Analysis

Description: At Statistics Netherlands (SN) for some economic sectors two partly-independent intra-annual turnover index series are available: a monthly series based on survey data and a quarterly series based on value added tax data for the smaller units and re-used survey data for the other units. SN aims to benchmark the monthly turnover index series to the quarterly census data on a quarterly basis. This cannot currently be done because the tax data has a different quarterly pattern: the turnover is relatively large in the fourth quarter of the year and smaller in the first quarter. With the current study we aim to describe this deviating quarterly pattern at micro level. In the past we developed a mixture model using absolute turnover levels that could explain part of the quarterly patterns. Because the absolute turnover levels differ between the two series, in the current study we use a model based on relative quarterly turnover levels within a year.

Description: Being able to quantify the accuracy (bias, variance) of published output is crucial in official statistics. Output in official statistics is nearly always divided into subpopulations according to some classification variable, such as mean income by categories of educational level. Such output is also referred to as domain statistics. In the current paper, we limit ourselves to binary classification variables. In practice, misclassifications occur and these contribute to the bias and variance of domain statistics. Existing analytical and numerical methods to estimate this effect have two disadvantages. The first disadvantage is that they require that the misclassification probabilities are known beforehand and the second is that the bias and variance estimates are biased themselves. In the current paper we present a new method, a Gaussian mixture model estimated by an Expectation-Maximisation (EM) algorithm combined with a bootstrap, referred to as the EM bootstrap method. This new method does not require that the misclassification probabilities are known beforehand, although it is more efficient when a small audit sample is used that yields a starting value for the misclassification probabilities in the EM algorithm. We compared the performance of the new method with currently available numerical methods: the bootstrap method and the SIMEX method. Previous research has shown that for non-linear parameters the bootstrap outperforms the analytical expressions. For nearly all conditions tested, the bias and variance estimates that are obtained by the EM bootstrap method are closer to their true values than those obtained by the bootstrap and SIMEX methods. We end this paper by discussing the results and possible future extensions of the method.

Description:

The Multiple Imputation of Latent Classes (MILC) method combines multiple imputation and latent class analysis to correct for misclassification in combined datasets. Furthermore, MILC generates a multiply imputed dataset which can be used to estimate different statistics in a straightforward manner, ensuring that uncertainty due to misclassification is incorporated when estimating the total variance. In this paper, it is investigated how the MILC method can be adjusted to be applied for census purposes. More specifically, it is investigated how the MILC method deals with a finite and complete population register, how the MILC method can simultaneously correct misclassification in multiple latent variables and how multiple edit restrictions can be incorporated. A simulation study shows that the MILC method is in general able to reproduce cell frequencies in both low- and high-dimensional tables with low amounts of bias. In addition, variance can also be estimated appropriately, although variance is overestimated when cell frequencies are small.

Description:

The widely used formulas for the variance of the ratio estimator may lead to serious underestimates when the sample size is small; see Sukhatme (1954), Koop (1968), Rao (1969), and Cochran (1977, pages 163-164). In order to solve this classical problem, we propose in this paper new estimators for the variance and the mean square error of the ratio estimator that do not suffer from such a large negative bias. Similar estimation formulas can be derived for alternative ratio estimators as discussed in Tin (1965). We compare three mean square error estimators for the ratio estimator in a simulation study.

Description:

The aim of automatic editing is to use a computer to detect and amend erroneous values in a data set, without human intervention. Most automatic editing methods that are currently used in official statistics are based on the seminal work of Fellegi and Holt (1976). Applications of this methodology in practice have shown systematic differences between data that are edited manually and automatically, because human editors may perform complex edit operations. In this paper, a generalization of the Fellegi-Holt paradigm is proposed that can incorporate a large class of edit operations in a natural way. In addition, an algorithm is outlined that solves the resulting generalized error localization problem. It is hoped that this generalization may be used to increase the suitability of automatic editing in practice, and hence to improve the efficiency of data editing processes. Some first results on synthetic data are promising in this respect.

Description:

A considerable limitation of current methods for automatic data editing is that they treat all edits as hard constraints. That is to say, an edit failure is always attributed to an error in the data. In manual editing, however, subject-matter specialists also make extensive use of soft edits, i.e., constraints that identify (combinations of) values that are suspicious but not necessarily incorrect. The inability of automatic editing methods to handle soft edits partly explains why in practice many differences are found between manually edited and automatically edited data. The object of this article is to present a new formulation of the error localisation problem which can distinguish between hard and soft edits. Moreover, it is shown how this problem may be solved by an extension of the error localisation algorithm of De Waal and Quere (2003).

Description:

In surveys a response may be incomplete or some items may be inconsistent or, as in the case of two-phase sampling, items may be unavailable. In these cases it may be expedient to impute values for the missing items. While imputation is not a particularly good solution to any specific estimation problem, it does permit the production of arbitrary estimates in a consistent way.

The survey statistician may have to cope with a mixture of numerical and categorical items, subject to a variety of constraints. He should evaluate his technique, especially with respect to bias. He should make sure that imputed items are clearly identified and summary reports produced.

A variety of imputation techniques in current use is described and discussed, with particular reference to the practical problems involved.

Description: At Statistics Netherlands (SN) for some economic sectors two partly-independent intra-annual turnover index series are available: a monthly series based on survey data and a quarterly series based on value added tax data for the smaller units and re-used survey data for the other units. SN aims to benchmark the monthly turnover index series to the quarterly census data on a quarterly basis. This cannot currently be done because the tax data has a different quarterly pattern: the turnover is relatively large in the fourth quarter of the year and smaller in the first quarter. With the current study we aim to describe this deviating quarterly pattern at micro level. In the past we developed a mixture model using absolute turnover levels that could explain part of the quarterly patterns. Because the absolute turnover levels differ between the two series, in the current study we use a model based on relative quarterly turnover levels within a year.

Description: Being able to quantify the accuracy (bias, variance) of published output is crucial in official statistics. Output in official statistics is nearly always divided into subpopulations according to some classification variable, such as mean income by categories of educational level. Such output is also referred to as domain statistics. In the current paper, we limit ourselves to binary classification variables. In practice, misclassifications occur and these contribute to the bias and variance of domain statistics. Existing analytical and numerical methods to estimate this effect have two disadvantages. The first disadvantage is that they require that the misclassification probabilities are known beforehand and the second is that the bias and variance estimates are biased themselves. In the current paper we present a new method, a Gaussian mixture model estimated by an Expectation-Maximisation (EM) algorithm combined with a bootstrap, referred to as the EM bootstrap method. This new method does not require that the misclassification probabilities are known beforehand, although it is more efficient when a small audit sample is used that yields a starting value for the misclassification probabilities in the EM algorithm. We compared the performance of the new method with currently available numerical methods: the bootstrap method and the SIMEX method. Previous research has shown that for non-linear parameters the bootstrap outperforms the analytical expressions. For nearly all conditions tested, the bias and variance estimates that are obtained by the EM bootstrap method are closer to their true values than those obtained by the bootstrap and SIMEX methods. We end this paper by discussing the results and possible future extensions of the method.

Description:

The Multiple Imputation of Latent Classes (MILC) method combines multiple imputation and latent class analysis to correct for misclassification in combined datasets. Furthermore, MILC generates a multiply imputed dataset which can be used to estimate different statistics in a straightforward manner, ensuring that uncertainty due to misclassification is incorporated when estimating the total variance. In this paper, it is investigated how the MILC method can be adjusted to be applied for census purposes. More specifically, it is investigated how the MILC method deals with a finite and complete population register, how the MILC method can simultaneously correct misclassification in multiple latent variables and how multiple edit restrictions can be incorporated. A simulation study shows that the MILC method is in general able to reproduce cell frequencies in both low- and high-dimensional tables with low amounts of bias. In addition, variance can also be estimated appropriately, although variance is overestimated when cell frequencies are small.

Description:

The widely used formulas for the variance of the ratio estimator may lead to serious underestimates when the sample size is small; see Sukhatme (1954), Koop (1968), Rao (1969), and Cochran (1977, pages 163-164). In order to solve this classical problem, we propose in this paper new estimators for the variance and the mean square error of the ratio estimator that do not suffer from such a large negative bias. Similar estimation formulas can be derived for alternative ratio estimators as discussed in Tin (1965). We compare three mean square error estimators for the ratio estimator in a simulation study.

Description:

The aim of automatic editing is to use a computer to detect and amend erroneous values in a data set, without human intervention. Most automatic editing methods that are currently used in official statistics are based on the seminal work of Fellegi and Holt (1976). Applications of this methodology in practice have shown systematic differences between data that are edited manually and automatically, because human editors may perform complex edit operations. In this paper, a generalization of the Fellegi-Holt paradigm is proposed that can incorporate a large class of edit operations in a natural way. In addition, an algorithm is outlined that solves the resulting generalized error localization problem. It is hoped that this generalization may be used to increase the suitability of automatic editing in practice, and hence to improve the efficiency of data editing processes. Some first results on synthetic data are promising in this respect.

Description:

A considerable limitation of current methods for automatic data editing is that they treat all edits as hard constraints. That is to say, an edit failure is always attributed to an error in the data. In manual editing, however, subject-matter specialists also make extensive use of soft edits, i.e., constraints that identify (combinations of) values that are suspicious but not necessarily incorrect. The inability of automatic editing methods to handle soft edits partly explains why in practice many differences are found between manually edited and automatically edited data. The object of this article is to present a new formulation of the error localisation problem which can distinguish between hard and soft edits. Moreover, it is shown how this problem may be solved by an extension of the error localisation algorithm of De Waal and Quere (2003).

Description:

In surveys a response may be incomplete or some items may be inconsistent or, as in the case of two-phase sampling, items may be unavailable. In these cases it may be expedient to impute values for the missing items. While imputation is not a particularly good solution to any specific estimation problem, it does permit the production of arbitrary estimates in a consistent way.

The survey statistician may have to cope with a mixture of numerical and categorical items, subject to a variety of constraints. He should evaluate his technique, especially with respect to bias. He should make sure that imputed items are clearly identified and summary reports produced.

A variety of imputation techniques in current use is described and discussed, with particular reference to the practical problems involved.