The research presented in this dissertation touches on all aspects of survey methodology, from questionnaire design to final estimation. We first approach the questionnaire development stage by proposing a method of developing matrix sampling designs, a design where a subset of questions are administered to a respondent in such a way that the administered questions are predictive of the omitted questions. The proposed methodology compares favorably to previous methods when applied to data collected from a household survey conducted in the Nampula province of Mozambique. We approach the data collection stage by proposing a structured procedure of implementing small-scale surveys in such a way that non-sampling error attributed to data collection is minimized. This proposed methodology requires the inclusion of the statistician in the data editing process during data collection. We implemented the structured procedure during the collection of household survey data in the city of Maputo, the capital of Mozambique. We found indications that the data resulting from the structured procedure is of higher quality than the data with no editing. Finally, we approach the estimation phase of sample surveys by proposing a model-based approach to the estimation of the mean squared error associated with synthetic (indirect) estimates. Previous methodology aggregates estimates for stability, while our proposed methodology allows area-specific estimates. We applied the proposed mean squared error estimation methodology and methods found during literature review to simulated data and estimates from 2010 Census Coverage Measurement (CCM). We found that our proposed mean squared error estimation methodology compares favorably to the previous methods, while allowing for area-specific estimates. / Ph. D.

Left heart disease often results in left heart failure and right ventricular dysfunction which is challenging to diagnose with traditional diagnostic approaches. To address this a novel empirical 4-point right ventricular dysfunction score was created at Sahlgrenska University Hospital to overcome the limitations of single variables for diagnosing right ventricular dysfunction. In this study, we used machine learning, more specifically XGBoost coupled with interactive machine learning to develop four different models for predicting death or receiving a left ventricular assist device in patients with left heart disease (n=486). Features were selected from the dataset using recursive feature elimination with the default number of features. The initial model with 29 features, called the baseline model served as the foundation of the three additional models, each adjusted based on feedback from a clinician. The first step of feedback included removing features due to high correlation, creating a modified model with 12 features, the second step was to use 12 well-known characteristics of left and right ventricular dysfunction creating an empirical model, and adjusting the prediction threshold from 50% to 60%. The third step was to reduce the number of features to 5 based on empirical grounds. The models were compared to the right ventricular dysfunction score using the metrics area under the curve, f1 score, positive likelihood ratio, and negative likelihood ratio. The predictive efficacy of the machine learning models was superior compared to the right ventricular dysfunction score. The results also indicated that the models did neither improve nor deteriorate when reducing the number of features. However, insufficient accuracy indicates that none of the machine learning models are clinically viable. These results show the potential of machine learning in enhancing prognostic stratification in patients with left heart disease although further refinement is necessary for clinical use. / Vänstersidig hjärtsjukdom resulterar ofta i vänstersidig hjärtsvikt och högerkammarsvikt vilket är utmanade att diagnostisera med traditionella diagnostiska metoder. För att komma undan med begränsningen med enskilda variabler för att diagnostisera högerkammarsvikt skapades ett 4 poängs högerkammarsvikt score vid Sahlgrenska Universitetssjukhuset. I denna studie användes en XGBoost-algoritm kombinerat med interaktiv maskininlärning för att utveckla fyra olika prediktions modeller för att förutsäga dödlighet eller risken att få en mekanisk hjärtpump för vänster kammare hos patienter med vänster hjärtsvikt (n=486). Variabler valdes från datamängden med hjälp av rekursiv funktionseliminering med ett standardantal variabler. Den initiala modellen med 29 variabler kallades baslinjemodellen och fungerade som grunden för de tre ytterligare modellerna som justerades baserat på klinikerns feedback. Det först steget inkluderade att ta bort variabler med inbördes hög korrelation och vi skapade en modifierad modell med 12 variabler. I det andra steget i den empiriska modellen använde vi 12 kända egenskaperna vid vänsterkammar- och högerkammarsvikt och för båda justerades tröskelvärdet för prediktion från 50% till 60%. I ett tredje steg skapade vi en förenklad modell med 5 variabler ut ifrån klinisk grund. Modellerna jämfördes med höger hjärtsvikts 4 poängskalan med hjälp av mätvariablerna area under kurvan, f1-poäng, positivt sannolikhets ratio och negativt sannolikhets ratio. Detta avslöjade att maskininlärnings modellerna hade bättre prediktiv förmåga än 4-poängs högerkammarsvikt score. Dessutom visade resultatet att modellerna inte försämrades eller förbättrades när variabler valdes bort eller när nya modeller skapades på klinisk grund. Dock hade maskininlärnings modellerna otillräcklig noggrannhet för klinisk användning.

Diese Dissertation beschäftigt sich mit Methoden zur Behandlung von nicht-ignorierbaren fehlenden Daten und Stichprobenverzerrungen – zwei häufig auftretenden Problemen bei der Analyse von Umfragedaten. Beide Datenprobleme können die Qualität der Analyseergebnisse erheblich beeinträchtigen und zu irreführenden Inferenzen über die Population führen. Daher behandle ich innerhalb von drei verschiedenen Forschungsartikeln, Methoden, die eine Durchführung von sogenannten Sensitivitätsanalysen in Bezug auf Missing- und Selektionsmechanismen ermöglichen und dabei auf typische Survey-Daten angewandt werden können. Im Rahmen des ersten und zweiten Artikels entwickele ich Verfahren zur multiplen Imputation von binären und ordinal Mehrebenen-Daten, welche es zulassen, einen potenziellen Missing Not at Random (MNAR) Mechanismus zu berücksichtigen. In unterschiedlichen Simulationsstudien konnte bestätigt werden, dass die neuen Imputationsmethoden in der Lage sind, in allen betrachteten Szenarien unverzerrte sowie effiziente Schätzungen zuliefern. Zudem konnte ihre Anwendbarkeit auf empirische Daten aufgezeigt werden. Im dritten Artikel untersuche ich ein Maß zur Quantifizierung und Adjustierung von nicht ignorierbaren Stichprobenverzerrungen in Anteilswerten, die auf der Basis von nicht-probabilistischen Daten geschätzt wurden. Es handelt sich hierbei um die erste Anwendung des Index auf eine echte nicht-probabilistische Stichprobe abseits der Forschergruppe, die das Maß entwickelt hat. Zudem leite ich einen allgemeinen Leitfaden für die Verwendung des Index in der Praxis ab und validiere die Fähigkeit des Maßes vorhandene Stichprobenverzerrungen korrekt zu erkennen. Die drei vorgestellten Artikel zeigen, wie wichtig es ist, vorhandene Schätzer auf ihre Robustheit hinsichtlich unterschiedlicher Annahmen über den Missing- und Selektionsmechanismus zu untersuchen, wenn es Hinweise darauf gibt, dass die Ignorierbarkeitsannahme verletzt sein könnte und stellen erste Lösungen zur Umsetzung bereit. / This thesis deals with methods for the appropriate handling of non-ignorable missing data and sample selection, which are two common challenges of survey data analysis. Both issues can dramatically affect the quality of analysis results and lead to misleading inferences about the population. Therefore, in three different research articles, I treat methods for the performance of so-called sensitivity analyses with regards to the missing data and selection mechanism that are usable with typical survey data. In the first and second article, I provide novel procedures for the multiple imputation of binary and ordinal multilevel data that are supposed to be Missing not At Random (MNAR). The methods’ suitability to produce unbiased and efficient estimates could be demonstrated in various simulation studies considering different data scenarios. Moreover, I could show their applicability to empirical data. In the third article, I investigate a measure to quantify and adjust non-ignorable selection bias in proportions estimated based on non-probabilistic data. In doing so, I provide the first application of the suggested index to a real non-probability sample outside its original research group. In addition, I derive general guidelines for its usage in practice, and validate the measure’s performance in properly detecting selection bias. The three presented articles highlight the necessity to assess the sensitivity of estimates towards different assumptions about the missing-data and selection mechanism if it seems realistic that the ignorability assumption might be violated, and provide first solutions to enable such robustness checks for specific data situations.

Les logiciels utilisés sont Splus et R. / Résumé La technique connue comme l'imputation multiple semble être la technique la plus appropriée pour résoudre le problème de non-réponse. La littérature mentionne des méthodes qui modélisent la nature et la structure des valeurs manquantes. Une des méthodes les plus populaires est l'algorithme « Pan » de (Schafer & Yucel, 2002). Les imputations rapportées par cette méthode sont basées sur un modèle linéaire multivarié à effets mixtes pour la variable réponse. La méthode « BHLC » de (Murua et al, 2005) est une extension de « Pan » dont le modèle est bayésien hiérarchique avec groupes. Le but principal de ce travail est d'étudier le problème de sélection du modèle pour l'imputation multiple en termes d'efficacité et d'exactitude des prédictions des valeurs manquantes. Nous proposons une mesure de performance liée à la prédiction des valeurs manquantes. La mesure est une erreur quadratique moyenne reflétant la variance associée aux imputations multiples et le biais de prédiction. Nous montrons que cette mesure est plus objective que la mesure de variance de Rubin. Notre mesure est calculée en augmentant par une faible proportion le nombre de valeurs manquantes dans les données. La performance du modèle d'imputation est alors évaluée par l'erreur de prédiction associée aux valeurs manquantes. Pour étudier le problème objectivement, nous avons effectué plusieurs simulations. Les données ont été produites selon des modèles explicites différents avec des hypothèses particulières sur la structure des erreurs et la distribution a priori des valeurs manquantes. Notre étude examine si la vraie structure d'erreur des données a un effet sur la performance du choix des différentes hypothèses formulées pour le modèle d'imputation. Nous avons conclu que la réponse est oui. De plus, le choix de la distribution des valeurs manquantes semble être le facteur le plus important pour l'exactitude des prédictions. En général, les choix les plus efficaces pour de bonnes imputations sont une distribution de student avec inégalité des variances dans les groupes pour la structure des erreurs et une loi a priori choisie pour les valeurs manquantes est la loi normale avec moyenne et variance empirique des données observées, ou celle régularisé avec grande variabilité. Finalement, nous avons appliqué nos idées à un cas réel traitant un problème de santé. Mots clés : valeurs manquantes, imputations multiples, modèle linéaire bayésien hiérarchique, modèle à effets mixtes. / Abstract The technique known as multiple imputation seems to be the most suitable technique for solving the problem of non-response. The literature mentions methods that models the nature and structure of missing values. One of the most popular methods is the PAN algorithm of Schafer and Yucel (2002). The imputations yielded by this method are based on a multivariate linear mixed-effects model for the response variable. A Bayesian hierarchical clustered and more flexible extension of PAN is given by the BHLC model of Murua et al. (2005). The main goal of this work is to study the problem of model selection for multiple imputation in terms of efficiency and accuracy of missing-value predictions. We propose a measure of performance linked to the prediction of missing values. The measure is a mean squared error, and hence in addition to the variance associated to the multiple imputations, it includes a measure of bias in the prediction. We show that this measure is more objective than the most common variance measure of Rubin. Our measure is computed by incrementing by a small proportion the number of missing values in the data and supposing that those values are also missing. The performance of the imputation model is then assessed through the prediction error associated to these pseudo missing values. In order to study the problem objectively, we have devised several simulations. Data were generated according to different explicit models that assumed particular error structures. Several missing-value prior distributions as well as error-term distributions are then hypothesized. Our study investigates if the true error structure of the data has an effect on the performance of the different hypothesized choices for the imputation model. We concluded that the answer is yes. Moreover, the choice of missing-value prior distribution seems to be the most important factor for accuracy of predictions. In general, the most effective choices for good imputations are a t-Student distribution with different cluster variances for the error-term, and a missing-value Normal prior with data-driven mean and variance, or a missing-value regularizing Normal prior with large variance (a ridge-regression-like prior). Finally, we have applied our ideas to a real problem dealing with health outcome observations associated to a large number of countries around the world. Keywords: Missing values, multiple imputation, Bayesian hierarchical linear model, mixed effects model.

Les données manquantes sont fréquentes dans les enquêtes et peuvent entraîner d’importantes erreurs d’estimation de paramètres. Ce mémoire méthodologique en sociologie porte sur l’influence des données manquantes sur l’estimation de l’effet d’un programme de prévention. Les deux premières sections exposent les possibilités de biais engendrées par les données manquantes et présentent les approches théoriques permettant de les décrire. La troisième section porte sur les méthodes de traitement des données manquantes. Les méthodes classiques sont décrites ainsi que trois méthodes récentes. La quatrième section contient une présentation de l’Enquête longitudinale et expérimentale de Montréal (ELEM) et une description des données utilisées. La cinquième expose les analyses effectuées, elle contient : la méthode d’analyse de l’effet d’une intervention à partir de données longitudinales, une description approfondie des données manquantes de l’ELEM ainsi qu’un diagnostic des schémas et du mécanisme. La sixième section contient les résultats de l’estimation de l’effet du programme selon différents postulats concernant le mécanisme des données manquantes et selon quatre méthodes : l’analyse des cas complets, le maximum de vraisemblance, la pondération et l’imputation multiple. Ils indiquent (I) que le postulat sur le type de mécanisme MAR des données manquantes semble influencer l’estimation de l’effet du programme et que (II) les estimations obtenues par différentes méthodes d’estimation mènent à des conclusions similaires sur l’effet de l’intervention. / Missing data are common in empirical research and can lead to significant errors in parameters’ estimation. This dissertation in the field of methodological sociology addresses the influence of missing data on the estimation of the impact of a prevention program. The first two sections outline the potential bias caused by missing data and present the theoretical background to describe them. The third section focuses on methods for handling missing data, conventional methods are exposed as well as three recent ones. The fourth section contains a description of the Montreal Longitudinal Experimental Study (MLES) and of the data used. The fifth section presents the analysis performed, it contains: the method for analysing the effect of an intervention from longitudinal data, a detailed description of the missing data of MLES and a diagnosis of patterns and mechanisms. The sixth section contains the results of estimating the effect of the program under different assumptions about the mechanism of missing data and by four methods: complete case analysis, maximum likelihood, weighting and multiple imputation. They indicate (I) that the assumption on the type of MAR mechanism seems to affect the estimate of the program’s impact and, (II) that the estimates obtained using different estimation methods leads to similar conclusions about the intervention’s effect.

Problemas frequentes nas análises estatísticas de informações meteorológicas são a ocorrência de dados faltantes e ausência de conhecimento acerca da homogeneidade das informações contidas no banco de dados. O objetivo deste trabalho foi testar e classificar a homogeneidade da série de precipitação pluvial da estação climatológica convencional da ESALQ, no período de 1917 a 1997, e comparar três métodos de imputação de dados, em diferentes intensidades amostrais (5%, 10% e 15%) de informações faltantes, geradas de forma aleatória. Foram utilizados três testes de homogeneidade da série: Pettitt, Buishand e normal padrão. Para o \"preenchimento\" das informações faltantes, foram comparados três métodos de imputação múltipla: PMM (Predictive Mean Matching), random forest e regressão linear via método bootstrap, em cada intensidade amostral de informações faltantes. Os métodos foram utilizados por meio do pacote MICE (Multivariate Imputation by Chained Equations) do R. A comparação entre cada procedimento de imputação foi feita por meio da raiz do erro quadrático médio, índice de exatidão de Willmott e o índice de desempenho. A série de chuva foi entendida como de classe 1, ou seja, \"útil\" - Nenhum sinal claro de falta de homogeneidade foi aparente e, o método que resultou em menores valores da raiz quadrada dos erros e maiores índices foi o PMM, em especial na intensidade de 10% de informações faltantes. O índice de desempenho para os três métodos de imputação de dados em todas as intensidades de observações faltantes foi considerado \"Péssimo\" / Frequent problems in the statistical analyzes of meteorological information are the occurrence of missing data and missing of knowledge about the homogeneity of the information contained in the data base. The objective of this work was to test and classify the homogeneity of the rainfall series of the conventional climatological station of the ESALQ from 1917 to 1997 and to compare three methods of data imputation in different sample intensities (5%, 10% and 15%), of missing data, generated in a random way. Three homogeneity tests were used: Pettitt, Buishand and standard normal. For the \"filling\" of missing information, three methods of multiple imputation were compared: PMM (Predictive Mean Matching), random forest and linear regression via bootstrap method, in each sampling intensity of missing information. The methods were used by means of the MICE (Multivariate Imputation by Chained Equations) package of R. The comparison of each imputation procedure was done by root mean square error, Willmott\'s accuracy index and performance index. The rainfall series was understood to be class 1 \"useful\" - No clear sign of lack of homogeneity was apparent and the method that resulted in smaller values of the square root of the errors and higher indexes was the PMM, in particular the intensity of 10% of missing information. The performance index for the three methods of imputation the data at all missing observation intensities was considered \"Terrible\"

Geralmente, nos experimentos genótipo por ambiente (G × E) é comum observar o comportamento dos genótipos em relação a distintos atributos nos ambientes considerados. A análise deste tipo de experimentos tem sido abordada amplamente para o caso de um único atributo. Nesta tese são apresentadas algumas alternativas de análise considerando genótipos, ambientes e atributos simultaneamente. A primeira, é baseada no método de mistura de máxima verossimilhança de agrupamento - Mixclus e a análise de componentes principais de 3 modos - 3MPCA, que permitem a análise de tabelas de tripla entrada, estes dois métodos têm sido muito usados na área da psicologia e da química, mas pouco na agricultura. A segunda, é uma metodologia que combina, o modelo de efeitos aditivos com interação multiplicativa - AMMI, modelo eficiente para a análise de experimentos (G × E) com um atributo e a análise de procrustes generalizada, que permite comparar configurações de pontos e proporcionar uma medida numérica de quanto elas diferem. Finalmente, é apresentada uma alternativa para realizar imputação de dados nos experimentos (G × E), pois, uma situação muito frequente nestes experimentos, é a presença de dados faltantes. Conclui-se que as metodologias propostas constituem ferramentas úteis para a análise de experimentos (G × E) multiatributo. / Usually, in the experiments genotype by environment (G×E) it is common to observe the behaviour of genotypes in relation to different attributes in the environments considered. The analysis of such experiments have been widely discussed for the case of a single attribute. This thesis presents some alternatives of analysis, considering genotypes, environments and attributes simultaneously. The first, is based on the mixture maximum likelihood method - Mixclus and the three-mode principal component analysis, these two methods have been very used in the psychology and chemistry, but little in agriculture. The second, is a methodology that combines the additive main effects and multiplicative interaction models - AMMI, efficient model for the analysis of experiments (G×E) with one attribute, and the generalised procrustes analysis, which allows compare configurations of points and provide a numerical measure of how much they differ. Finally, an alternative to perform data imputation in the experiments (G×E) is presented, because, a very frequent situation in these experiments, is the presence of missing values. It is concluded that the proposed methodologies are useful tools for the analysis of experiments (G×E) multi-attribute.

Les politiques environnementales, notamment celles recourant aux instruments fiscaux, ont pris une place de plus en plus importante dans un grand nombre de pays durant les trois dernières décennies. Tous les pays de l’OCDE ont introduit des taxes liées à l'environnement et un nombre croissant d'entre eux procèdent à une réforme dite "verte" de leur fiscalité. L’utilisation de la taxe comme un instrument pour la politique environnementale a suscité un large débat parmi les chercheurs sur ses impacts sur la croissance économique, mais sans parvenir à un consensus sur la nature de ces effets. Certains trouvent un effet négatif, alors que d’autres montrent un impact positif. Deux points ont attiré notre attention sur ce sujet. Premièrement, les études empiriques qui vérifient la validité de ces résultats sont très rares. Deuxièmement, la majorité des modèles théoriques qui ont étudié l’effet de la fiscalité environnementale sur la croissance économique supposent que le gouvernement finance ses dépenses uniquement par les taxes et que le budget d’État est équilibré à chaque période, évitant ainsi tout fardeau associé au remboursement de la dette publique. Par conséquent, cette thèse a pour objectif d’abord d’explorer empiriquement la nature de la relation entre la fiscalité environnementale et la croissance économique, et si cette relation est sensible au niveau d'autres variables dans l'économie. Ensuite, nous examinons les canaux par lesquels cette taxe peut affecter la croissance économique, et si l'existence et le niveau de la dette publique peuvent modifier cet effet. / Environmental policies, especially those using fiscal instruments, have become more and more important in a large number of countries over the last three decades. All OECD countries have introduced environmentally related taxes, and a growing number of them are carrying out a so-called "green" reform of their taxation. The use of the tax as an instrument for environmental policy has sparked wide debate among researchers on its impacts on economic growth, but without reaching consensus on the nature of these effects. Some find a negative effect; while others show a positive impact. Two points raised our attention on this subject. First, the empirical studies that verify the validity of these results are very rare. Second, the majority of theoretical models that have studied the effect of environmental taxation on economic growth assume that the government finances its expenditures solely through taxes and that the state budget is balanced each period, thus avoiding any burden associated to repayment of public debt. Therefore, this thesis aims firstly to explore empirically the nature of the relationship between environmental taxation and economic growth, and whether this relationship is sensitive to the level of other variables in the economy. We examine then the channels through which this tax can affect economic growth, and whether the existence and level of public debt can modify this effect.

La croissance économique et ses moteurs représentent le principal sujet préoccupant les chercheurs en macroéconomie depuis longtemps. Investir en capital humain à travers le système éducatif joue un rôle important pour stimuler la croissance et le développement économique, cette accentuation a pris place depuis la naissance innovante de la théorie de la croissance endogène. L'attention et les efforts dévoués à l'investissement dans le capital humain peuvent être déstabilisés par le retour global et récent de la crise de la dette souveraine dans plusieurs pays, dette qui poursuit son ascension depuis 2007, et les politiques d'ajustement nécessaires d'après-crise. Des judicieuses politiques de redressement devraient être composées d'un mélange des activités encourageant la croissance économique, y compris l'investissement dans le capital humain, l'austérité et le long terme. L'objectif principal de cette thèse est de fournir des nouvelles évidences empiriques sur la relation dette-croissance économique et leurs externalités sur la formation de capital humain, les estimations sont réalisées sur un jeu de données récent et complet couvrant 22 années et 76 pays dans le monde. L'ensemble des variables utilisées englobe de nombreux agrégats macroéconomiques tel que : taux de croissance annuel du PIB, la dette publique en % de PIB, les dépenses publiques d'éducation en % de PIB, le moyen d'année de scolarité, le taux d'inflation, et d'autres. En utilisant une technique d'estimation semi-paramétrique appropriée qui offre des solutions pour de nombreux problèmes concernant les données, les résultats empiriques suggèrent un impact négatif et hétérogène de dette et des dépenses d'éducation publiques sur la croissance du PIB. Là où, l'utilisation des dépenses d'éducation dans l'ensemble de l'échantillon est inefficace, les décideurs politiques devraient ajuster et bien gérer la fonction de ces dépenses en même temps de viser des efforts publics pour réduire les niveaux élevés d'endettement et d'augmenter la croissance économique. Nous montrons également que l'utilisation des outils d'analyse textuelle en économie, offre une lecture rapide et globale des courants de recherche contenus dans la littérature empirique et théorique de la croissance économique. / Economic growth and its driving forces have been the maintopic preoccupying economic researchers since long time in macroeconomic branch. Public investment in human capital through educational system plays an ultimate role in boosting economic growth and development, this role has taken a place since the innovative dawn of endogenous growth theory. The focus and efforts of investing in human capital could be destabilized by the global and recent return of sovereign debt crisis in several countries, which continues its rise since theearly 2007, and the after-crisis necessary adjusting policies. Getting back wise policies should be composed of mixture of growth fostering activities, including the investment in human capital, austerity and forbearance.The main purpose of this thesis is to provide new empirical inferences on debt-growth relationship and its interaction with human capital formation. Estimates are carried on a recent and complete data set that spans over 22 years and involves 76 countries worldwide. The range of invested variables encompasses many macroeconomic aggregates such as : GDP annual growthrates, public debt to GDP ratio, and public education expenditure to GDP ratio, average schooling years, inflation rate, and others. Using a superior estimation semi-parametric technic which accounts for some data issues, the empirical results suggest a heterogeneous impact of public debt and education expenditures levels on GDP growth rates. Henceforth, the use of education expenditure in the whole sample is inefficient,where policy makers should adjust and well manage the function of these expenditure in line with the public efforts to reduce debt high levels and rise economic growth. We also show that the use of textual analysis tools in economic studies, such in growth literature, offers a rapid and total lecture of the hidden research trends embodied in the huge empirical and theoretical literature of economic growth.

Gelman, King, 及Liu(1998)針對一連串且互相獨立的橫斷面調查提出多重設算程序，且對不同調查的參數以階層模式(hierarchical model)連結。本文為介紹複雜抽樣(分層或群集抽樣)之下，若Q個連續變數有遺漏現象時，如何結合對象之個別特性，各層或各群集的參數，以及連結各層或各群集參數的階層模式，以設算遺漏值及估計模式中之參數。 對遺漏值的處理採用單調資料擴展演算法，只需對破壞單調資料型態的遺漏值進行設算。由於考慮到不同的群集或層往往呈現不同的特性，因而以階層模式連絡各群集或各層的參數，並將Gelman, King, Liu(1998)的推導結果擴展到將個別對象之特性納入考量之上。對各群集而言，他們的共變異數矩陣Ψ及Σ為影響群內其他參數的收斂情形，由模擬獲得的結果，沒有證據顯示應懷疑收斂的問題。 / Gelman, king, and Liu (1998) use multiple imputation for a series of cross section survey, and link the parameter of different survey by hierarchical model. This text introduces a method to impute missing value and estimate the parameters affected by hierarchical model if Q continuous variables has missing value under complex survey. For each cluster, the parameters are influenced by their variance-covariance matrix Ψ and Σ. The result obtained from the simulation have no clear evidence to doubt the convergence of parameters.