Im Rahmen der Item-Response-Theorie evaluiert die kumulative Dissertationsschrift verschiedene Methoden und Modelle zur Identifikation von Kontexteffekten in Large-Scale Assessments. Solche Effekte können etwa in quantitativen empirischen Schulleistungsstudien auftreten und zu verzerrten Item- und Personenparametern führen. Um in Einzelfällen abschätzen zu können, ob Kontexteffekte auftreten und dadurch die Gefahr verzerrter Parameter gegeben ist (und falls ja, in welcher Weise), müssen IRT-Modelle entwickelt werden, die zusätzlich zu Item- und Personeneffekten Kontexteffekte parametrisieren. Solch eine Parametrisierung ist im Rahmen Generalisierter Allgemeiner Linearer Modelle möglich. In der Dissertation werden Positionseffekte als ein Beispiel für Kontexteffekte untersucht, und es werden die statistischen Eigenschaften dieses Messmodells im Rahmen einer Simulationsstudie evaluiert. Hier zeigt sich vor allem die Bedeutung des Testdesigns: Um unverfälschte Parameter zu gewinnen, ist nicht nur ein adäquates Messmodell, sondern ebenso ein adäquates, also ausbalanciertes Testdesign notwendig. Der dritte Beitrag der Dissertation befasst sich mit dem Problem fehlender Werte auf Hintergrundvariablen in Large-Scale Assessments. Als Kontexteffekt wird in diesem Beispiel derjenige Effekt verstanden, der die Wahrscheinlichkeit eines fehlenden Wertes auf einer bestimmten Variablen systematisch beeinflusst. Dabei wurde das Prinzip der multiplen Imputation auf das Problem fehlender Werte auf Hintergrundvariablen übertragen. Anders als bisher praktizierte Ansätze (Dummy-Codierung fehlender Werte) konnten so in einer Simulationsstudie für fast alle Simulationsbedingungen unverfälschte Parameter auf der Personenseite gefunden werden. / The present doctoral thesis evaluates various methods and models of the item response theory to parametrize context effects in large-scale assessments. Such effects may occur in quantitative educational assessments and may cause biased item and person parameter estimates. To decide whether context effects occur in individual cases and lead to biased parameters, specific IRT models have to be developed which parametrize context effects additionally to item and person effects. The present doctoral thesis consists of three single contributions. In the first contribution, a model for the estimation of context effects in an IRT framework is introduced. Item position effects are examined as an example of context effects in the framework of generalized linear mixed models. Using simulation studies, the statistical properties of the model are investigated, which emphasizes the relevance of an appropriate test design. A balanced incomplete test design is necessary not only to obtain valid item parameters in the Rasch model, but to guarantee for unbiased estimation of position effects in more complex IRT models. The third contribution deals with the problem of missing background data in large-scale assessments. The effect which predicts the probability of a missing value on a certain variable, is considered as a context effect. Statistical methods of multiple imputation were brought up to the problem of missing background data in large-scale assessments. In contrast to other approaches used so far in practice (dummy coding of missing values) unbiased population and subpopulation estimates were received in a simulation study for most conditions.

Cette thèse examine les questions sociologiques relatives à la relation entre la confiance dans les institutions démocratiques et les éléments de la modernité, en particulier la diversité des populations. Tout en testant des hypothèses fondées sur la théorie, la thèse étudie et développe d'abord des stratégies méthodologiques pour surmonter les défis communs de la recherche comparative en sciences sociales, y compris la combinaison de données au niveau individuel et national, les données manquantes, et la mesure de la diversité de la population. Il se compose de trois articles. Le premier article vise à identifier des approches méthodologiques efficaces pour l'imputation des données manquantes dans les données longitudinales combinées au niveau individuel et au niveau national. Le défi que représentent les données manquantes est décrit (les données manquantes sont presque toujours présentes dans les données de recherche comparative longitudinale compte tenu de la diversité des situations et des capacités de production de données des pays) avant de définir et de tester trois approches d'imputation combinant l'imputation multiple multiniveau et l'imputation de séries chronologiques. Ces méthodes comprennent 1. modèles multiniveaux avec effets aléatoires par pays (ML RE), 2. modèles multiniveaux avec pentes aléatoires variables longitudinales (ML RS), et 3. l'imputation de séries chronologiques univariées en deux étapes pour les variables de second niveau, suivie de modèles multiniveaux à effets aléatoires pour les variables individuelles (TS+ML RE). L'approche d'imputation multiniveau, y compris des pentes aléatoires pour les variables de l'année et de l'année carrée par pays, s'est avérée très efficace pour imputer les valeurs manquantes qui suivaient sans problème les tendances observées dans les données d'un pays, tout en incorporant des informations provenant de covariables et des données et tendances d'autres pays. On a constaté qu'une méthode d'imputation de séries chronologiques en deux étapes complétait l'imputation des données longitudinales au niveau national beaucoup plus rapidement, mais donnait de moins bons résultats lorsque des données limitées étaient présentes, en particulier lorsque des données manquaient à l'une ou l'autre extrémité d'une période de temps. Les trois approches testées ont produit des imputations qui, lorsqu'elles sont utilisées pour tester des modèles statistiques, produisent des résultats similaires, mais pas identiques. La décision d'utiliser une méthode d'imputation fondée sur un modèle pour imputer les données manquantes, en évitant la production d'estimations biaisées et en permettant l'utilisation de toutes les observations, peut dans de nombreux cas être la décision méthodologique la plus importante, après quoi l'utilisation d'une méthode d'imputation et d'un modèle intégrant des données longitudinales à plusieurs niveaux permet de produire des données imputées de haute qualité. La décision d'utiliser une méthode d'imputation fondée sur un modèle pour imputer les données manquantes, en évitant la production d'estimations biaisées et en permettant l'utilisation de toutes les observations, peut dans de nombreux cas être la décision méthodologique la plus importante, après quoi l'utilisation d'une méthode d'imputation et d'un modèle intégrant des données longitudinales à plusieurs niveaux permet de produire des données imputées de haute qualité. Des données imputées de haute qualité permettent alors aux chercheurs de mieux mesurer et résumer les phénomènes quantitatifs et de tester les hypothèses de recherche. Cet article et ses conclusions liées à la sélection et à la mise en œuvre de méthodologies d'imputation plus optimales constituent une contribution importante à la littérature, car les résultats et les conclusions de fond publiés dans les articles de recherche peuvent différer selon qu'un chercheur applique une solution meilleure ou moins bonne à un problème de données manquantes. Le deuxième article étudie les mesures de la diversité dans le contexte de l'étude sociologique comparative de la démocratie et identifie la nécessité d'examiner les relations non linéaires entre la diversité et les variables de résultat. Les données décrivant les pourcentages de groupes ethniques de plus de 150 pays sont utilisées pour calculer quatre mesures de la diversité ethnique. Les quatre mesures de la diversité : la variance généralisée, le pourcentage minoritaire, le pourcentage de la deuxième plus grande minorité ou groupe saillant, et l'entropie, sont comparées les unes aux autres pour les niveaux de corrélation et les différences de distribution. Les quatre mesures se sont avérées être des mesures fiables et valides de la diversité. La variance généralisée, le pourcentage minoritaire et l'entropie (dans une mesure légèrement moindre) se sont avérés fortement corrélés avec des corrélations d'ordre de classement presque parfaites, tandis que le deuxième plus grand pourcentage de minorité variait dans l'ordre de classement et les valeurs par rapport aux autres mesures. Cependant, la variable de diversité de variance généralisée a montré les caractéristiques de distribution les plus favorables, n'exige pas que les données soient écartées et s'est avérée former les relations statistiques les plus solides avec les mesures de la démocratie. En tant que telle, la variance généralisée s'avère être le choix optimal pour mesurer la diversité. Des preuves minimes de corrélations linéaires bivariées ont été trouvées entre les mesures de la diversité et les mesures de la démocratie, sauf en Europe où les valeurs de mesure de la démocratie variaient peu. Au lieu de cela, les tendances observées indiquaient des relations quadratiques. Les modèles à plusieurs niveaux ont révélé des associations significatives entre les mesures de la diversité au carré et la participation de la société civile et la liberté d'expression. Comme les études empiriques et les théories ont mis en évidence les effets complexes et parfois opposés de la diversité sur les résultats sociaux, les résultats indiquent l'avantage, et peut-être la nécessité, de l'évaluation des relations non linéaires dans l'étude des relations entre la diversité et les résultats sociaux. Le troisième article, qui met en œuvre les avancées méthodologiques des deux premiers articles, étudié les relations hypothétiques dérivées de la théorie entre plusieurs caractéristiques macro-sociopolitiques, y compris la diversité ethnique et le niveau de démocratie, et les variables de résultat de la confiance individuelle dans le congrès ou le parlement et la présence du mouvement antisystème national. Le contexte de l'Europe de l'Est et de l'Asie centrale entre 1993 et 2016 a été étudié en intégrant plus de 500 000 réponses individuelles à des enquêtes dans 27 pays. Des caractéristiques annuelles au niveau national indiquant une modernisation de la société sous la forme d'une plus grande différenciation et d'un développement humain ont été testées pour les associations avec la confiance individuelle dans le congrès ou le parlement. Les caractéristiques agrégées au niveau des pays, y compris les moyennes des données d'enquête au niveau individuel, ont été étudiées plus en détail en relation avec les cotes de présence d'antisystèmes. Les différences d'effets entre les pays classés en démocraties, démocraties partielles et autocraties ont été examinées et des différences substantielles dans l'ampleur et la directionnalité des associations ont été constatées. Les résultats suggèrent que la diversité de la population était associée à une plus grande confiance dans les institutions démocratiques et à une moindre présence des mouvements antisystèmes dans les démocraties. D'autres caractéristiques des pays indiquant la réalisation des idéaux modernes et démocratiques, telles que des niveaux d'éducation moyens plus élevés, une plus grande liberté d'expression, un PIB par habitant plus élevé et une plus grande participation aux élections, étaient généralement associées à une plus grande confiance dans le parlement ou le congrès dans les démocraties. De cette façon, la congruence entre les caractéristiques sociales indiquant le fonctionnement moderne, dynamique, pluraliste et démocratique d'une société était liée à une plus grande confiance au niveau individuel dans les institutions à l'apogée de nombreux paradigmes démocratiques d'organisation sociale – parlements et congrès. En résumé, malgré les défis méthodologiques majeurs auxquels sont confrontés les chercheurs comparatistes intéressés par la combinaison de données au niveau individuel et national pour étudier les relations longitudinales associées à la confiance institutionnelle démocratique, à la modernité et à la diversité, de multiples solutions permettant une meilleure évaluation ont été trouvées, permettant de tester des hypothèses complexes fondées sur la théorie. L'imputation multiple peut être mise en œuvre lorsque des données manquantes sont présentes afin de générer efficacement des imputations suivant les tendances longitudinales incorporant de grandes quantités de données connexes. La diversité est parfois un sujet complexe, mais la mesure de la variance généralisée de la diversité est un choix méthodologique optimal dans la recherche comparative et les relations non linéaires doivent être examinées lors de l'étude de la relation entre la diversité et les résultats sociaux. On a supposé que le pluralisme allait de pair avec la modernité démocratique, prenant de nombreuses formes, dont celle de la diversité ethnique. Des preuves ont été trouvées de relations linéaires et non linéaires quadratiques entre la diversité et la confiance dans les institutions démocratiques et des niveaux inférieurs de présence du mouvement antisystème. De nombreuses autres mesures indiquant la diversification sociale et le développement humain se sont également révélées positivement liées à la confiance individuelle dans le parlement ou le Congrès, ce qui soutient généralement les hypothèses selon lesquelles la différenciation et le pluralisme peuvent caractériser et jouer des rôles fonctionnels dans les sociétés démocratiques modernes, tandis que des niveaux élevés d'homogénéité ethnique peuvent également former des associations positives. Cette thèse apporte des avancées méthodologiques et teste des perspectives et des hypothèses sociologiques de longue date à l'aide d'une étude empirique à grande échelle. Qu'il s'agisse de l'imputation des données manquantes, La mesure de la diversité et ses associations, ou des relations entre les dimensions de la modernité et la confiance individuelle dans les institutions démocratiques, les trois articles jettent les bases de recherches futures visant à étudier les hypothèses et les dimensions de certaines des questions les plus urgentes de la sociologie. / This thesis examines sociological questions pertaining to the relationship between trust in democratic institutions and elements of modernity, particularly population diversity. While ultimately testing theory-driven hypotheses, the thesis first studies and develops methodological strategies for overcoming common challenges in comparative social science research, including the combination of individual-level and country-level data, missing data, and the measurement of population diversity and its complex relationships. It comprises three articles. The first article seeks to identify effective methodological approaches to the imputation of missing data in combined longitudinal individual-level and country-level data. The challenge that missing data presents is described (missing data is almost always present in longitudinal comparative research data given a diversity of country circumstances and capacities for data production) before defining and testing three imputation approaches combining multilevel model multiple imputation and time series imputation. These methods include 1. multilevel models with country random effects (ML RE), 2. multilevel models with longitudinal variable random slopes (ML RS), and 3. two-step univariate time-series imputation for second-level variables followed by multilevel models with random effects for individual-level variables (TS+ML RE). The multilevel multiple imputation approach including random slopes for year and year squared variables per country was found to be highly effective at imputing missing values that smoothly followed observed trends in a country’s data while also incorporating information from related covariates and from the data and trends of other countries. A two-step time series imputation approach was found to complete imputation of country-level longitudinal data much faster but performed worse where limited data was present, particularly where data was missing at either end of a time span. All three tested approaches produced imputations that, when used to test statistical models, produced similar yet not identical results. The decision to use a model-based imputation approach to impute missing data, averting production of biased estimates and enabling use of all observations, may in many cases be the most important methodological decision, whereafter use of an imputation method and model incorporating longitudinal multilevel data enables production of high-quality imputed data. High quality imputed data then enables researchers to be better able to measure and summarize quantitative phenomena and to test research hypotheses. This article and its findings related to selection and implementation of more optimal imputation methodologies, is an important contribution to the literature because the results and substantive conclusions published in research articles can differ depending on whether a researcher applies a better or worse solution to a missing data problem. The second article studies diversity measures in the context of comparative sociological study of democracy and identifies the need for the examination of nonlinear relationships between diversity and outcomes of interest. Data describing ethnic group percentages from over 150 countries are used to calculate four measures of ethnic diversity. The four measures of diversity: generalized variance, minority percent, second-largest minority percent, and entropy, are compared with one another for levels of correlation and for distributional differences. The four measures were found to be reliable and valid measures of diversity. Generalized variance, minority percent, and entropy (to a slightly lesser extent) were found to be highly correlated with near perfect rank-order correlations while second-largest minority percent varied in rank-order and values when compared to the other measures. However, the generalized variance diversity variable showed the most favorable distributional characteristics, requires no data be discarded, and was found to form the strongest statistical relationships with democracy measures. As such, generalized variance is shown to be the optimal diversity measure choice. Minimal evidence of bivariate linear correlations were found between diversity measures and democracy measures except within Europe which had minimal variation in democracy measure values. Instead observed trends indicated quadratic relationships. Multilevel models found significant associations between squared diversity measures and civil society participation and freedom of expression. As empirical studies and theories have pointed toward complex and sometimes opposing effects of diversity on social outcomes, results here indicate the benefit of, and perhaps necessity for, evaluation of nonlinear relationships when studying relationships between diversity and social outcomes. The third article, implementing methodological advances from the first two articles, studied theory-derived hypothesized relationships between several macro sociopolitical characteristics, including ethnic diversity and level of democracy, and outcome variables of individual trust in congress or parliament and national antisystem movement presence. The context of Eastern Europe and Central Asia between years 1993 and 2016 were studied incorporating over 500,000 individual survey responses in 27 countries. Yearly country-level characteristics indicating societal modernization in the form of greater differentiation and human development were tested for associations with individual trust in congress or parliament. Aggregate country-level characteristics, including individual-level survey data averages, were further studied in relation to antisystem presence ratings. Differences in effects across countries categorized as democracies, partial democracies, and autocracies were examined and substantial differences in associations’ magnitudes and directionality were found. Results suggest that population diversity was associated with greater trust in democratic institutions and less antisystem movement presence in democracies. Other country characteristics indicating the fulfillment of modern and democratic ideals such as higher average education levels, greater freedom of expression, higher GDP per person, and greater election participation were generally associated with higher trust in parliament or congress in democracies. In this way, congruence across social characteristics indicative of a society’s modern, dynamic, pluralistic, democratic functioning were related to greater individual-level trust in the institutions at the peak of many democratic paradigms of social organization – parliaments and congresses. In summary, despite the major methodological challenges that face comparative researchers interested in combining individual-level and country-level data to study longitudinal relationships associated with democratic institutional trust, modernity, and diversity, multiple solutions enabling better evaluation were found enabling the testing of complex theory-based hypotheses. Multiple imputation can be implemented where missing data is present to effectively generate imputations following longitudinal trends incorporating large quantities of related data. Diversity is a complex topic, yet the generalized variance measure of diversity is an optimal methodological choice in comparative research and nonlinear relationships should be examined when studying diversity’s relationship with social outcomes. Pluralism was hypothesized to go hand in hand with democratic modernity, taking numerous forms including that of ethnic diversity. Evidence was found of linear and nonlinear quadratic relationships between diversity and trust in democratic institutions and lower levels of antisystem movement presence. Numerous other measures indicative of social diversification and human development were likewise found to be positively related to individual trust in parliament or congress, generally supporting hypotheses that differentiation and pluralism may characterize as well as serve functional roles in modern democratic societies while that high levels ethnic homogeneity can also form positive associations. This dissertation contributes methodological advances and tests longstanding sociological perspectives and hypotheses utilizing a large-scale empirical study. Whether interested in missing data imputation, diversity’s measurement and associations, or the relationships between dimensions of modernity and individual trust in democratic institutions, the three articles lay a groundwork for future research to study hypotheses and dimensions of some of sociology’s most pressing issues.

Longitudinal studies of cognition are preferred to cross-sectional stud- ies, since they offer a direct assessment of age-related cognitive change (within-person change). Statistical methods for analyzing age-related change are widely available. There are, however, a number of challenges accompanying such analyzes, including cohort differences, ceiling- and floor effects, and attrition. These difficulties challenge the analyst and puts stringent requirements on the statistical method being used. The objective of Paper I is to develop a classifying method to study discrepancies in age-related cognitive change. The method needs to take into account the complex issues accompanying studies of cognitive aging, and specifically work out issues related to attrition. In a second step, we aim to identify predictors explaining stability or decline in cognitive performance in relation to demographic, life-style, health-related, and genetic factors. In the second paper, which is a continuation of Paper I, we investigate brain characteristics, structural and functional, that differ between suc- cessful aging elderly and elderly with an average cognitive performance over 15-20 years. In Paper III we develop a Bayesian model to estimate the causal effect of living arrangement (living alone versus living with someone) on cog- nitive decline. The model must balance confounding variables between the two living arrangement groups as well as account for non-ignorable attrition. This is achieved by combining propensity score matching with a pattern mixture model for longitudinal data. In paper IV, the objective is to adapt and implement available impu- tation methods to longitudinal fMRI data, where some subjects are lost to follow-up. We apply these missing data methods to a real dataset, and evaluate these methods in a simulation study.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Multi-state models are used in this dissertation to model panel data, also known as longitudinal or cross-sectional time-series data. These are data sets which include units that are observed across two or more points in time. These models have been used extensively in medical studies where the disease states of patients are recorded over time. A theoretical overview of the current multi-state Markov models when applied to panel data is presented and based on this theory, a simulation procedure is developed to generate panel data sets for given Markov models. Through the use of this procedure a simulation study is undertaken to investigate the properties of the standard likelihood approach when fitting Markov models and then to assess its shortcomings. One of the main shortcomings highlighted by the simulation study, is the unstable estimates obtained by the standard likelihood models, especially when fitted to small data sets. A Bayesian approach is introduced to develop multi-state models that can overcome these unstable estimates by incorporating prior knowledge into the modelling process. Two Bayesian techniques are developed and presented, and their properties are assessed through the use of extensive simulation studies. Firstly, Bayesian multi-state models are developed by specifying prior distributions for the transition rates, constructing a likelihood using standard Markov theory and then obtaining the posterior distributions of the transition rates. A selected few priors are used in these models. Secondly, Bayesian multi-state imputation techniques are presented that make use of suitable prior information to impute missing observations in the panel data sets. Once imputed, standard likelihood-based Markov models are fitted to the imputed data sets to estimate the transition rates. Two different Bayesian imputation techniques are presented. The first approach makes use of the Dirichlet distribution and imputes the unknown states at all time points with missing observations. The second approach uses a Dirichlet process to estimate the time at which a transition occurred between two known observations and then a state is imputed at that estimated transition time. The simulation studies show that these Bayesian methods resulted in more stable results, even when small samples are available. / AFRIKAANSE OPSOMMING: Meerstadium-modelle word in hierdie verhandeling gebruik om paneeldata, ook bekend as longitudinale of deursnee tydreeksdata, te modelleer. Hierdie is datastelle wat eenhede insluit wat oor twee of meer punte in tyd waargeneem word. Hierdie tipe modelle word dikwels in mediese studies gebruik indien verskillende stadiums van ’n siekte oor tyd waargeneem word. ’n Teoretiese oorsig van die huidige meerstadium Markov-modelle toegepas op paneeldata word gegee. Gebaseer op hierdie teorie word ’n simulasieprosedure ontwikkel om paneeldatastelle te simuleer vir gegewe Markov-modelle. Hierdie prosedure word dan gebruik in ’n simulasiestudie om die eienskappe van die standaard aanneemlikheidsbenadering tot die pas vanMarkov modelle te ondersoek en dan enige tekortkominge hieruit te beoordeel. Een van die hoof tekortkominge wat uitgewys word deur die simulasiestudie, is die onstabiele beramings wat verkry word indien dit gepas word op veral klein datastelle. ’n Bayes-benadering tot die modellering van meerstadiumpaneeldata word ontwikkel omhierdie onstabiliteit te oorkom deur a priori-inligting in die modelleringsproses te inkorporeer. Twee Bayes-tegnieke word ontwikkel en aangebied, en hulle eienskappe word ondersoek deur ’n omvattende simulasiestudie. Eerstens word Bayes-meerstadium-modelle ontwikkel deur a priori-verdelings vir die oorgangskoerse te spesifiseer en dan die aanneemlikheidsfunksie te konstrueer deur van standaard Markov-teorie gebruik te maak en die a posteriori-verdelings van die oorgangskoerse te bepaal. ’n Gekose aantal a priori-verdelings word gebruik in hierdie modelle. Tweedens word Bayesmeerstadium invul tegnieke voorgestel wat gebruik maak van a priori-inligting om ontbrekende waardes in die paneeldatastelle in te vul of te imputeer. Nadat die waardes ge-imputeer is, word standaard Markov-modelle gepas op die ge-imputeerde datastel om die oorgangskoerse te beraam. Twee verskillende Bayes-meerstadium imputasie tegnieke word bespreek. Die eerste tegniek maak gebruik van ’n Dirichletverdeling om die ontbrekende stadium te imputeer by alle tydspunte met ’n ontbrekende waarneming. Die tweede benadering gebruik ’n Dirichlet-proses om die oorgangstyd tussen twee waarnemings te beraam en dan die ontbrekende stadium te imputeer op daardie beraamde oorgangstyd. Die simulasiestudies toon dat die Bayes-metodes resultate oplewer wat meer stabiel is, selfs wanneer klein datastelle beskikbaar is.

Spatial-temporal autologistic models are useful models for binary data that are measured repeatedly over time on a spatial lattice. They can account for effects of potential covariates and spatial-temporal statistical dependence among the data. However, the traditional parametrization of spatial-temporal autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, where its non-negative autocovariates could bias the realizations toward 1. In order to achieve interpretable parameters, a centered spatial-temporal autologistic regression model has been developed. Two efficient statistical inference approaches, expectation-maximization pseudo-likelihood approach (EMPL) and Monte Carlo expectation-maximization likelihood approach (MCEML), have been proposed. Also, Bayesian inference is considered and studied. Moreover, the performance and efficiency of these three inference approaches across various sizes of sampling lattices and numbers of sampling time points through both simulation study and a real data example have been studied. In addition, We consider the imputation of missing values is for spatial-temporal autologistic regression models. Most existing imputation methods are not admissible to impute spatial-temporal missing values, because they can disrupt the inherent structure of the data and lead to a serious bias during the inference or computing efficient issue. Two imputation methods, iteration-KNN imputation and maximum entropy imputation, are proposed, both of them are relatively simple and can yield reasonable results. In summary, the main contributions of this dissertation are the development of a spatial-temporal autologistic regression model with centered parameterization, and proposal of EMPL, MCEML, and Bayesian inference to obtain the estimations of model parameters. Also, iteration-KNN and maximum entropy imputation methods have been presented for spatial-temporal missing data, which generate reliable imputed values with the reasonable efficient imputation time.

Em estudos multiambientais, o processo de recomendação de genótipos com maior produção e a determinação de genótipos estáveis são de suma importância para os melhoristas. Porém, quando ocorre falta de genótipo em um ou mais ambientes este processo passa a ter dificuldades. Pois, este procedimento depende de métodos estatísticos que necessitam de uma matriz de dados sem dados em falta. Desde 1976 diversos matemáticos e estatísticos estudam, continuamente, uma forma de lidar com dados em falta em dados multiambientais buscando obter um método que estime, de forma precisa, as unidades ausentes sem perda de informação. Desta forma, esta pesquisa propõe um novo método de imputação baseado na metodologia AMMI fazendo reamostragens Bootstrap Não-paramétrico na matriz de médias de interação genótipos e ambientes (G × E), o modelo de imputação AMMI Bootstrap Não-paramétrico (IAMMI-BNP). Para estudo de simulação foi considerado o conjunto de dados referente a procedência S. of Ravenshoe - Mt Pandanus - QLD (14.420) de Eucalyptus grandis coletada na Austrália em 1983. Com a finalidade de obter estimativas precisas dos valores em falta, foi considerado dois estudos de simulação. O primeiro considerou 2000 reamostragens no sentido linha da matriz de interação G × E considerando duas porcentagens de perda de dados (10% e 20 %). O segundo estudo de simulação, considerou 200 reamostragens na matriz de falta (10%) e três diferentes modelos de IAMMI-BNP: IAMMI0-BNP, que considera apenas os efeitos principais do modelo AMMI; IAMMI1-BNP e IAMMI2-BNP que considera um e dois eixos multiplicados do modelo AMMI, respectivamente. De forma geral, de acordo com os métodos de comparação o método de imputação proposto nos dois estudos de simulação forneceu valores imputados próximos dos originais. Considerando os estudos de simulação com 10% de perda, a eficiência do método de imputação proposto foi melhor quando se utilizou o modelo IAMMI2-BNP (com dois eixos multiplicativos). O teste das ordens assinaladas de Wilcoxon mostrou que os valores imputados não influenciaram na estimativa da média, indicando que valores médios dos dados imputados de cada ambiente foram estatisticamente semelhantes aos valores médios originais. / In multienvironment studies, the process of recommendation of genotypes with higher production and the determination of stable environments are of utmost importance for plant breeders. However, when there is missing of genotype in one or more environments this process show difficulties. Therefore, this procedure depends on statistical methods that complete data matrix requered. Since 1976 various mathematical and statistical study, continually, one way of dealing with the loss of information on data multienvironments, seeking to obtain a method that estimate, precisely, the missing units without loss of information. In this way, the purpose of this study is develop a new method of apportionment based on the methodology AMMI doing reamostragens bootstrap nonparametric in the array of means of genotype x environment interaction (GE). For the study of simulation was considered the data set concerning the origin of S. Mexico City - Mt Pandanus - QLD (14,420) of Eucalyptus grandis collected in Australia in 1983. It was performed two studies of simulation. The first performed 2000 resampling on the lines of the interaction matrix G X E, for two percentages of missing data (10% and 20%). The second simulation study considered 200 replicates in the missing data set (10 %) and three different models of IMAMMI-BNP: AMAMMI0-BNP, which considers only the main effects of the AMMI model; IAMMI1-BNP and IAMMI2-BNP which considers one and two axes multiplied by the AMMI model, respectively. In general, according to the comparison methods, the imputation method proposed in the two simulation studies provided imputed values similar to the originals. Considering the simulation studies with 10 % loss, the efficiency of the proposed imputation method was better when using the IAMMI2-BNP model (with two multiplicative axes). The Wilcoxon test of the orders showed that the values imputed had no influence on the mean estimate, indicating that mean values of the data imputed from each environment were statistically similar to the original mean values.

A crescente preocupação com o meio ambiente pressiona a sociedade como um todo para a uma mudança rumo a hábitos mais sustentáveis. No setor produtivo, o impulso se dá pelo desenvolvimento de técnicas mais eficientes de produção, embasados em pesquisas e experimentos de campo. No setor florestal, além da preocupação com a técnicas de manejo e com o solo, o principal recurso a ser preservado é a água. Por meio do monitoramento de rios em bacias hidrográficas, séries históricas são coletadas, possibilitando o uso da teoria de séries temporais para ajuste de modelos pela metodologia Box e Jenkins. Em casos de monitoramentos de microbacias pareadas, existe a possibilidade de se comparar séries temporais, como descrito no presente trabalho. Em duas microbacias pareadas localizadas na região centro-leste do estado do Paraná, em uma fazenda no município de Telêmaco Borba, dados correspondendo a duas séries temporais distintas de vazão específica foram coletados. Devido a presença de falhas nos conjuntos de dados, uma metodologia para imputação foi utilizada de duas maneiras diferentes, possibilitando a posterior comparação das duas séries temporais pela metodologia de séries temporais. De acordo com os resultados, verifica-se que ambas as séries são diferentes tanto para o teste de comparação das funções de autocorrelação, quanto para o teste de comparação de séries temporais proposto por Silva, Ferreira e Sáfadi (2000). Portanto, segundo a caracterização dos estudos em microbacias pareadas, pode-se constatar que o manejo florestal empregado nos dois locais influenciam de forma diferente no comportamento da variável avaliada. / The growing concern for the enviroment presses society as a whole for a change towards sustainable habits. Regarding the production systems, more efficient production techniques based on research and field experiments are needed. As for forestry, besides the concern with management techniques and with soil preparation, the main resource to be preserved is water. Time series are collected by monitoring rivers in drainage basins, making possible the use of time series theory for fitting models based on Box and Jenkins methodology. When studying paired drainage basins, it is possible to compare time series, as described in this work. Two time series consisting of specific flow data were collected in a farm situated in the municipality of Telêmaco Borba, Eastern Paraná state, in two paired drainage basins. Because there were missing data, imputation techniques were used, making it possible to compare the two time series. Results showed that the time series are different for the comparison of the autocorrelation test and the time series comparison test proposed by Silva, Ferreira e Sáfadi (2000). Therefore, according to studies involving paired drainage basins, different forest management techniques influence differently the behavior of the response variable in the different drainage basins.

Em estudos multiambientais, o processo de recomendação de genótipos com maior produção e a determinação de genótipos estáveis são de suma importância para os melhoristas. Porém, quando ocorre falta de genótipo em um ou mais ambientes este processo passa a ter dificuldades. Pois, este procedimento depende de métodos estatísticos que necessitam de uma matriz de dados sem dados em falta. Desde 1976 diversos matemáticos e estatísticos estudam, continuamente, uma forma de lidar com dados em falta em dados multiambientais buscando obter um método que estime, de forma precisa, as unidades ausentes sem perda de informação. Desta forma, esta pesquisa propõe um novo método de imputação baseado na metodologia AMMI fazendo reamostragens Bootstrap Não-paramétrico na matriz de médias de interação genótipos e ambientes (G × E), o modelo de imputação AMMI Bootstrap Não-paramétrico (IAMMI-BNP). Para estudo de simulação foi considerado o conjunto de dados referente a procedência S. of Ravenshoe - Mt Pandanus - QLD (14.420) de Eucalyptus grandis coletada na Austrália em 1983. Com a finalidade de obter estimativas precisas dos valores em falta, foi considerado dois estudos de simulação. O primeiro considerou 2000 reamostragens no sentido linha da matriz de interação G × E considerando duas porcentagens de perda de dados (10% e 20 %). O segundo estudo de simulação, considerou 200 reamostragens na matriz de falta (10%) e três diferentes modelos de IAMMI-BNP: IAMMI0-BNP, que considera apenas os efeitos principais do modelo AMMI; IAMMI1-BNP e IAMMI2-BNP que considera um e dois eixos multiplicados do modelo AMMI, respectivamente. De forma geral, de acordo com os métodos de comparação o método de imputação proposto nos dois estudos de simulação forneceu valores imputados próximos dos originais. Considerando os estudos de simulação com 10% de perda, a eficiência do método de imputação proposto foi melhor quando se utilizou o modelo IAMMI2-BNP (com dois eixos multiplicativos). O teste das ordens assinaladas de Wilcoxon mostrou que os valores imputados não influenciaram na estimativa da média, indicando que valores médios dos dados imputados de cada ambiente foram estatisticamente semelhantes aos valores médios originais. / In multienvironment studies, the process of recommendation of genotypes with higher production and the determination of stable environments are of utmost importance for plant breeders. However, when there is missing of genotype in one or more environments this process show difficulties. Therefore, this procedure depends on statistical methods that complete data matrix requered. Since 1976 various mathematical and statistical study, continually, one way of dealing with the loss of information on data multienvironments, seeking to obtain a method that estimate, precisely, the missing units without loss of information. In this way, the purpose of this study is develop a new method of apportionment based on the methodology AMMI doing reamostragens bootstrap nonparametric in the array of means of genotype x environment interaction (GE). For the study of simulation was considered the data set concerning the origin of S. Mexico City - Mt Pandanus - QLD (14,420) of Eucalyptus grandis collected in Australia in 1983. It was performed two studies of simulation. The first performed 2000 resampling on the lines of the interaction matrix G X E, for two percentages of missing data (10% and 20%). The second simulation study considered 200 replicates in the missing data set (10 %) and three different models of IMAMMI-BNP: AMAMMI0-BNP, which considers only the main effects of the AMMI model; IAMMI1-BNP and IAMMI2-BNP which considers one and two axes multiplied by the AMMI model, respectively. In general, according to the comparison methods, the imputation method proposed in the two simulation studies provided imputed values similar to the originals. Considering the simulation studies with 10 % loss, the efficiency of the proposed imputation method was better when using the IAMMI2-BNP model (with two multiplicative axes). The Wilcoxon test of the orders showed that the values imputed had no influence on the mean estimate, indicating that mean values of the data imputed from each environment were statistically similar to the original mean values.

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La plupart des systèmes experts actuels reposent sur les connaissances de surface (le savoir-faire) d'un expert du domaine d'application. Plus récemment, une autre approche s'est développée. Elle vise a exploiter les connaissances profondes (théoriques) acquises dans le domaine d'application. La thèse étudie cette dernière approche dans le cadre du projet pic (poste de travail intelligent pour le comptable). Les aspects méthodologiques sont développés dans la première partie. Une nouvelle classe d'applications des systèmes experts est proposée: l'interprétation comparative. Elle a pour but de mettre en évidence et expliquer la cause des différences entre deux états d'un système. Une methode générale permettant d'aborder ce probleme est présentée, ainsi que des techniques la mettant en œuvre sur des modèles qualitatifs et numériques. Les contributions au projet pic sont développées dans la seconde partie. Un générateur de systèmes experts d'interprétation comparative est d'abord présenté. Il a servi a la réalisation de deux systèmes: le premier pour l'analyse de la performance d'une entreprise par la methode des surplus, le second pour le diagnostic financier d'entreprise. Un système expert pour la déduction des écritures comptables utilisant également l'approche profonde est ensuite présenté. A la lumière de ces deux dernières applications déjà abordées par les systèmes experts utilisant des connaissances de surface, les deux approches de conception de systèmes experts sont comparées