
1.6
3.0
4.2
7.2
8.2
6.9
8.0
0.1
1.1
25,000-49,999
3.4
4.2
3.7
9.3
10.1
8.8
9.6
2.8
3.5
50,000-99,999
3.4
1.5
1.0
7.5
7.3
7.3
7.0
3.1
2.8
100,000-249,999
4.2
1.4
1.4
6.6
6.0
3.3
2.9
4.0
3.4
250,000 or more
5.9
5.4
5.0
6.3
4.4
7.3
5.5
8.7
6.9
1980 to 1990 Population Growth
Decrease of more than 10.0%
−0.5
3.9
10.5
3.7
3.9
7.9
8.0
−1.7
−1.5
Decrease 0.1-10.0%
1.5
2.6
5.5
5.0
6.4
5.4
6.8
−0.7
0.6
0.0-4.9%
3.6
5.3
5.1
9.2
9.9
8.2
8.9
2.7
3.4
5.0-14.9%
4.2
4.9
4.1
9.9
10.2
9.6
10.0
3.4
3.6
15.0-24.9%
9.2
9.0
7.5
16.0
15.6
15.6
15.2
8.0
7.6
25.0% or more
0.7
7.3
−0.3
15.2
15.7
16.2
16.9
3.9
4.1
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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology
Model
Log Number Under 21
Log Number Under 18
Log Number Under 21, Fixed State Effects
Log Rate Under 21
Rate Under 21
Log Hybrid Rate-Number Under 21
Category
C.1
C.2
C.3
C.4
C.4a
C.5
C.5a
C.6
C.6a
Percent Group Quarters Residents, 1990
Less than 1.0%
−1.1
7.5
3.8
11.3
10.7
13.7
13.2
1.8
1.1
1.0-4.9%
1.7
4.3
5.0
6.7
7.4
7.4
8.1
1.5
2.1
5.0-9.9%
10.4
4.3
9.5
11.9
14.2
11.3
13.5
3.3
5.3
10.0-41.0%
19.4
−0.3
12.4
17.0
19.0
9.9
11.8
2.0
3.8
Status in CPS, 1989-1991
In CPS sample
4.0
3.6
3.9
7.0
6.6
8.9
8.6
4.3
3.9
In CPS, no poor children 5-17
3.6
6.0
3.1
15.4
13.9
4.6
3.5
5.8
4.5
Not in CPS sample
1.8
5.1
6.7
8.2
9.7
9.5
11.0
−0.3
1.1
NOTE: See notes to Table C-4.
SOURCE: Data from U.S. Census Bureau.
Summary of Category Differences
Three of the eleven characteristics examined show no pronounced patterns of overprediction or underprediction of the number of poor school-age children for any of the models:
percentage of poor school-age children from the 1980 census;
percentage of black population in 1990; and
persistent rural poverty from 1960 to 1990.
Four characteristics show patterns for all or all but one model in which some categories of counties are over(under)predicted relative to other counties:
census geographic division;
percentage of change in population from 1980 to 1990 (population growth);
percentage of Hispanic population in 1990; and
economic type, for rural counties.
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The remaining four characteristics exhibit mixed patterns, in which some models give evidence of over(under)prediction for counties in some categories and other models do not:
metropolitan status of county;
1990 population size;
percentage of group quarters residents in 1990; and
status in CPS sample.
Of these four characteristics, over(under)prediction for those models in which it occurs is most pronounced for population size and percentage of group quarters residents.
Overall, there is no clearly best or worst model in terms of differences from the 1990 census estimates for categories of counties. Each model exhibits strengths and weaknesses (keeping in mind that the analysis is based on a single evaluation). On balance, the log number (under 18) model (C.2) performs somewhat better than the other models.
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