The class of models which is studied in this paper, multi-unit longitudinal models, combines both the cross-sectional and the longitudinal aspects of observations. Many empirical investigations involve the analysis of data structures that are both cross-sectional (observations are taken on several units at a specific time period or at a specific location) and longitudinal (observations on the same unit are taken over time or space). Multi-unit longitudinal data structures arise in economics and business where panels of subjects are studied over time, biostatistics where groups of patients on different treatments are observed over time, and in situations where data are taken over time and space. Modelling issues in multi-unit longitudinal models with random coefficients and patterned correlation structure are illustrated in the context of two data sets. The first data set deals with short time series data on annual death rates and alcohol consumption for twenty-five European countries. The second data set deals with glaceologic time series data on snow temperature at 14 different locations within a small glacier in the Austrian Alps. A practical model building approach, consisting of model specification, estimation, and diagnostic checking, is outlined. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Après une synthèse des principales avancées en microfinance, la thèse offre un aperçu sur les institutions de microfinance (Imf) dans les pays en développement entre 2000 et 2009. Une étude approfondie du marché de l’Afrique Subsaharienne est également proposée. Elle sert de prélude à l’analyse économétrique des déterminants des performances financière et sociale des Imf dans cette région ainsi qu’à l’examen des arbitrages entre les deux objectifs. Le modèle est également estimé avec les données de l’Amérique Latine et Caraïbes afin de tester, entre autres, sa robustesse spatiale. Les résultats montrent que malgré la forte croissance affichée, les Imf demeurent fragiles à cause des retards de paiement et de la faible rentabilité. En outre, il n’existe pas de modèle universel de la microfinance sans spécificités régionales. La commercialisation du secteur est remise en cause car même si elle ne s’accompagne pas nécessairement d’une déviation de la mission sociale, elle n’améliore pas la performance financière. Enfin, la richesse du secteur provient de sa segmentation alors que sa faiblesse est due à son manque d’organisation, avec une concurrence se traduisant par une recrudescence des risques au lieu d’une diversification des produits. / After a summary of the main achievements in microfinance, the thesis provides an overview of microfinance institutions (MFIs) in developing countries between 2000 and 2009. A thorough study of microfinance in sub-Saharan Africa is also proposed. It serves as a prelude to the econometric analysis of the determinants of financial and social performances of MFIs and to the review of the trade-offs between the two objectives in this region. The model is also estimated with data from Latin America and the Caribbean to test, amongst others, its spatial robustness. The results show that despite their strong growth, MFIs remain fragile because of arrears and low profitability. In addition, there is no universal model of microfinance without regional specificities. The commercialization of the sector is called into question because although it does not necessarily lead to social mission drift, it does notimprove financial performance. Finally, the richness of the sector comes from itssegmentation while its weakness is due to its lack of organization, with competition leading to increasing risk rather than product diversification.

Em experimentos agronômicos são comuns ensaios planejados para estudar determinadas culturas por meio de múltiplas mensurações realizadas na mesma unidade amostral ao longo do tempo, espaço, profundidade entre outros. Essa forma com que as mensurações são coletadas geram conjuntos de dados que são chamados de dados longitudinais. Nesse contexto, é de extrema importância a utilização de metodologias estatísticas que sejam capazes de identificar possíveis padrões de variação e correlação entre as mensurações. A possibilidade de inclusão de efeitos aleatórios e de modelagem das estruturas de covariâncias tornou a metodologia de modelos lineares mistos uma das ferramentas mais apropriadas para a realização desse tipo de análise. Entretanto, apesar de todo o desenvolvimento teórico e computacional, a utilização dessa metodologia em delineamentos mais complexos envolvendo dados longitudinais e tratamentos adicionais, como os utilizados na área de forragicultura, ainda é passível de estudos. Este trabalho envolveu o uso do diagrama de Hasse e da estratégia top-down na construção de modelos lineares mistos no estudo de cortes sucessivos de forragem provenientes de um experimento de adubação com boro em alfafa (Medicago sativa L.) realizado no campo experimental da Embrapa Pecuária Sudeste. Primeiramente, considerou-se uma abordagem qualitativa para todos os fatores de estudo e devido à complexidade do delineamento experimental optou-se pela construção do diagrama de Hasse. A incorporação de efeitos aleatórios e seleção de estruturas de covariâncias para os resíduos foram realizadas com base no teste da razão de verossimilhanças calculado a partir de parâmetros estimados pelo método da máxima verossimilhança restrita e nos critérios de informação de Akaike (AIC), Akaike corrigido (AICc) e bayesiano (BIC). Os efeitos fixos foram testados por meio do teste Wald-F e, devido aos efeitos significativos das fontes de variação associadas ao fator longitudinal, desenvolveu-se um estudo de regressão. A construção do diagrama de Hasse foi fundamental para a compreensão e visualização simbólica do relacionamento de todos os fatores presentes no estudo, permitindo a decomposição das fontes de variação e de seus graus de liberdade, garantindo que todos os testes fossem realizados corretamente. A inclusão de efeito aleatório associado à unidade experimental foi essencial para a modelagem do comportamento de cada unidade e a estrutura de componentes de variância com heterogeneidade, incorporada aos resíduos, foi capaz de modelar eficientemente a heterogeneidade de variâncias presente nos diferentes cortes da cultura da alfafa. A verificação do ajuste foi realizada por meio de gráficos de diagnósticos de resíduos. O estudo de regressão permitiu avaliar a produtividade de matéria seca da parte aérea da planta (kg ha-1) de cortes consecutivos da cultura da alfafa, envolvendo a comparação de adubações com diferentes fontes e doses de boro. Os melhores resultados de produtividade foram observados para a combinação da fonte ulexita com as doses 3, 6 e 9 kg ha-1 de boro. / Assays aimed at studying some crops through multiple measurements performed in the same sample unit along time, space, depth etc. have been frequently adopted in agronomical experiments. This type of measurement originates a dataset named longitudinal data, in which the use of statistical procedures capable of identifying possible standards of variation and correlation among measurements has great importance. The possibility of including random effects and modeling of covariance structures makes the methodology of mixed linear models one of the most appropriate tools to perform this type of analysis. However, despite of all theoretical and computational development, the use of such methodology in more complex designs involving longitudinal data and additional treatments, such as those used in forage crops, still needs to be studied. The present work covered the use of the Hasse diagram and the top-down strategy in the building of mixed linear models for the study of successive cuts from an experiment involving boron fertilization in alfalfa (Medicago sativa L.) carried out in the field area of Embrapa Southeast Livestock. First, we considered a qualitative approach for all study factors and we chose the Hasse diagram building due to the model complexity. The inclusion of random effects and selection of covariance structures for residues were performed based on the likelihood ratio test, calculated based on parameters estimated through the restricted maximum likelihood method, the Akaike\'s Information Criterion (AIC), the Akaike\'s information criterion corrected (AICc) and the Bayesian Information Criterion (BIC). The fixed effects were analyzed through the Wald-F test and we performed a regression study due to the significant effects of the variation sources associated with the longitudinal factor. The Hasse diagram building was essential for understanding and symbolic displaying regarding the relation among all factors present in the study, thus allowing variation sources and their degrees of freedom to be decomposed, assuring that all tests were correctly performed. The inclusion of random effect associated with the sample unit was essential for modeling the behavior of each unity. Furthermore, the structure of variance components with heterogeneity, added to the residues, was capable of modeling efficiently the heterogeneity of variances present in the different cuts of alfalfa plants. The fit was checked by residual diagnostic plots. The regression study allowed us to evaluate the productivity of shoot dry matter (kg ha-1) related to successive cuts of alfalfa plants, involving the comparison of fertilization with different boron sources and doses. We observed the best productivity in the combination of the source ulexite with the doses 3, 6 and 9 kg ha-1 boron.

推薦系統的出現是為了解決訊息過載的問題，其需求隨著科技的進步、網路的普及而增加，相關技術也越發多樣且成熟。廣泛應用於各領域的統計模型也在技術的行列中。 推薦系統的運作仰賴使用者偏好訊息，而使用者對項目所組成的偏好空間往往十分巨大且不平衡，統計上需要相對複雜的隨機效應模型或混合效應模型來描繪這樣的變數結構，且通常需要計算效率相對低的反覆疊代過程來估計模型參數。因此Perry（2014）、Gao & Owen（2016）先後提出以動差法處理階層線性模型與兩因子隨機效應模型，是一種犧牲統計效率換取計算效率的做法。 本研究便是採用統計模型中的隨機效應模型法，分別以最大概似法和動差法估計參數，與同為協同過濾技術觀點的矩陣分解法進行分析比較。透過預測準確度和運算效率兩個層面，來評估各演算法在MoiveLens這筆資料上的推薦表現。 根據試驗結果歸納出隨機效應模型法無論以什麼樣的參數估計方式，在預測準確度的表現上都不如矩陣分解法來得好；但以動差法估計參數在穩定度上與矩陣分解法的表現差不多，且在運算效率上好很多。 / The recommender system (RS) appeared to solve the problem of information overload. The demand of the RS has increased with the advancement of technology and the popularity of the Internet, and related techniques have become more diverse and mature. The statistical models widely used in various fields are also in the list of techniques. The operation of the RS relies on user preference information, and the space of users’ preference to items is often large and unbalanced. Statistically, relatively complex random effects models or mixed effects models are needed to describe such variable structures, and often require a large number of iterations to estimate model parameters. Perry (2014), Gao & Owen (2016) proposed using the moment-based method to deal with hierarchical linear models and two-factor random effects models, respectively, expressing an idea of sacrificing statistical efficiency in exchange for computational efficiency. In this study, we analyze and compare the random effects model, using the maximum likelihood method and the moment-based method to estimate the parameters with the matrix factorization. Through the prediction accuracy and computational efficiency to evaluate the performance of each algorithm on the MoiveLens data. According to the experiment results, the random effects model is not as good as the matrix factorization in terms of the prediction accuracy no matter what kind of parameter estimation method is used; however, the performance of the moment-based parameter estimation is consistent with the matrix factorization in terms of the prediction stability, and much better in terms of the efficiency.

MCom (Economics) / Department of Economics / The need to realise steady economic growth, measured in this research by Gross Domestic Product (GDP), has ignited a plethora of studies about the contributors of economic growth and their optimal levels. Government expenditure is one contributor to economic growth. From a theoretical standpoint, optimal government size is depicted by an inverted U-curve known as the Armey curve which is hypothesised between the relationship of government size and economic growth. Empirical literature provides evidence that optimal government size is between 20-30 percent a share of GDP. However, little has been done to investigate the optimal level of isolated components of government spending that maximizes economic growth. One component of government spending that has gained limelight over the past decade is that of social assistance. Defined as public expenditure spent as cash and food transfers to the poor, this research uses social assistance expenditure to assess its optimal level that maximizes growth. This is important because some policymakers are concerned about the ballooning budgets directed at social assistance, and argue that the scarce resources need to be transferred to other social services sectors such as health and education. Basing on the panel-data accessed from the World Bank, this research uses the quadratic equation model to determine the optimal level of social assistance for African and Organisation for Economic Co-Operation and Development (OECD) countries covering the period 2009-15. The finding is that the optimal level of social assistance spending for African and OECD countries is 3.2 percent of GDP and 29.4 percent of GDP respectively. The study also finds that both African and OECD countries operate below the optimal levels and it is suggested that they need to increase social assistance spending in order to realize positive contributions to economic growth. / NRF

Thesis (M. Com. (Economics)) -- University of Limpopo, 2021 / The main aim of the study is to analyze determinants of sovereign credit ratings (SCRs) for Southern African Development Community (SADC) countries, namely Angola, Botswana, Mozambique, South Africa and Zambia. The analysis is based on the SCRs given by Standard and Poor’s (S&P). The selected explanatory variables are gross domestic product (GDP) per capita, inflation, external debt, foreign direct investment (FDI) inflows and control of corruption for the period 1990-2016, based on annual data. The panel root test results, namely IPS, LLC, ADF Fisher and PP Fisher, show that GDP per capita, external debt and FDI are stationary at 5% level of significance. The Hausman test results indicates that the identified explanatory variable explains 80% of SCRs. The model observed a positive relationship between SCR, inflation and control of corruption. It also observed a negative correlation between SCR, GDP per capita, external debt and FDI. The Pedroni residual cointegration test results indicate that there is no long-run relationship among variables and no autocorrelation as shown by serial correlation LM test results. The study recommends that the selected member states of SADC develop strategic plans for reducing budget deficits. This will help countries to manage their debts, especially foreign currency denoted debt and to attract foreign investment. Keywords: Sovereign credit ratings, fixed effects model, random effects, Hausman test.

In this thesis, we set out to model the market risk exposure for 251 stocks in the S&P 500 index, during a ten-year period between 2011-04-30 and 2021-03-31. The study brings to light a model not often mentioned in the scientific literature focused on market risk estimation, the linear mixed model. The linear mixed model makes it possible to model a time-varying market risk, as well as adding structure to the idiosyncratic risk, which is often assumed to be a stationary process. The results show that the mixed model is able to produce more accurate estimates for the market risk, compared to the baseline, which is here defined as a CAPM model. The success of the mixed model, which we in the study will refer to as the ADAPT model (adaptive APT), most certainly lies in its ability to create a hierarchical regression model. This makes it possible to not just view the set of observations as a single population, but let us group the observations into different clusters and in such a way makes it possible to construct a time-varying exposure. In the last part of the thesis, we highlight possible improvements for future works, which could make the estimation even more accurate and also more efficient.

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