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Das Ziel dynamischer Mikrosimulationen ist es, die Entwicklung von Systemen über das Verhalten der einzelnen enthaltenen Bestandteile zu simulieren, um umfassende szenariobasierte Analysen zu ermöglichen. Im Bereich der Wirtschafts- und Sozialwissenschaften wird der Fokus üblicherweise auf Populationen bestehend aus Personen und Haushalten gelegt. Da politische und wirtschaftliche Entscheidungsprozesse meist auf lokaler Ebene getroffen werden, bedarf es zudem kleinräumiger Informationen, um gezielte Handlungsempfehlungen ableiten zu können. Das stellt Forschende wiederum vor große Herausforderungen im Erstellungsprozess regionalisierter Simulationsmodelle. Dieser Prozess reicht von der Generierung geeigneter Ausgangsdatensätze über die Erfassung und Umsetzung der dynamischen Komponenten bis hin zur Auswertung der Ergebnisse und Quantifizierung von Unsicherheiten. Im Rahmen dieser Arbeit werden ausgewählte Komponenten, die für regionalisierte Mikrosimulationen von besonderer Relevanz sind, beschrieben und systematisch analysiert.
Zunächst werden in Kapitel 2 theoretische und methodische Aspekte von Mikrosimulationen vorgestellt, um einen umfassenden Überblick über verschiedene Arten und Möglichkeiten der Umsetzung dynamischer Modellierungen zu geben. Im Fokus stehen dabei die Grundlagen der Erfassung und Simulation von Zuständen und Zustandsänderungen sowie die damit verbundenen strukturellen Aspekte im Simulationsprozess.
Sowohl für die Simulation von Zustandsänderungen als auch für die Erweiterung der Datenbasis werden primär logistische Regressionsmodelle zur Erfassung und anschließenden wahrscheinlichkeitsbasierten Vorhersage der Bevölkerungsstrukturen auf Mikroebene herangezogen. Die Schätzung beruht insbesondere auf Stichprobendaten, die in der Regel neben einem eingeschränktem Stichprobenumfang keine oder nur unzureichende regionale Differenzierungen zulassen. Daher können bei der Vorhersage von Wahrscheinlichkeiten erhebliche Differenzen zu bekannten Totalwerten entstehen. Um eine Harmonisierung mit den Totalwerten zu erhalten, lassen sich Methoden zur Anpassung von Wahrscheinlichkeiten – sogenannte Alignmentmethoden – anwenden. In der Literatur werden zwar unterschiedliche Möglichkeiten beschrieben, über die Auswirkungen dieser Verfahren auf die Güte der Modelle ist jedoch kaum etwas bekannt. Zur Beurteilung verschiedener Techniken werden diese im Rahmen von Kapitel 3 in umfassenden Simulationsstudien unter verschiedenen Szenarien umgesetzt. Hierbei kann gezeigt werden, dass durch die Einbindung zusätzlicher Informationen im Modellierungsprozess deutliche Verbesserungen sowohl bei der Schätzung der Parameter als auch bei der Vorhersage der Wahrscheinlichkeiten erzielt werden können. Zudem lassen sich dadurch auch bei fehlenden regionalen Identifikatoren in den Modellierungsdaten kleinräumige Wahrscheinlichkeiten erzeugen. Insbesondere die Maximierung der Likelihood des zugrundeliegenden Regressionsmodells unter der Nebenbedingung, dass die bekannten Totalwerte eingehalten werden, weist in allen Simulationsstudien überaus gute Ergebnisse auf.
Als eine der einflussreichsten Komponenten in regionalisierten Mikrosimulationen erweist sich die Umsetzung regionaler Mobilität. Gleichzeitig finden Wanderungen in vielen Mikrosimulationsmodellen keine oder nur unzureichende Beachtung. Durch den unmittelbaren Einfluss auf die gesamte Bevölkerungsstruktur führt ein Ignorieren jedoch bereits bei einem kurzen Simulationshorizont zu starken Verzerrungen. Während für globale Modelle die Integration von Wanderungsbewegungen über Landesgrenzen ausreicht, müssen in regionalisierten Modellen auch Binnenwanderungsbewegungen möglichst umfassend nachgebildet werden. Zu diesem Zweck werden in Kapitel 4 Konzepte für Wanderungsmodule erstellt, die zum einen eine unabhängige Simulation auf regionalen Subpopulationen und zum anderen eine umfassende Nachbildung von Wanderungsbewegungen innerhalb der gesamten Population zulassen. Um eine Berücksichtigung von Haushaltsstrukturen zu ermöglichen und die Plausibilität der Daten zu gewährleisten, wird ein Algorithmus zur Kalibrierung von Haushaltswahrscheinlichkeiten vorgeschlagen, der die Einhaltung von Benchmarks auf Individualebene ermöglicht. Über die retrospektive Evaluation der simulierten Migrationsbewegungen wird die Funktionalität der Wanderdungskonzepte verdeutlicht. Darüber hinaus werden über die Fortschreibung der Population in zukünftige Perioden divergente Entwicklungen der Einwohnerzahlen durch verschiedene Konzepte der Wanderungen analysiert.
Eine besondere Herausforderung in dynamischen Mikrosimulationen stellt die Erfassung von Unsicherheiten dar. Durch die Komplexität der gesamten Struktur und die Heterogenität der Komponenten ist die Anwendung klassischer Methoden zur Messung von Unsicherheiten oft nicht mehr möglich. Zur Quantifizierung verschiedener Einflussfaktoren werden in Kapitel 5 varianzbasierte Sensitivitätsanalysen vorgeschlagen, die aufgrund ihrer enormen Flexibilität auch direkte Vergleiche zwischen unterschiedlichsten Komponenten ermöglichen. Dabei erweisen sich Sensitivitätsanalysen nicht nur für die Erfassung von Unsicherheiten, sondern auch für die direkte Analyse verschiedener Szenarien, insbesondere zur Evaluation gemeinsamer Effekte, als überaus geeignet. In Simulationsstudien wird die Anwendung im konkreten Kontext dynamischer Modelle veranschaulicht. Dadurch wird deutlich, dass zum einen große Unterschiede hinsichtlich verschiedener Zielwerte und Simulationsperioden auftreten, zum anderen aber auch immer der Grad an regionaler Differenzierung berücksichtigt werden muss.
Kapitel 6 fasst die Erkenntnisse der vorliegenden Arbeit zusammen und gibt einen Ausblick auf zukünftige Forschungspotentiale.
The Eurosystem's Household Finance and Consumption Survey (HFCS) collects micro data on private households' balance sheets, income and consumption. It is a stylised fact that wealth is unequally distributed and that the wealthiest own a large share of total wealth. For sample surveys which aim at measuring wealth and its distribution, this is a considerable problem. To overcome it, some of the country surveys under the HFCS umbrella try to sample a disproportionately large share of households that are likely to be wealthy, a technique referred to as oversampling. Ignoring such types of complex survey designs in the estimation of regression models can lead to severe problems. This thesis first illustrates such problems using data from the first wave of the HFCS and canonical regression models from the field of household finance and gives a first guideline for HFCS data users regarding the use of replicate weight sets for variance estimation using a variant of the bootstrap. A further investigation of the issue necessitates a design-based Monte Carlo simulation study. To this end, the already existing large close-to-reality synthetic simulation population AMELIA is extended with synthetic wealth data. We discuss different approaches to the generation of synthetic micro data in the context of the extension of a synthetic simulation population that was originally based on a different data source. We propose an additional approach that is suitable for the generation of highly skewed synthetic micro data in such a setting using a multiply-imputed survey data set. After a description of the survey designs employed in the first wave of the HFCS, we then construct new survey designs for AMELIA that share core features of the HFCS survey designs. A design-based Monte Carlo simulation study shows that while more conservative approaches to oversampling do not pose problems for the estimation of regression models if sampling weights are properly accounted for, the same does not necessarily hold for more extreme oversampling approaches. This issue should be further analysed in future research.
Official business surveys form the basis for national and regional business statistics and are thus of great importance for analysing the state and performance of the economy. However, both the heterogeneity of business data and their high dynamics pose a particular challenge to the feasibility of sampling and the quality of the resulting estimates. A widely used sampling frame for creating the design of an official business survey is an extract from an official business register. However, if this frame does not accurately represent the target population, frame errors arise. Amplified by the heterogeneity and dynamics of business populations, these errors can significantly affect the estimation quality and lead to inefficiencies and biases. This dissertation therefore deals with design-based methods for optimising business surveys with respect to different types of frame errors.
First, methods for adjusting the sampling design of business surveys are addressed. These approaches integrate auxiliary information about the expected structures of frame errors into the sampling design. The aim is to increase the number of sampled businesses that are subject to frame errors. The element-specific frame error probability is estimated based on auxiliary information about frame errors observed in previous samples. The approaches discussed consider different types of frame errors and can be incorporated into predefined designs with fixed strata.
As the second main pillar of this work, methods for adjusting weights to correct for frame errors during estimation are developed and investigated. As a result of frame errors, the assumptions under which the original design weights were determined based on the sampling design no longer hold. The developed methods correct the design weights taking into account the errors identified for sampled elements. Case-number-based reweighting approaches, on the one hand, attempt to reconstruct the unknown size of the individual strata in the target population. In the context of weight smoothing methods, on the other hand, design weights are modelled and smoothed as a function of target or auxiliary variables. This serves to avoid inefficiencies in the estimation due to highly scattering weights or weak correlations between weights and target variables. In addition, possibilities of correcting frame errors by calibration weighting are elaborated. Especially when the sampling frame shows over- and/or undercoverage, the inclusion of external auxiliary information can provide a significant improvement of the estimation quality. For those methods whose quality cannot be measured using standard procedures, a procedure for estimating the variance based on a rescaling bootstrap is proposed. This enables an assessment of the estimation quality when using the methods in practice.
In the context of two extensive simulation studies, the methods presented in this dissertation are evaluated and compared with each other. First, in the environment of an experimental simulation, it is assessed which approaches are particularly suitable with regard to different data situations. In a second simulation study, which is based on the structural survey in the services sector, the applicability of the methods in practice is evaluated under realistic conditions.
Survey data can be viewed as incomplete or partially missing from a variety of perspectives and there are different ways of dealing with this kind of data in the prediction and the estimation of economic quantities. In this thesis, we present two selected research contexts in which the prediction or estimation of economic quantities is examined under incomplete survey data.
These contexts are first the investigation of composite estimators in the German Microcensus (Chapters 3 and 4) and second extensions of multivariate Fay-Herriot (MFH) models (Chapters 5 and 6), which are applied to small area problems.
Composite estimators are estimation methods that take into account the sample overlap in rotating panel surveys such as the German Microcensus in order to stabilise the estimation of the statistics of interest (e.g. employment statistics). Due to the partial sample overlaps, information from previous samples is only available for some of the respondents, so the data are partially missing.
MFH models are model-based estimation methods that work with aggregated survey data in order to obtain more precise estimation results for small area problems compared to classical estimation methods. In these models, several variables of interest are modelled simultaneously. The survey estimates of these variables, which are used as input in the MFH models, are often partially missing. If the domains of interest are not explicitly accounted for in a sampling design, the sizes of the samples allocated to them can, by chance, be small. As a result, it can happen that either no estimates can be calculated at all or that the estimated values are not published by statistical offices because their variances are too large.
Non-probability sampling is a topic of growing relevance, especially due to its occurrence in the context of new emerging data sources like web surveys and Big Data.
This thesis addresses statistical challenges arising from non-probability samples, where unknown or uncontrolled sampling mechanisms raise concerns in terms of data quality and representativity.
Various methods to quantify and reduce the potential selectivity and biases of non-probability samples in estimation and inference are discussed. The thesis introduces new forms of prediction and weighting methods, namely
a) semi-parametric artificial neural networks (ANNs) that integrate B-spline layers with optimal knot positioning in the general structure and fitting procedure of artificial neural networks, and
b) calibrated semi-parametric ANNs that determine weights for non-probability samples by integrating an ANN as response model with calibration constraints for totals, covariances and correlations.
Custom-made computational implementations are developed for fitting (calibrated) semi-parametric ANNs by means of stochastic gradient descent, BFGS and sequential quadratic programming algorithms.
The performance of all the discussed methods is evaluated and compared for a bandwidth of non-probability sampling scenarios in a Monte Carlo simulation study as well as an application to a real non-probability sample, the WageIndicator web survey.
Potentials and limitations of the different methods for dealing with the challenges of non-probability sampling under various circumstances are highlighted. It is shown that the best strategy for using non-probability samples heavily depends on the particular selection mechanism, research interest and available auxiliary information.
Nevertheless, the findings show that existing as well as newly proposed methods can be used to ease or even fully counterbalance the issues of non-probability samples and highlight the conditions under which this is possible.
The publication of statistical databases is subject to legal regulations, e.g. national statistical offices are only allowed to publish data if the data cannot be attributed to individuals. Achieving this privacy standard requires anonymizing the data prior to publication. However, data anonymization inevitably leads to a loss of information, which should be kept minimal. In this thesis, we analyze the anonymization method SAFE used in the German census in 2011 and we propose a novel integer programming-based anonymization method for nominal data.
In the first part of this thesis, we prove that a fundamental variant of the underlying SAFE optimization problem is NP-hard. This justifies the use of heuristic approaches for large data sets. In the second part, we propose a new anonymization method belonging to microaggregation methods, specifically designed for nominal data. This microaggregation method replaces rows in a microdata set with representative values to achieve k-anonymity, ensuring each data row is identical to at least k − 1 other rows. In addition to the overall dissimilarities of the data rows, the method accounts for errors in resulting frequency tables, which are of high interest for nominal data in practice. The method employs a typical two-step structure: initially partitioning the data set into clusters and subsequently replacing all cluster elements with representative values to achieve k-anonymity. For the partitioning step, we propose a column generation scheme followed by a heuristic to obtain an integer solution, which is based on the dual information. For the aggregation step, we present a mixed-integer problem formulation to find cluster representatives. To this end, we take errors in a subset of frequency tables into account. Furthermore, we show a reformulation of the problem to a minimum edge-weighted maximal clique problem in a multipartite graph, which allows for a different perspective on the problem. Moreover, we formulate a mixed-integer program, which combines the partitioning and the aggregation step and aims to minimize the sum of chi-squared errors in frequency tables.
Finally, an experimental study comparing the methods covered or developed in this work shows particularly strong results for the proposed method with respect to relative criteria, while SAFE shows its strength with respect to the maximum absolute error in frequency tables. We conclude that the inclusion of integer programming in the context of data anonymization is a promising direction to reduce the inevitable information loss inherent in anonymization, particularly for nominal data.
Data fusions are becoming increasingly relevant in official statistics. The aim of a data fusion is to combine two or more data sources using statistical methods in order to be able to analyse different characteristics that were not jointly observed in one data source. Record linkage of official data sources using unique identifiers is often not possible due to methodological and legal restrictions. Appropriate data fusion methods are therefore of central importance in order to use the diverse data sources of official statistics more effectively and to be able to jointly analyse different characteristics. However, the literature lacks comprehensive evaluations of which fusion approaches provide promising results for which data constellations. Therefore, the central aim of this thesis is to evaluate a concrete plethora of possible fusion algorithms, which includes classical imputation approaches as well as statistical and machine learning methods, in selected data constellations.
To specify and identify these data contexts, data and imputation-related scenario types of a data fusion are introduced: Explicit scenarios, implicit scenarios and imputation scenarios. From these three scenario types, fusion scenarios that are particularly relevant for official statistics are selected as the basis for the simulations and evaluations. The explicit scenarios are the fulfilment or violation of the Conditional Independence Assumption (CIA) and varying sample sizes of the data to be matched. Both aspects are likely to have a direct, that is, explicit, effect on the performance of different fusion methods. The summed sample size of the data sources to be fused and the scale level of the variable to be imputed are considered as implicit scenarios. Both aspects suggest or exclude the applicability of certain fusion methods due to the nature of the data. The univariate or simultaneous, multivariate imputation solution and the imputation of artificially generated or previously observed values in the case of metric characteristics serve as imputation scenarios.
With regard to the concrete plethora of possible fusion algorithms, three classical imputation approaches are considered: Distance Hot Deck (DHD), the Regression Model (RM) and Predictive Mean Matching (PMM). With Decision Trees (DT) and Random Forest (RF), two prominent tree-based methods from the field of statistical learning are discussed in the context of data fusion. However, such prediction methods aim to predict individual values as accurately as possible, which can clash with the primary objective of data fusion, namely the reproduction of joint distributions. In addition, DT and RF only comprise univariate imputation solutions and, in the case of metric variables, artificially generated values are imputed instead of real observed values. Therefore, Predictive Value Matching (PVM) is introduced as a new, statistical learning-based nearest neighbour method, which could overcome the distributional disadvantages of DT and RF, offers a univariate and multivariate imputation solution and, in addition, imputes real and previously observed values for metric characteristics. All prediction methods can form the basis of the new PVM approach. In this thesis, PVM based on Decision Trees (PVM-DT) and Random Forest (PVM-RF) is considered.
The underlying fusion methods are investigated in comprehensive simulations and evaluations. The evaluation of the various data fusion techniques focusses on the selected fusion scenarios. The basis for this is formed by two concrete and current use cases of data fusion in official statistics, the fusion of EU-SILC and the Household Budget Survey on the one hand and of the Tax Statistics and the Microcensus on the other. Both use cases show significant differences with regard to different fusion scenarios and thus serve the purpose of covering a variety of data constellations. Simulation designs are developed from both use cases, whereby the explicit scenarios in particular are incorporated into the simulations.
The results show that PVM-RF in particular is a promising and universal fusion approach under compliance with the CIA. This is because PVM-RF provides satisfactory results for both categorical and metric variables to be imputed and also offers a univariate and multivariate imputation solution, regardless of the scale level. PMM also represents an adequate fusion method, but only in relation to metric characteristics. The results also imply that the application of statistical learning methods is both an opportunity and a risk. In the case of CIA violation, potential correlation-related exaggeration effects of DT and RF, and in some cases also of RM, can be useful. In contrast, the other methods induce poor results if the CIA is violated. However, if the CIA is fulfilled, there is a risk that the prediction methods RM, DT and RF will overestimate correlations. The size ratios of the studies to be fused in turn have a rather minor influence on the performance of fusion methods. This is an important indication that the larger dataset does not necessarily have to serve as a donor study, as was previously the case.
The results of the simulations and evaluations provide concrete implications as to which data fusion methods should be used and considered under the selected data and imputation constellations. Science in general and official statistics in particular benefit from these implications. This is because they provide important indications for future data fusion projects in order to assess which specific data fusion method could provide adequate results along the data constellations analysed in this thesis. Furthermore, with PVM this thesis offers a promising methodological innovation for future data fusions and for imputation problems in general.