Analysis

Description: Estimation at fine levels of aggregation is necessary to better describe society. Small area estimation model-based approaches that combine sparse survey data with rich data from auxiliary sources have been proven useful to improve the reliability of estimates for small domains. Considered here is a scenario where small area model-based estimates, produced at a given aggregation level, needed to be disaggregated to better describe the social structure at finer levels. For this scenario, an allocation method was developed to implement the disaggregation, overcoming challenges associated with data availability and model development at such fine levels. The method is applied to adult literacy and numeracy estimation at the county-by-group-level, using data from the U.S. Program for the International Assessment of Adult Competencies. In this application the groups are defined in terms of age or education, but the method could be applied to estimation of other equity-deserving groups.

Description: We present a novel methodology to benchmark county-level estimates of crop area totals to a preset state total subject to inequality constraints and random variances in the Fay-Herriot model. For planted area of the National Agricultural Statistics Service (NASS), an agency of the United States Department of Agriculture (USDA), it is necessary to incorporate the constraint that the estimated totals, derived from survey and other auxiliary data, are no smaller than administrative planted area totals prerecorded by other USDA agencies except NASS. These administrative totals are treated as fixed and known, and this additional coherence requirement adds to the complexity of benchmarking the county-level estimates. A fully Bayesian analysis of the Fay-Herriot model offers an appealing way to incorporate the inequality and benchmarking constraints, and to quantify the resulting uncertainties, but sampling from the posterior densities involves difficult integration, and reasonable approximations must be made. First, we describe a single-shrinkage model, shrinking the means while the variances are assumed known. Second, we extend this model to accommodate double shrinkage, borrowing strength across means and variances. This extended model has two sources of extra variation, but because we are shrinking both means and variances, it is expected that this second model should perform better in terms of goodness of fit (reliability) and possibly precision. The computations are challenging for both models, which are applied to simulated data sets with properties resembling the Illinois corn crop.

Description:

Sample-based calibration occurs when the weights of a survey are calibrated to control totals that are random, instead of representing fixed population-level totals. Control totals may be estimated from different phases of the same survey or from another survey. Under sample-based calibration, valid variance estimation requires that the error contribution due to estimating the control totals be accounted for. We propose a new variance estimation method that directly uses the replicate weights from two surveys, one survey being used to provide control totals for calibration of the other survey weights. No restrictions are set on the nature of the two replication methods and no variance-covariance estimates need to be computed, making the proposed method straightforward to implement in practice. A general description of the method for surveys with two arbitrary replication methods with different numbers of replicates is provided. It is shown that the resulting variance estimator is consistent for the asymptotic variance of the calibrated estimator, when calibration is done using regression estimation or raking. The method is illustrated in a real-world application, in which the demographic composition of two surveys needs to be harmonized to improve the comparability of the survey estimates.

Description:

The National Agricultural Statistics Service (NASS) of the United States Department of Agriculture (USDA) is responsible for estimating average cash rental rates at the county level. A cash rental rate refers to the market value of land rented on a per acre basis for cash only. Estimates of cash rental rates are useful to farmers, economists, and policy makers. NASS collects data on cash rental rates using a Cash Rent Survey. Because realized sample sizes at the county level are often too small to support reliable direct estimators, predictors based on mixed models are investigated. We specify a bivariate model to obtain predictors of 2010 cash rental rates for non-irrigated cropland using data from the 2009 Cash Rent Survey and auxiliary variables from external sources such as the 2007 Census of Agriculture. We use Bayesian methods for inference and present results for Iowa, Kansas, and Texas. Incorporating the 2009 survey data through a bivariate model leads to predictors with smaller mean squared errors than predictors based on a univariate model.

Description:

Benchmarking lower level estimates to upper level estimates is an important activity at the United States Department of Agriculture’s National Agricultural Statistical Service (NASS) (e.g., benchmarking county estimates to state estimates for corn acreage). Assuming that a county is a small area, we use the original Fay-Herriot model to obtain a general Bayesian method to benchmark county estimates to the state estimate (the target). Here the target is assumed known, and the county estimates are obtained subject to the constraint that these estimates must sum to the target. This is an external benchmarking; it is important for official statistics, not just NASS, and it occurs more generally in small area estimation. One can benchmark these estimates by “deleting” one of the counties (typically the last one) to incorporate the benchmarking constraint into the model. However, it is also true that the estimates may change depending on which county is deleted when the constraint is included in the model. Our current contribution is to give each small area a chance to be deleted, and we call this procedure the random deletion benchmarking method. We show empirically that there are differences in the estimates as to which county is deleted and that there are differences of these estimates from those obtained from random deletion as well. Although these differences may be considered small, it is most sensible to use random deletion because it does not give preferential treatment to any county and it can provide small improvement in precision over deleting the last one benchmarking as well.

Description: Estimation at fine levels of aggregation is necessary to better describe society. Small area estimation model-based approaches that combine sparse survey data with rich data from auxiliary sources have been proven useful to improve the reliability of estimates for small domains. Considered here is a scenario where small area model-based estimates, produced at a given aggregation level, needed to be disaggregated to better describe the social structure at finer levels. For this scenario, an allocation method was developed to implement the disaggregation, overcoming challenges associated with data availability and model development at such fine levels. The method is applied to adult literacy and numeracy estimation at the county-by-group-level, using data from the U.S. Program for the International Assessment of Adult Competencies. In this application the groups are defined in terms of age or education, but the method could be applied to estimation of other equity-deserving groups.

Description: We present a novel methodology to benchmark county-level estimates of crop area totals to a preset state total subject to inequality constraints and random variances in the Fay-Herriot model. For planted area of the National Agricultural Statistics Service (NASS), an agency of the United States Department of Agriculture (USDA), it is necessary to incorporate the constraint that the estimated totals, derived from survey and other auxiliary data, are no smaller than administrative planted area totals prerecorded by other USDA agencies except NASS. These administrative totals are treated as fixed and known, and this additional coherence requirement adds to the complexity of benchmarking the county-level estimates. A fully Bayesian analysis of the Fay-Herriot model offers an appealing way to incorporate the inequality and benchmarking constraints, and to quantify the resulting uncertainties, but sampling from the posterior densities involves difficult integration, and reasonable approximations must be made. First, we describe a single-shrinkage model, shrinking the means while the variances are assumed known. Second, we extend this model to accommodate double shrinkage, borrowing strength across means and variances. This extended model has two sources of extra variation, but because we are shrinking both means and variances, it is expected that this second model should perform better in terms of goodness of fit (reliability) and possibly precision. The computations are challenging for both models, which are applied to simulated data sets with properties resembling the Illinois corn crop.

Description:

Sample-based calibration occurs when the weights of a survey are calibrated to control totals that are random, instead of representing fixed population-level totals. Control totals may be estimated from different phases of the same survey or from another survey. Under sample-based calibration, valid variance estimation requires that the error contribution due to estimating the control totals be accounted for. We propose a new variance estimation method that directly uses the replicate weights from two surveys, one survey being used to provide control totals for calibration of the other survey weights. No restrictions are set on the nature of the two replication methods and no variance-covariance estimates need to be computed, making the proposed method straightforward to implement in practice. A general description of the method for surveys with two arbitrary replication methods with different numbers of replicates is provided. It is shown that the resulting variance estimator is consistent for the asymptotic variance of the calibrated estimator, when calibration is done using regression estimation or raking. The method is illustrated in a real-world application, in which the demographic composition of two surveys needs to be harmonized to improve the comparability of the survey estimates.

Description:

The National Agricultural Statistics Service (NASS) of the United States Department of Agriculture (USDA) is responsible for estimating average cash rental rates at the county level. A cash rental rate refers to the market value of land rented on a per acre basis for cash only. Estimates of cash rental rates are useful to farmers, economists, and policy makers. NASS collects data on cash rental rates using a Cash Rent Survey. Because realized sample sizes at the county level are often too small to support reliable direct estimators, predictors based on mixed models are investigated. We specify a bivariate model to obtain predictors of 2010 cash rental rates for non-irrigated cropland using data from the 2009 Cash Rent Survey and auxiliary variables from external sources such as the 2007 Census of Agriculture. We use Bayesian methods for inference and present results for Iowa, Kansas, and Texas. Incorporating the 2009 survey data through a bivariate model leads to predictors with smaller mean squared errors than predictors based on a univariate model.

Description:

Benchmarking lower level estimates to upper level estimates is an important activity at the United States Department of Agriculture’s National Agricultural Statistical Service (NASS) (e.g., benchmarking county estimates to state estimates for corn acreage). Assuming that a county is a small area, we use the original Fay-Herriot model to obtain a general Bayesian method to benchmark county estimates to the state estimate (the target). Here the target is assumed known, and the county estimates are obtained subject to the constraint that these estimates must sum to the target. This is an external benchmarking; it is important for official statistics, not just NASS, and it occurs more generally in small area estimation. One can benchmark these estimates by “deleting” one of the counties (typically the last one) to incorporate the benchmarking constraint into the model. However, it is also true that the estimates may change depending on which county is deleted when the constraint is included in the model. Our current contribution is to give each small area a chance to be deleted, and we call this procedure the random deletion benchmarking method. We show empirically that there are differences in the estimates as to which county is deleted and that there are differences of these estimates from those obtained from random deletion as well. Although these differences may be considered small, it is most sensible to use random deletion because it does not give preferential treatment to any county and it can provide small improvement in precision over deleting the last one benchmarking as well.