The Bicentennial Census New Directions for Methodology in 1990: 30th Anniversary Edition (2015) / Chapter Skim
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7 Adjustment of Population Counts
7 Adjustment of Population Counts
Pages 245-282
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From page 245... ...
Thus, concerns about the consequences of differential coverage error have increased as has pressure for the Census Bureau to reduce differential coverage error. Both improvements in the actual census count and subsequent statistical adjustment of that count have been urged.
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From page 246... ...
As reviewed in Chapter 2, there is evidence that differential coverage errors importantly affect both political representation and fund allocation. The panel believes that adjustment procedures should focus on minimizing these errors.
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From page 247... ...
In the remainder of this chapter, we summarize some of the technical information pertinent to these questions and present the recommendations to which we are led. Many technical questions remain to be answered if adjustment procedures are to be developed in time for their use in the 1990 census.
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From page 248... ...
Given the likelihood that the cen sus will continue to produce different rates of undercoverage for vari ous population groups, and given the equity problems caused thereby, we recommend that work proceed on the development of adjustment procedures and that adjustment be implemented if there is reasonable confidence that it will reduce differential coverage errors. We note that there are several different methods of adjustment that have been suggested so far, and we anticipate that others will be proposed.
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From page 249... ...
A User's View of Loss Functions and Adjustment Concern about census coverage error arises less because of net national undercoverage than because of differential undercoverage by geographic location and demographic group. Differential undercoverage causes differences in political representation and distribution of public monies from the allocation that would result if a completely accurate census could be taken, differences that may work to thwart the intent of laws governing represen
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From page 250... ...
Furthermore, knowledge of a subsequent adjustment might reduce public cooperation, thus lowering the completeness of the census count. For an effective adjustment procedure to be widely accepted, given that not all localities will benefit, it is important that there be as widespread under tanding and agreement as possible within the professional commu s nity of statisticians that a general reduction in differential coverage error is sufficiently desirable to accept adverse impacts on some individual localities.
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From page 251... ...
Loss Functions and Adjustment The classical yardstick used by sample survey researchers to assess the accuracy of a single number, chosen principally for its convenient mathe matical properties, is the square of the deviation between the number and its true value. Whatever loss function we use to assess the accuracy of a single number, we still must determine a rule for amalgamating the losses associated with each number into an overall loss function for the entire set of numbers produced.
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From page 252... ...
Again, the area with twice the population size contributed twice as much to the overall loss function. Both of these loss functions, squared error divided by the true value and by the estimated value, are commonly used in the analysis of contingency tables.1 1 ote N that squared relative error (relative to either the true or estimated value)
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From page 253... ...
In our example, the loss for the area of 10,000 population would count twice as heavily as the loss for the smaller area in the overall loss function. Research on Loss Functions and Adjustment One characteristic of the loss functions given above is that they are general in nature and not specific to census data uses, except in distinguishing absolute and differential inaccuracy.
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From page 254... ...
studied the effect of a very simple synthetic adjustment (see the discussion of synthetic estimation in a subsequent section) , using only two demographic groups, on population proportions across geographic areas using a number of different loss functions: (1)
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From page 255... ...
We recommend that the Census Bureau investigate the construc tion of adjustment procedures that are robust to a reasonable range of loss functions.
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From page 256... ...
However, the models underlying the methods used for carrying down coverage evaluation information to small areas are rough and make little provision for a small area's special characteristics. Even if a model is effective by any reasonable definition of the term, it is possible that some very small areas will be adjusted to totals that differ substantially from the census counts.
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From page 257... ...
For every underlying model of the census and coverage evaluation error process, estimates of over- and undercoverage and any adjusted census data derived from such estimates will have a range of variation associated with them. A program to estimate the distribution of errors arising from the evaluation and adjustment procedures is needed.
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From page 258... ...
Such calculations would be interesting and useful in assessing the impact of the adjustment procedures on local-area estimates. We suggest that the Census Bureau explore methods of implementing estimates of error distribution.
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From page 259... ...
We recommend that the Census Bureau explore methods for providing estimates of errors associated with estimates of census over- and undercoverage, with a view to publishing such error estimates along with coverage evaluation results and any adjusted cen sus data that may be issued. CONSIDERATIONS OF INTERNAL CONSISTENCY Adjustment of census data could create problems of internal consistency of macro-and microdata from the census.
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From page 260... ...
The issue of internal consistency is important in relation to the possibility of adjusting census counts on the basis of combining coverage evaluation survey results with modeling. Should adjustment be used, two basic alternatives would arise: a set of adjusted population estimates could coexist with the unadjusted counts implicit in the census microdataset; or the microdataset could be adjusted.
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From page 261... ...
Careful evaluation of these methods is essential to the implementation of an appropriate adjustment procedure.
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From page 262... ...
We recommend that one of these methods be used to achieve internal consistency of census figures. CONSIDERATIONS OF TIMING As currently specified by law, the Census Bureau is required to meet two deadlines for specific data products from the decennial census: a deadline for the submission of state population counts within 9 months after Census Day for purposes of reapportionment of the House of Representatives, and a deadline for submission of small-area population counts within 12 months after Census Day for purposes of redistricting (see Chapter 2)
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From page 263... ...
Continued reliance for a decade on less accurate census data because adjustments to increase accuracy could not be completed by a specific date would, under that scenario, deny the country the potential benefits of more accurate data for uses other than apportionment. The burden of choice among the above scenarios, which is essentially political, should not be left to the Census Bureau alone.
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From page 264... ...
PROCEDURES FOR ADJUSTMENT Inputs to Adjustment Procedures Adjustment of the census must be based on one or more sources of information on the number of persons likely to have been missed, either n ationally or in a given geographic region. Efforts to obtain good estimates of census over- and undercoverage have now been under way for four decades, and several methods exist for estimating coverage error (see Chapter 4)
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From page 265... ...
Below we discuss possible technical approaches to the use of information generated from coverage evaluation programs for purposes of adjusting the decennial census data. Since the estimates derived directly from the coverage evaluation programs are necessarily restricted to a limited number of large areas, and since it is desirable for many purposes that the adjustment apply to small areas, adjustment procedures naturally separate into two components: (1)
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From page 266... ...
Indeed, the panel recommends in Chapter 8 that the Census Bureau, as part of its 1990 research program, work on developing other techniques of coverage evaluation, specifically, reverse record checks and systematic observation. Given the substantial indeterminacies involved, not surprisingly, different evaluation programs yield differing estimates of census errors.
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From page 267... ...
That is, instead of directly producing estimates for political entities such as states, which have heterogeneous populations and therefore on average do not differ very greatly in coverage error, estimates can be produced for combinations of areas that are homogeneous on variables believed to be related to the undercount. For example, one domain might comprise central cities in northeastern industrial states and another nonmetropolitan areas in the Southwest.
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From page 268... ...
For example, suppose that there were two demographic groups, I and II, and we were calculating a synthetic estimate of the undercount for a small area A1 within the larger area A Also suppose, for the larger area, the census and a coverage evaluation program each estimated the population counts illustrated in Table 7.1.
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From page 269... ...
Iterative proportional fitting is currently used by the Census Bureau to force certain tables produced from the sampled long-form records to be essentially consistent with the corresponding short-form data produced on a percent basis2 (see Appendix 3.2)
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From page 270... ...
Suppose that one determined from PEP or another coverage evaluation program that certain percentages of persons belonging to various demographic groups living in a particular domain were missed in the census. Then, instead of reweighting the records for the individuals belonging to each of these demographic groups, as one would in a synthetic adjustment, the number undercounted could be added by duplicating at random the records of people already counted in the census in that domain and demographic group.
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From page 271... ...
-- describe the Census Bureau's adjustment research and testing program, the former document 3 Itmay be confusing to some that we recommend synthetic estimation but not regression, when regression is merely a generalization of the synthetic method. The synthetic method is a special type of regression in that it has only one covariate, the census count, which is presumed to be well-behaved for even fairly small areas.
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From page 272... ...
In order to carry out an adjustment, there will have to be a pretest of a coverage evaluation program. This same paper mentions two pretests, one of a post-enumeration survey akin to the 1980 census PEP program, and the other a pre-enumeration survey, whose purpose is to determine the time savings achieved by taking the independent sample survey before the census, balanced against the possible effects on data quality introduced by sensitization of the population (see Chapter 8 for a discussion of this point)
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From page 273... ...
, some of which were discussed above; (2) examine appropriate loss functions specific to special uses of the census data, for example, examine the revenue sharing formula; and, finally (3)
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From page 274... ...
The panel recognizes that considerable work is still necessary and likely to lead to improved procedures for adjusting census data. We therefore support the Census Bureau's stated plans to pursue, internally, research and development of adjustment procedures, and we also recommend that the Census Bureau vigorously promote and support related statistical research in the academic community.
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From page 275... ...
The effect of these estimates on redistricting or reapportionment could also be examined. Since publication of our interim report, the Census Bureau undercount research staff has been actively pursuing research along these lines.
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From page 276... ...
a study of the impact of adjustment on uses of census data.
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From page 277... ...
ADJUSTMENT OF POPULATION COUNTS 277 APPENDIX 7.1 A QUICK LOOK AT LOSS FUNCTIONS AND APPORTIONMENT4 The method currently used to apportion the House of Representatives derives from Hill (1911)
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From page 278... ...
278 THE BICENTENNIAL CENSUS The function L, the Huntington criterion, does not have the form of a loss function in a strict sense. But it is equivalent to an index of mis proportionality, as defined above in Chapter 7.
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From page 279... ...
For example, how to combine information from the raw data collected in the decennial census and information from the coverage evaluation programs is the fundamental statistical problem faced in the determination of a method for adjustment. In addition, the combination of postcensal estimates based on sampled longform responses for small areas with information from more highly aggregated areas that enclose the smaller areas, investigated by Fay and Herriot (1979)
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From page 280... ...
In the case of adjustment, one possible hierarchical model might be developed based on the following reasoning. For major central cities and states and remainders of states with these cities in them, or for homogeneous regions, it is reasonable to consider modeling the ratio of the census counts to the true counts, that is, percentages of undercount.
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From page 281... ...
An examination of the table shows that the estimates of area totals using synthetic estimation are further from the truth than the unadjusted census estimates for areas I and III, and no better for area II. That is, the synthetic values 108 and 92 are not equal to the true counts of 100, which is the case for the unadjusted census counts.
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