The overall theme of this thesis focuses on methods for functional regression and nonlinear mixed-effects models with applications to PET data. The first part considers the problem of variable selection in regression models with functional responses and scalar predictors. We pose the function-on-scalar model as a multivariate regression problem and use group-MCP for variable selection. We account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance. Our method is illustrated by the application to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control. The second part introduces a functional data analytic approach for the estimation of the IRF, which is necessary for describing the binding behavior of the radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which shrinkage and roughness penalties are incorporated to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data. The third part discusses a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a compartment model. The traditional NLS estimators of the population parameters are applied in a two-stage analysis, which brings instability issue and neglects the variation in rate parameters. In contrast, we propose to estimate the rate parameters by fitting nonlinear mixed-effects (NLME) models, in which all the subjects are modeled simultaneously by allowing rate parameters to have random effects and population parameters can be estimated directly from the joint model. Simulations are conducted to compare the power of detecting group effect in both rate parameters and summarized measures of tests based on both NLS and NLME models. We apply our NLME approach to clinical PET data to illustrate the model building procedure.

Magister Philosophiae - MPhil / Decentralisation is the transfer of power, responsibilities, capacities and resources from the centre to the sub-units of the government. The main objective is to foster the capacity of local government to deliver services to the local communities in an effective manner.1 In a multilevel system of government, various institutions are established at different levels of government to deliver goods and services to the people. In delivering goods and services, these institutions usually combine efforts within the same and different levels of government. As a mechanism for improved service delivery, decentralisation has become increasingly important in the recent past together with the enhanced citizen participation in decision making process in the matters that affect the people. However, for decentralisation to be effective in achieving its intended objectives, it should be supported by intergovernmental relations and cooperative governance. Intergovernmental relations exist between and across various institutions and actors.2 They are relationships which develop or exist between governmental units of all types and levels in a multilevel system of government.3 These relations are significant in a multilevel system of government because it is impossible to distribute powers and functions among governments within a nation state into watertight compartments.4 The IGRs help in dispute resolution that may emerge from the overlap of powers and functions across tiers of government consequently hampering the smooth functioning of the government system.

Climate change is experienced most through the medium of water. The ability of water institutions and the factors that enable or hinder them to purposefully adapt to the new and additional challenges brought by climate change require better understanding. Factors that influence their perception of climate change impacts and initiatives being taken for adaptation are shaped by various enabling factors and barriers through the interaction with both governmental and non-governmental institutions across administrative scales. Better understanding of these adaptation enablers and barriers is essential for devising adaptation strategies. This research aims to identify and expound the characteristics that enable or hinder institutions to adapt for water management, and hence, it evaluates the involvement of key governmental and non-governmental institutions in India and the inter-institutional networks between them. It surveyed webpages and online documents of sixty Union Government institutions and interviewed representatives from twenty-six governmental, non-governmental, research and academic institutions operating at the national level and another twenty-six institutions operating within the State of Himachal Pradesh in India to assess the characteristics that enable or hinder adaptation. While the online projection of institutional involvement and interaction among key Union Government institutions on climate change and water indicate a more centralized network pointing to Planning Commission and Ministry of Environment and Forest, the interview responses indicated a more distributed network with both Ministries of Water Resources and Environment and Forest recognized as key institutions thereby indicating a potential variation in perception of who is in-charge. Moreover, online documents show institutions that are involved in water have less mention of climate change compared to Union Government ministries involved in less climate-sensitive sectors indicating that impacts of climate change on water are potentially ignored. While it is evident that research and consulting institutions engaging with both national and state level institutions play a key role in enabling adaptation, various barriers pertaining to data and information accessibility, inadequacy of resources and implementation gaps exist particularly due to inter-institutional network fragmentations. Although barriers identified in this study bear resemblance to barriers identified by other researchers in other contexts, this research shows similar barriers can emerge from different underlying causes and are highly interconnected; thereby indicating the need for addressing adaptation barriers collectively as a wider governance issue. Since many of the adaptation barriers emerge from wider governance challenges and are related to larger developmental issues, the findings have important policy implications. Among the various issues that the government needs to address is improving the inter-institutional networks between water institutions so that information dissemination, sharing of learning experiences and data accessibility is improved and prescriptive legislations are seen to be inadequate in this regard. Restructuring the way officials in government water institutions are recruited and deployed is suggested as a potential solution for improving the inter-institutional networks. The research elucidates that inter-institutional networks and transboundary institutions are two pillars that supports adaptation and also bridges the gap between adaptive capacity and adaptation manifestation that enable water institutions to cross the chasm of adaptation barriers. Thus the thesis presents an important analysis of key characteristics that enable or hinder water management institutions to adapt to climate change which have been so far under acknowledged by other studies through the analysis of the state of climate change adaptation in India. Therefore, this study provides valuable insights for developing countries, particularly, facing similar challenges of adapting water management for climate change.

In the last three decades recursive residuals and estimation have received extensive attention as important and powerful tools in providing a diagnostic test of the structural change and functional misspecification in regression models. Recursive residuals and their relationship with recursive estimation of regression parameters have been developed for fixed effect models. Such residuals and estimation have been used to test the constancy of regression models over time and their usage has been suggested for almost all areas of regression model validation. These recursive techniques have not been developed for some of the more recent generalisations of Linear Models such as Linear Mixed Models (LMM) and their important extension to Generalised Linear Mixed Models (GLMM) which provide a suitable framework to analyse a variety of special problems in an unified way. The aim of this thesis is to extend the idea of recursive residuals and estimation to Mixed Models particularly for LMM and GLMM. Recurrence formulae are developed and recursive residuals are defined. / Doctor of Philosophy (PhD)

<p>Det råder delade meningar om hur den Europeiska unionen kommer att utvecklas i framtiden. Skeptiker menar att den kommer utvecklas i riktning mot en federation och undergräva medlemsstaternas suveränitet, medan andra menar att det europeiska samarbetet främst är en frihandelsförening. Syftet med min uppsats är att undersöka hur det inom EU:s institutioner resoneras kring frågor rörande EU:s framtida integration, samt kring frågor rörande demokrati. Det material jag analyserar är ett urval av EU-dokument, där jag med kvalitativ textanalys, utifrån ett teoretiskt ramverk bestående av tre stycken integrationsteorier, försöker förstå hur EU:s institutioner ser på unionens framtida integration samt frågor rörande demokrati. Resultatet av undersökningen gav en mångfacetterad bild av hur det resoneras kring dessa frågor på högsta EU-nivå. Speciellt belysande var hur kommissionen resonerar kring demokrati jämfört med andra EU-institutioner.</p>

Det råder delade meningar om hur den Europeiska unionen kommer att utvecklas i framtiden. Skeptiker menar att den kommer utvecklas i riktning mot en federation och undergräva medlemsstaternas suveränitet, medan andra menar att det europeiska samarbetet främst är en frihandelsförening. Syftet med min uppsats är att undersöka hur det inom EU:s institutioner resoneras kring frågor rörande EU:s framtida integration, samt kring frågor rörande demokrati. Det material jag analyserar är ett urval av EU-dokument, där jag med kvalitativ textanalys, utifrån ett teoretiskt ramverk bestående av tre stycken integrationsteorier, försöker förstå hur EU:s institutioner ser på unionens framtida integration samt frågor rörande demokrati. Resultatet av undersökningen gav en mångfacetterad bild av hur det resoneras kring dessa frågor på högsta EU-nivå. Speciellt belysande var hur kommissionen resonerar kring demokrati jämfört med andra EU-institutioner.

Secure symmetrical multilevel diversity coding (S-SMDC) is a source coding problem, where a total of L - N discrete memoryless sources (S1,...,S_L-N) are to be encoded by a total of L encoders. This thesis considers a natural generalization of SMDC to the secure communication setting with an additional eavesdropper. In a general S-SMDC system, a legitimate receiver and an eavesdropper have access to a subset U and A of the encoder outputs, respectively. Which subsets U and A will materialize are unknown a priori at the encoders. No matter which subsets U and A actually occur, the sources (S1,...,Sk) need to be perfectly reconstructable at the legitimate receiver whenever |U| = N +k, and all sources (S1,...,S_L-N) need to be kept perfectly secure from the eavesdropper as long as |A| <= N. A precise characterization of the entire admissible rate region is established via a connection to the problem of secure coding over a three-layer wiretap network and utilizing some properties of basic polyhedral structure of the admissible rate region. Building on this result, it is then shown that superposition coding remains optimal in terms of achieving the minimum sum rate for the general secure SMDC problem.

Hierarchical models are applicable to modeling data from complex surveys or longitudinal data when a clustered or multistage sample design is employed. The focus of this thesis is to investigate inference for discrete hierarchical models in the presence of missing data. This thesis is divided into two parts: in the first part, methods are developed to analyze the discrete and ordinal response data from hierarchical longitudinal studies. Several approximation methods have been developed to estimate the parameters for the fixed and random effects in the context of generalized linear models. The thesis focuses on two likelihood-based estimation procedures, the pseudo likelihood (PL) method and the adaptive Gaussian quadrature (AGQ) method. The simulation results suggest that AGQ is preferable to PL when the goal is to estimate the variance of the random intercept in a complex hierarchical model. AGQ provides smaller biases for the estimate of the variance of the random intercept. Furthermore, it permits greater flexibility in accommodating user-defined likelihood functions. In the second part, simulated data are used to develop a method for modeling longitudinal binary data when non-response depends on unobserved responses. This simulation study modeled three-level discrete hierarchical data with 30% and 40% missing data using a missing not at random (MNAR) missing-data mechanism. It focused on a monotone missing data-pattern. The imputation methods used in this thesis are: complete case analysis (CCA), last observation carried forward (LOCF), available case missing value (ACMVPM) restriction, complete case missing value (CCMVPM) restriction, neighboring case missing value (NCMVPM) restriction, selection model with predictive mean matching method (SMPM), and Bayesian pattern mixture model. All three restriction methods and the selection model used the predictive mean matching method to impute missing data. Multiple imputation is used to impute the missing values. These m imputed values for each missing data produce m complete datasets. Each dataset is analyzed and the parameters are estimated. The results from the m analyses are then combined using the method of Rubin(1987), and inferences are made from these results. Our results suggest that restriction methods provide results that are superior to those of other methods. The selection model provides smaller biases than the LOCF methods but as the proportion of missing data increases the selection model is not better than LOCF. Among the three restriction methods the ACMVPM method performs best. The proposed method provides an alternative to standard selection and pattern-mixture modeling frameworks when data are not missing at random. This method is applied to data from the third Waterloo Smoking Project, a seven-year smoking prevention study having substantial non-response due to loss-to-follow-up.

The most recent development in the field of Item Response Theory (IRT) has been the evaluation of IRT models as multilevel models, known as Multilevel IRT models (MLIRT). These models offer several statistical and practical advantages over ordinary IRT models. However, models such as 2-PL MLIRT models have not been studied yet. This dissertation consists of two studies, a simulation and a substantiation for an urban school district dataset. The simulation study tested the performance of twoparameter (2-PL) MLIRT models with predictor variables under various conditions that included 3 test lengths (15, 30, and 60 items), 4 sample sizes (200, 500, 1000, and 2000), 2 correlation conditions between the predictor variable and the ability (or attitude) parameter (rpb=.35 and .8), and 4 binomial distributions of the predictor variable (p=0.1, 0.25, 0.4, and 0.5). The bias and Root Mean Square Deviation (RMSD) values of the item parameters indicated that the distribution of the predictor variable and the correlation between the predictor and the ability (or attitude) parameter did not affect the estimates of 2-PL MLIRT models. These models performed well for sample sizes as low as 500 and test lengths as low as 15 which is lower than the required sample size for ordinary IRT models. Even for a sample size of 200, sufficiently accurate estimates were obtained with more than 300 iterations. The second study investigated the characteristics of the items that measured urban teachers’ perceptions of cultural awareness and beliefs about teaching African American children and tested whether these perceptions were influenced by the teachers’ gender, ethnicity, or teaching experience. Teacher beliefs about teaching African American students, culturally responsive management, and cultural awareness factors were influenced by the ethnicity of the teachers. Culturally responsive management, home and community support, and curriculum and instructional strategies factors were influenced by the teaching experience of the teachers. Items that were biased based on ethnicity or teaching experience were identified. None of the items exhibited gender bias. The study identified items that could be used over other items when the need for a shorter instrument or more informative categories arises.

The purpose of the study was to examine multilevel regression models in the context of multilevel structural equation modeling (SEM) in terms of accuracy of parameter estimates, standard errors, and fit indices in normal and nonnormal data under various sample sizes and differing estimators (maximum likelihood, generalized least squares, and weighted least squares). The finding revealed that the regression coefficients were estimated with little to no bias among the study design conditions investigated. However, the number of clusters (group level) appeared to have the greatest impact on bias among the parameter estimate standard errors at both level-1 and level-2. In small sample sizes (i.e., 300 and 500) the standard errors were negatively biased. When the number of clusters was 30 and cluster size was held at 10, the level-1 standard errors were biased downward by approximately 20% for the maximum likelihood and generalized least squares estimators, while the weighted least squares estimator produced level-1 standard errors that were negatively biased by 25%. Regarding the level-2 standard errors, the level-2 standard errors were biased downward by approximately 24% in nonnormal data, especially when the correlation among variables was fixed at .5 and kurtosis was held constant at 7. In this same setting (30 clusters with cluster size fixed at 10), when kurtosis was fixed at 4 and the correlation among variables was held at .7, both the maximum likelihood and generalized least squares estimators resulted in standard errors that were biased downward by approximately 11%. Regarding fit statistics, negative bias was noted among each of the fit indices investigated when the number of clusters ranged from 30 to 50 and cluster size was fixed at 10. The least amount of bias was associated with the maximum likelihood estimator in each of the data normality conditions examined. As sample size increased, bias decreased to near zero when the sample size was equal to or greater than 1,500 with similar results reported across estimation methods. Recommendations for the substantive researcher are presented and areas of future research are presented.