Weighting and estimation
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All (12) (0 to 10 of 12 results)
- Articles and reports: 12-001-X198800214588Description:
Suppose that undercount rates in a census have been estimated and that block-level estimates of the undercount have been computed. It may then be desirable to create a new roster of households incorporating the estimated omissions. It is proposed here that such a roster be created by weighting the enumerated households. The household weights are constrained by linear equations representing the desired total counts of persons in each estimation class and the desired total count of households. Weights are then calculated that satisfy the constraints while making the fitted table as close as possible to the raw data. The procedure may be regarded as an extension of the standard “raking” methodology to situations where the constraints do not refer to the margins of a contingency table. Continuous as well as discrete covariates may be used in the adjustment, and it is possible to check directly whether the constraints can be satisfied. Methods are proposed for the use of weighted data for various Census purposes, and for adjustment of covariate information on characteristics of omitted households, such as income, that are not directly considered in undercount estimation.
Release date: 1988-12-15 - Articles and reports: 12-001-X198800214589Description:
The U.S. Bureau of the Census uses dual system estimates (DSEs) for measuring census coverage error. The dual system estimate uses data from the original enumeration and a Post Enumeration Survey. In measuring the accuracy of the DSE, it is important to know that the DSE is subject to several components of nonsampling error, as well as sampling error. This paper gives models of the total error and the components of error in the dual system estimates. The models relate observed indicators of data quality, such as a matching error rate, to the first two moments of the components of error. The propagation of error in the DSE is studied and its bias and variance are assessed. The methodology is applied to the 1986 Census of Central Los Angeles County in the Census Bureau’s Test of Adjustment Related Operations. The methodology also will be useful to assess error in the DSE for the 1990 census as well as other applications.
Release date: 1988-12-15 - Articles and reports: 12-001-X198800214591Description:
To estimate census undercount, a post-enumeration survey (PES) is taken, and an attempt is made to find a matching census record for each individual in the PES; the rate of successful matching provides an estimate of census coverage. Undercount estimation is performed within poststrata defined by geographic, demographic, and housing characteristics, X. Portions of X are missing for some individuals due to survey nonresponse; moreover, a match status Y cannot be determined for all individuals. A procedure is needed for imputing the missing values of X and Y. This paper reviews the imputation methods used in the 1986 Test of Adjustment Related Operations (Schenker 1988) and proposes two alternative model-based methods: (1) a maximum-likelihood contingency-table estimation procedure that ignores the missing-data mechanism; and (2) a new Bayesian contingency table estimation procedure that does not ignore the missing-data mechanism. The first method is computationally simpler, but the second is preferred on conceptual and scientific grounds.
Release date: 1988-12-15 - 4. When are census counts improved by adjustment? ArchivedArticles and reports: 12-001-X198800214592Description:
There are persuasive arguments for and against adjustment of the U.S. decennial census counts, although many of them are based on political rather than technical considerations. The decision whether or not to adjust depends crucially on the method of adjustment. Moreover, should adjustment take place using say a synthetic-based or a regression-based method, at which level should this occur and how should aggregation and disaggregation proceed? In order to answer these questions sensibly, a model of undercount errors is needed which is “level-consistent” in the sense that it is preserved for areas at the national, state, county, etc. level. Such a model is proposed in this article; like subareas are identified with strata such that within a stratum the subareas’ adjustment factors have a common stratum mean and have variances inversely proportional to their census counts. By taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that combine information from the stratum average and the sample value, can be constructed. These estimators are evaluated at the state level (51 states, including Washington, D.C.), and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3-8, for the noninstitutional population).
Release date: 1988-12-15 - Articles and reports: 12-001-X198800214593Description:
In Australia, population estimates have been obtained from census counts, incorporating an adjustment for under-enumeration in 1976, 1981 and 1986. The adjustments are based on the results of a Post Enumeration Survey and demographic analysis. This paper describes the methods used and the results obtained in adjusting the 1986 census. The formal use of sex ratios as suggested by Wolter (1986) is examined as a possible improvement of the less formal use made of these ratios in adjusting census counts.
Release date: 1988-12-15 - 6. A demographic approach to the evaluation of the 1986 Census and the estimates of Canada’s population ArchivedArticles and reports: 12-001-X198800214594Description:
A significant increase in coverage error in the 1986 Census is revealed by both the Reverse Record Check and the demographic method presented in this paper. Considerable attention is paid to an evaluation of the various components of population growth, especially interprovincial migration. The paper concludes with an overview of two alternative methods for generating postcensal estimates: the currently-in-use, census-based model, and a flexible model using all relevant data in combination with the census.
Release date: 1988-12-15 - Articles and reports: 12-001-X198800114596Description:
Dual system estimators of census undercount rely heavily on the assumption that persons in the evaluation survey can be accurately linked to the same persons in the census. Mismatches and erroneous non-matches, which are unavoidable, reduce the accuracy of the estimators. Studies have shown that the extent of the error can be so large relative to the size of census coverage error as to render the estimate unusable. In this paper, we propose a model for investigating the effect of matching error on the estimators of census undercount and illustrate its use for the 1990 census undercount evaluation program. The mean square error of the dual system estimator is derived under the proposed model and the components of MSE arising from matching error are defined and explained. Under the assumed model, the effect of matching error on the MSE of the estimator of census undercount is investigated. Finally, a methodology for employing the model for the optimal design of matching error evaluation studies will be illustrated and the form of the estimators will be given.
Release date: 1988-06-15 - Articles and reports: 12-001-X198800114598Description:
This paper discusses methods used to handle missing data in post-enumeration surveys for estimating census coverage error, as illustrated for the 1986 Test of Adjustment Related Operations (Diffendal 1988). The methods include imputation schemes based on hot-deck and logistic regression models as well as weighting adjustments. The sensitivity of undercount estimates from the 1986 test to variations in the imputation models is also explored.
Release date: 1988-06-15 - Articles and reports: 12-001-X198800114599Description:
As part of the planning for the 1990 Decennial Census, the Census Bureau investigated the feasibility of adjusting the census for the estimated undercount. A test census was conducted in Central Los Angeles County, in a mostly Hispanic area, in order to test the timing and operational aspects of adjusting the Census using a post-enumeration survey (PES). This paper presents the methodology and the results in producing a census that is adjusted for the population missed by the enumeration. The methodology used to adjust the test census included the sample design, dual-system estimation and small area estimation. The sample design used a block sample with blocks stratified by race/ethnicity. Matching was done by the computer with clerical review and resolution. The dual-system estimator, also called the Petersen estimator or capture-recapture, was used to estimate the population. Because of the nature of the census enumeration, corrections were made to the census counts before using them in the dual-system estimator. Before adjusting the small areas, a regression model was fit to the adjustment factor (the dual-system estimate divided by the census count) to reduce the effects of sampling variability. A synthetic estimator was used to carry the adjustment down to the block level. The results of the dual-system estimates are presented for the test site by the three major race/ethnic groups (Hispanic, Asian, Other) by tenure, by age and by sex. Summaries of the small area adjustments of the census enumeration, by block, are presented and discussed.
Release date: 1988-06-15 - Articles and reports: 12-001-X198800114600Description:
A personal computer program for variance estimation with large scale surveys is described. The program, called PC CARP, will compute estimates and estimated variances for totals, ratios, means, quantiles, and regression coefficients.
Release date: 1988-06-15
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Analysis (12)
Analysis (12) (0 to 10 of 12 results)
- Articles and reports: 12-001-X198800214588Description:
Suppose that undercount rates in a census have been estimated and that block-level estimates of the undercount have been computed. It may then be desirable to create a new roster of households incorporating the estimated omissions. It is proposed here that such a roster be created by weighting the enumerated households. The household weights are constrained by linear equations representing the desired total counts of persons in each estimation class and the desired total count of households. Weights are then calculated that satisfy the constraints while making the fitted table as close as possible to the raw data. The procedure may be regarded as an extension of the standard “raking” methodology to situations where the constraints do not refer to the margins of a contingency table. Continuous as well as discrete covariates may be used in the adjustment, and it is possible to check directly whether the constraints can be satisfied. Methods are proposed for the use of weighted data for various Census purposes, and for adjustment of covariate information on characteristics of omitted households, such as income, that are not directly considered in undercount estimation.
Release date: 1988-12-15 - Articles and reports: 12-001-X198800214589Description:
The U.S. Bureau of the Census uses dual system estimates (DSEs) for measuring census coverage error. The dual system estimate uses data from the original enumeration and a Post Enumeration Survey. In measuring the accuracy of the DSE, it is important to know that the DSE is subject to several components of nonsampling error, as well as sampling error. This paper gives models of the total error and the components of error in the dual system estimates. The models relate observed indicators of data quality, such as a matching error rate, to the first two moments of the components of error. The propagation of error in the DSE is studied and its bias and variance are assessed. The methodology is applied to the 1986 Census of Central Los Angeles County in the Census Bureau’s Test of Adjustment Related Operations. The methodology also will be useful to assess error in the DSE for the 1990 census as well as other applications.
Release date: 1988-12-15 - Articles and reports: 12-001-X198800214591Description:
To estimate census undercount, a post-enumeration survey (PES) is taken, and an attempt is made to find a matching census record for each individual in the PES; the rate of successful matching provides an estimate of census coverage. Undercount estimation is performed within poststrata defined by geographic, demographic, and housing characteristics, X. Portions of X are missing for some individuals due to survey nonresponse; moreover, a match status Y cannot be determined for all individuals. A procedure is needed for imputing the missing values of X and Y. This paper reviews the imputation methods used in the 1986 Test of Adjustment Related Operations (Schenker 1988) and proposes two alternative model-based methods: (1) a maximum-likelihood contingency-table estimation procedure that ignores the missing-data mechanism; and (2) a new Bayesian contingency table estimation procedure that does not ignore the missing-data mechanism. The first method is computationally simpler, but the second is preferred on conceptual and scientific grounds.
Release date: 1988-12-15 - 4. When are census counts improved by adjustment? ArchivedArticles and reports: 12-001-X198800214592Description:
There are persuasive arguments for and against adjustment of the U.S. decennial census counts, although many of them are based on political rather than technical considerations. The decision whether or not to adjust depends crucially on the method of adjustment. Moreover, should adjustment take place using say a synthetic-based or a regression-based method, at which level should this occur and how should aggregation and disaggregation proceed? In order to answer these questions sensibly, a model of undercount errors is needed which is “level-consistent” in the sense that it is preserved for areas at the national, state, county, etc. level. Such a model is proposed in this article; like subareas are identified with strata such that within a stratum the subareas’ adjustment factors have a common stratum mean and have variances inversely proportional to their census counts. By taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that combine information from the stratum average and the sample value, can be constructed. These estimators are evaluated at the state level (51 states, including Washington, D.C.), and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3-8, for the noninstitutional population).
Release date: 1988-12-15 - Articles and reports: 12-001-X198800214593Description:
In Australia, population estimates have been obtained from census counts, incorporating an adjustment for under-enumeration in 1976, 1981 and 1986. The adjustments are based on the results of a Post Enumeration Survey and demographic analysis. This paper describes the methods used and the results obtained in adjusting the 1986 census. The formal use of sex ratios as suggested by Wolter (1986) is examined as a possible improvement of the less formal use made of these ratios in adjusting census counts.
Release date: 1988-12-15 - 6. A demographic approach to the evaluation of the 1986 Census and the estimates of Canada’s population ArchivedArticles and reports: 12-001-X198800214594Description:
A significant increase in coverage error in the 1986 Census is revealed by both the Reverse Record Check and the demographic method presented in this paper. Considerable attention is paid to an evaluation of the various components of population growth, especially interprovincial migration. The paper concludes with an overview of two alternative methods for generating postcensal estimates: the currently-in-use, census-based model, and a flexible model using all relevant data in combination with the census.
Release date: 1988-12-15 - Articles and reports: 12-001-X198800114596Description:
Dual system estimators of census undercount rely heavily on the assumption that persons in the evaluation survey can be accurately linked to the same persons in the census. Mismatches and erroneous non-matches, which are unavoidable, reduce the accuracy of the estimators. Studies have shown that the extent of the error can be so large relative to the size of census coverage error as to render the estimate unusable. In this paper, we propose a model for investigating the effect of matching error on the estimators of census undercount and illustrate its use for the 1990 census undercount evaluation program. The mean square error of the dual system estimator is derived under the proposed model and the components of MSE arising from matching error are defined and explained. Under the assumed model, the effect of matching error on the MSE of the estimator of census undercount is investigated. Finally, a methodology for employing the model for the optimal design of matching error evaluation studies will be illustrated and the form of the estimators will be given.
Release date: 1988-06-15 - Articles and reports: 12-001-X198800114598Description:
This paper discusses methods used to handle missing data in post-enumeration surveys for estimating census coverage error, as illustrated for the 1986 Test of Adjustment Related Operations (Diffendal 1988). The methods include imputation schemes based on hot-deck and logistic regression models as well as weighting adjustments. The sensitivity of undercount estimates from the 1986 test to variations in the imputation models is also explored.
Release date: 1988-06-15 - Articles and reports: 12-001-X198800114599Description:
As part of the planning for the 1990 Decennial Census, the Census Bureau investigated the feasibility of adjusting the census for the estimated undercount. A test census was conducted in Central Los Angeles County, in a mostly Hispanic area, in order to test the timing and operational aspects of adjusting the Census using a post-enumeration survey (PES). This paper presents the methodology and the results in producing a census that is adjusted for the population missed by the enumeration. The methodology used to adjust the test census included the sample design, dual-system estimation and small area estimation. The sample design used a block sample with blocks stratified by race/ethnicity. Matching was done by the computer with clerical review and resolution. The dual-system estimator, also called the Petersen estimator or capture-recapture, was used to estimate the population. Because of the nature of the census enumeration, corrections were made to the census counts before using them in the dual-system estimator. Before adjusting the small areas, a regression model was fit to the adjustment factor (the dual-system estimate divided by the census count) to reduce the effects of sampling variability. A synthetic estimator was used to carry the adjustment down to the block level. The results of the dual-system estimates are presented for the test site by the three major race/ethnic groups (Hispanic, Asian, Other) by tenure, by age and by sex. Summaries of the small area adjustments of the census enumeration, by block, are presented and discussed.
Release date: 1988-06-15 - Articles and reports: 12-001-X198800114600Description:
A personal computer program for variance estimation with large scale surveys is described. The program, called PC CARP, will compute estimates and estimated variances for totals, ratios, means, quantiles, and regression coefficients.
Release date: 1988-06-15
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