The aim of this study is to record the status of the elementary school principalship in the State of Utah during the 1951-1952 school year. The problem arose from a situation in which the writer, as President of the Utah Elementary School Principal's Association, was continually asked questions pertaining to the status of this group, and because there was a scarcity of current information available upon which to base reliable answers to these requests. This situation led to the formulation of the study herein presented--a survey of conditions as they existed in Utah during the 1951-1952 school year. It should reveal conditions as they were, and serve as a basis for their improvement by the elementary principals of Utah. It should also be helpful to the institutions in the state engaged in training administrators for this position.

The principal component analysis can be carried out two ways. First the R-mode: R = K'K and the second is the Q-mode: Q = K K' where K is a data matrix centered by column or by row. The most commonly used method is the R-mode. It has been suggested that principal components computed from either the R-mode or the Q-mode may have the same interpretation. If this is true, then interpretation of the principal components could be put on a much more intuitive level in many applications. This will occur whenever one type of principal component is more intuitively related to the physical or natural system being studied than the other. The relationship between the principal components of the R-mode and the Q-mode have been investigated with the result that they show a perfect correlation between them. The conclusion that the principal components of the R-mode or the Q-mode have the same interpretation is established. An example is given to illustrate this work. The resulting interpretation is found to be the same as that obtained by Donald L. Phillips (1977) using different methods.

This thesis is concerned with the problem of selection of important variables in Principal Component Analysis (PCA) in such a way that the selected subsets of variables retain, as much as possible, the overall multivariate structure of the complete data. Throughout the thesis, the criteria used in order to meet this requirement are collectively referred to as measures of Multivariate Association (MVA). Most of the currently available selection methods may lead to inappropriate subsets, while Krzanowskis (1987) M(subscript)2-Procrustes criterion successfully identifies structure-bearing variables particularly when groups are present in the data. Our major objective, however, is to utilize the idea of multivariate association to select subsets of the original variables which preserve any (unknown) multivariate structure that may be present in the data.The first part of the thesis is devoted to a study of the choice of the number of components (say, k) to be used in the variable selection process. Various methods that exist in the literature for choosing k are described, and comparative studies on these methods are reviewed. Currently available methods based exclusively on the eigenvalues of the covariance or correlation matrices, and those based on cross-validation are unsatisfactory. Hence, we propose a new technique for choosing k based on the bootstrap methodology. A full comparative study of this new technique and the cross-validatory choice of k proposed by Eastment and Krzanowski (1982) is then carried out using data simulated from Monte Carlo experiment.The remainder of the thesis focuses on variable selection in PCA using measures of MVA. Various existing selection methods are described, and comparative studies on these methods available in the literature are reviewed. New methods for selecting variables, based of measures of MVA are then proposed and compared ++ / among themselves as well as with the M(subscript)2-procrustes criterion. This comparison is based on Monte Carlo simulation, and the behaviour of the selection methods is assessed in terms of the performance of the selected variables.In summary, the Monte Carlo results suggest that the proposed bootstrap technique for choosing k generally performs better than the cross-validatory technique of Eastment and Krzanowski (1982). Similarly, the Monte Carlo comparison of the variable selection methods shows that the proposed methods are comparable with or better than Krzanowskis (1987) M(subscript)2-procrustes criterion. These conclusions are mainly based on data simulated by means of Monte Carlo experiments. However, these techniques for choosing k and the various variable selection techniques are also evaluated on some real data sets. Some comments on alternative approaches and suggestions for possible extensions conclude the thesis.

Much of the recent literature on effective schools has intuitively connected the leadership role of the school principal , and school learning environment, to the achievement of organisational outcomes such as those related to teacher performance. Transformational leadership theory has cast these relations in a new perspective, where advocates have claimed that transformational leaders are more able to manipulate environmental contexts so as to achieve their organisational objectives compared to transactional and laissez-faire leadership styles. This study examines the effects of different types of secondary principals’ leadership behaviours on aspects of a school’s learning environment, and selected teacher outcomes. A synergy was achieved by undertaking two studies drawing upon a multi-method approach. Results are significant for those who exercise leadership authority in schools, and are contrary to the findings suggested by transformational leadership literature. Practitioners will welcome the opportunity to tailor leadership behaviours to achieve specific school learning environment and teacher outcome objectives, while those involved in principal training will recognise the potency of the behavioural aspects of the transformational and transactional paradigms / Doctor of Philosophy (PhD)

When a school community decides to implement innovative curricula, the responsibility for leadership of the associated professional learning processes lies with the principal. The onus is on principals to be leader learners. They adapt their leadership style to the context of the school. They encourage learning as a future-oriented, organisation-wide process. They encourage deep learning, and double-loop learning, and they nurture a culture of collaborative learning. They provide practical support for teacher leadership and teacher learning, and they understand that teachers have differing needs for support during a period of significant curriculum change. The research methodology used for this study involved a multiple case study design. Principals and staff from three Queensland state schools who participated in the trial of innovative curricula provided the data for the three case studies. The data collection at three schools related to the processes of professional learning at each site. Interviews conducted with the participants at each school, and observation of meetings and school documentation, provided the researcher with the data to develop a framework for principals who are interested in creating a professional learning community. Data collected from the schools generally supported the findings of the theorists. However, analysis of the data provided more detailed information than is currently available in the literature to inform the establishment of professional learning processes. Analysis of the data indicated that professional learning can be classified according to four themes: personal learning, leadership-related learning, learning related to innovation, and learning related to processes that support a collaborative culture. The findings from the literature review and the findings from the case studies were used to construct a framework for professional learning for principals who wish to create a learning organisation. The framework provides a foundation for professional learning programs for principals, and could be used by a range of people or groups, including district office personnel, professional associations, and networks of principals and aspiring leaders.

Despite research on the school principalship having evolved over past decades, the prevailing standpoint has largely remained an outsider's perspective upon external behavioural manifestations of principalship. Whilst valuable in their own right, such models of research accord little importance to the effect of thought and intention on behaviour. The purpose of this research was to articulate the notion of a principal's "microcosm" as a means of capturing the dynamics of meaning making in the principalship, when the cognitive world of the principal and the actual work of school leadership interact. The functional context was the expectations of catholic school authorities that schools will engage in processes of continuous self-renewal. Following comprehensive analysis of recent theoretical and research literature, a preliminary framework for the principal's microcosm was generated. A single-investigator, multiple-site case study methodology was utilised to conduct the field research, which was carried out in a provincial city of an Australian state. Three principals were selected as the subjects for in-depth exploration and analysis over a period of 16 months. A range of qualitative research strategies was employed, encompassing formal and informal interactions with the three principals and selected members of their professional communities. On the basis of the field study, a refined framework for the principal's microcosm was developed. Four major conclusions were identified. First, the notion of microcosm offers promise as an explanatory and analytical tool for focussing upon the complexities of change in school settings. Second, metaphor was observed to be integral to microcosm and its usefulness for comprehending leader behaviours was identified. The third conclusion concerned the potential of the construct microcosm for facilitating leader development through assisting individual leaders to reflect upon and to critically examine personal meanings embedded within their own professional practice. Finally, this research makes a contribution to clarifying the nature of catholic education itself.

Linear factor models have attracted considerable interest over recent years especially in the econometrics literature. The intuitively appealing idea to explain a panel of economic variables by a few common factors is one of the reasons for their popularity. From a statistical viewpoint, the need to reduce the cross-section dimension to a much smaller factor space dimension is obvious considering the large data sets available in economics and finance. One of the characteristics of the traditional factor model is that the process is stationary in the time dimension. This appears restrictive, given the fact that over long time periods it is unlikely that e.g. factor loadings remain constant. For example, in the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), typical empirical results show that factor loadings are time-varying, which in the CAPM is caused by time-varying second moments. In this thesis we generalize the tools of factor analysis for the study of stochastic processes whose behavior evolves over time. In particular, we introduce a new class of factor models with loadings that are allowed to be smooth functions of time. To estimate the resulting nonstationary factor model we generalize the properties of the principal components technique to the time-varying framework. We mainly consider separately two classes of Evolutionary Factor Models: Evolutionary Static Factor Models (Chapter 2) and Evolutionary Dynamic Factor Models (Chapter 3). In Chapter 2 we propose a new approximate factor model where the common components are static but nonstationary. The nonstationarity is introduced by the time-varying factor loadings, that are estimated by the eigenvectors of a nonparametrically estimated covariance matrix. Under simultaneous asymptotics (cross-section and time dimension go to infinity simultaneously), we give conditions for consistency of our estimators of the time varying covariance matrix, the loadings and the factors. This paper generalizes to the locally stationary case the results given by Bai (2003) in the stationary framework. A simulation study illustrates the performance of these estimators. The estimators proposed in Chapter 2 are based on a nonparametric estimator of the covariance matrix whose entries are computed with the same moothing parameter. This approach has the advantage of guaranteeing a positive definite estimator but it does not adapt to the different degree of smoothness of the different entries of the covariance matrix. In Chapter 5 we give an additional theoretical result which explains how to construct a positive definite estimate of the covariance matrix while while permitting different smoothing parameters. This estimator is based on the Cholesky decomposition of a pre-estimator of the covariance matrix. In Chapter 3 we introduce the dynamics in our modeling. This model generalizes the dynamic (but stationary) factor model of Forni et al. (2000), as well as the nonstationary (but static) factor model of Chapter 2. In the stationary (dynamic) case, Forni et al. (2000) show that the common components are estimated by the eigenvectors of a consistent estimator of the spectral density matrix, which is a matrix depending only on the frequency. In the evolutionary framework the dynamics of the model is explained by a time-varying spectral density matrix. This operator is a function of time as well as of the frequency. In this chapter we show that the common components of a locally stationary dynamic factor model can be estimated consistently by the eigenvectors of a consistent estimator of the time-varying spectral density matrix. In Chapter 4 we apply our theoretical results to real data and compare the performance of our approach with that based on standard techniques. Chapter 6 concludes and mention the main questions for future research.

NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere.

As demands on school-based administrators continue to increase, so do their responsibilities. Historically the roles and responsibilities of school principals have been clearly delineated in both the legislation governing in-school administrators and also in principals' job descriptions. Principals typically know the expectations of their leadership roles, however, the same cannot be said for all vice-principals (VPs). The pattern that emerges is one that shows the VP as being a jack-of-all-trades. Typically, Saskatchewan rural VPs do not have clearly delineated expectations formally or informally in either legislation or job description. Most often VPs positions are advertised as containing a teaching component and "other duties as assigned." The 2001 Saskatchewan Teachers' Federation (STF) recommendations for improving in-school administration positions have led to little change (p. 3). The conceptual framework focused on the relationship between geographical location (distance), gender and rural Saskatchewan VP perceptions of employee-made and employer-made workplace obligations. VPs are a critical yet often overlooked component of school effectiveness. This emphasized the need for advancing our understanding of VPs' employment relationship and connecting this to the "VP role restructured" blueprint found in the literature. The purpose of this study was to investigate, explore and describe the pattern of the psychological contract among Saskatchewan rural VP's and facilitate better utilization of their skills and leadership. Quantitative and qualitative methods were used in this study. The quantitative data was derived from Rousseau's (2000) Psychological Contract Inventory (PCI) survey questionnaire. This survey was used to determine the extent of employee-made and employer-made workplace obligations from the VP perception. The sample consisted of 42 VPs employed in rural Saskatchewan schools. The qualitative data were generated from participant responses to the open-ended questions attached to the end of the PCI. The responses to the survey and the open-ended questions were analyzed according to the research questions, emerging themes and recurring themes. After the data were analyzed, relationships were revealed between geographical location, gender, and rural VPs' perceptions of workplace obligations. The findings in this study revealed VPs were generally in agreement that relationships between distance, gender and perceptions of workplace obligations were slight at best. It was also revealed that VPs' perceptions of employee-made and employer-made workplace obligations were characterized as well-being items representative of loyalty and security features of a relational psychological contract. VPs indicated a willingness to commit to the organization regardless of distance or gender. Participants almost unanimously expressed their aspirations for the inclusion of professional growth, skill enhancement and increased leadership responsibilities in their assigned, expected and assumed role behaviors. Participant responses were generally consistent with the literature. Derived from participants' qualitative responses, VPs lead busy work lives. As revealed in the findings, VPs indicated they had aspirations for enhanced leadership opportunities. This study generated many implications for practice, policy and research.

A novel and promising method of software development is the interactive style of development, where code is written and incrementally tested simultaneously. Interpreted dynamic languages such as Ruby, Python, and Lua support this interactive development style. However, because they lack semantic analysis as part of a compilation phase, they do not provide type-checking. The programmer is only informed of type errors when they are encountered in the execution of the programfar too late and often at a less-informative location in the code. We introduce a typing system for Ruby, where types will be determined before execution by inferring principal typings. This system overcomes the obstacles that interactive and dynamic program development imposes on type checking; yielding an effective type-checking facility for dynamic programming languages. Our development is embodied as an extension to irb, the Ruby interactive mode, allowing us to evaluate principal typings for interactive development.