We study how to perform effective Bayesian inference in high-dimensional sparse Factor Analysis models with a zero-norm, sparsity-inducing prior on the model parameters. Such priors represent a methodological ideal, but Bayesian inference in such models is usually regarded as impractical. We test this view. After empirically characterising the properties of existing algorithmic approaches, we use techniques from statistical mechanics to derive a theory of optimal learning in the restricted setting of sparse PCA with a single factor. Finally, we describe a novel `Dense Message Passing' algorithm (DMP) which achieves near-optimal performance on synthetic data generated from this model.DMP exploits properties of high-dimensional problems to operate successfully on a densely connected graphical model. Similar algorithms have been developed in the statistical physics community and previously applied to inference problems in coding and sparse classification. We demonstrate that DMP out-performs both a newly proposed variational hybrid algorithm and two other recently published algorithms (SPCA and emPCA) on synthetic data while it explains at least the same amount of variance, for a given level of sparsity, in two gene expression datasets used in previous studies of sparse PCA.A significant potential advantage of DMP is that it provides an estimate of the marginal likelihood which can be used for hyperparameter optimisation. We show that, for the single factor case, this estimate exhibits good qualitative agreement both with theoretical predictions and with the hyperparameter posterior inferred by a collapsed Gibbs sampler. Preliminary work on an extension to inference of multiple factors indicates its potential for selecting an optimal model from amongst candidates which differ both in numbers of factors and their levels of sparsity.

The diploma thesis deals with multivariate statistical methods and their environmental applications. The theoretical part is devoted to selected methods of linear regression analysis, method of principal components and the model of classical and robust factor analysis is also described. In the practical part of thesis, the main emission sources of PM1 aerosols in summer and winter period in Brno and Šlapanice are determined by using the classical factor analysis. The main aerosol emission sources in summer and winter in Šlapanice are also identified by using the robust factor analysis. Furthermore, the prediction of concentrations of PM1 aerosols in summer and winter period in Brno and Šlapanice is performed by using the linear regression model.

This study aimed to observe measurement invariance between community college students and university students in response to the Community of Inquiry (CoI) Survey instrument. Most studies of the CoI survey instruments have recorded and validated the instruments considering undergraduate or graduate students. This study sought to validate and prove the survey tool as a reliable instrument for the community college population. The study employed SEM and meta-analytic procedures to observe measurement invariance between a Monte Carlo generated general university sample population and the community college survey population. The findings are discussed, as well as the implications for CoI studies in the community college.

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Master of Science / Department of Statistics / Weixin Yao / Mixtures of factor analyzers have been popularly used to cluster the high dimensional data. However, the traditional estimation method is based on the normality assumptions of random terms and thus is sensitive to outliers. In this article, we introduce a robust estimation procedure of mixtures of factor analyzers using the trimmed likelihood estimator (TLE). We use a simulation study and a real data application to demonstrate the robustness of the trimmed estimation procedure and compare it with the traditional normality based maximum likelihood estimate.

This study focuses on the development of a validated and confirmed employee engagement measuring model for use by managers and academia. Data was collected from an array of South African managers by employing a structured 5-point Likert scale questionnaire. A total of 260 usable questionnaires could be analysed, signifying a high response rate of 80%. The Statistical Package for Social Sciences software (Version 18, Version 22.0 and AMOS for Windows) was used as the quantitative analytical software. The following statistical techniques were employed to analyse the data, namely the Kaiser-Meyer-Olkin measure of sampling adequacy, Bartlett‟s test of sphericity, Cronbach Alpha reliability coefficients, Exploratory factor analysis, Confirmatory factor analysis and the Pearson correlation coefficient. The development of the Measure Employee Engagement model wielded theoretical and empirical research. The format was structured into four logical stages, hence the presentation of the study in the approved article format. The study covers the following four steps (as per articles): Article one departed by performing a literature study of employee engagement constructs and its measuring criteria. It examined the application of a myriad of models in various application settings to identify the relevant constructs and measuring criteria. From these constructs and criteria, a draft questionnaire was constructed to collect the data on 11 employee engagement constructs. Validation of measuring criteria was performed to ensure that the criteria accurately measure the specific employee engagement construct. The data was also tested for acceptable reliability levels. The second article departs on the validation of the constructs and its measuring criteria, this time as a unified model and not, as performed in Article 1, the construct validation individually. The objective of this article was to simplify the complex model without deterioration of the measuring contribution thereof. This was achieved by employing factor analysis, and after four rounds of eliminating low-loading and dual-loading criteria, the questionnaire was reduced by 25 measuring criteria and seven factors were extracted explaining a favourable 69.75% of the variance. The simplified model was scrutinised to ascertain statistical validity thereof, an objective achieved with flying colours. The inter-correlations between the seven factors were satisfactory, underpinning the validity of the model. The third article focuses on confirming the employee engagement constructs statistically by means of Confirmatory Factor Analysis as well as to determine the goodness of the model fit. The results confirmed that all seven constructs were significant (p<0.05) and important according to the standardised regression weights. Surprisingly, the most important respondent construct Behavioural engagement had the lowest regression weight, while the lower rated Career growth opportunities showed a much higher regression weight – signifying a higher importance and influence on employee engagement. Regarding goodness of model fit, the CFI, RMSEA and Hoelter‟s indices‟ were used. These indices showed that the model as stated above to measure employee engagement is a good fit and that it can be operationalised to be employed in managerial application settings. Article four operationalised the model validated in Articles 2 and 3. The article thus reports on the actual measurement of the different employee engagement constructs as perceived by the respondents. The results showed that the respondents regarded all seven the constructs as important, with Behavioural employment being regarded as the most important one. Career growth opportunities, surprisingly, was rated the least important construct of employee engagement. Correlational analysis indicated that no significant correlation coefficients exist between the demographic variables and the constructs of employee engagement. The study consisted of both a literature study as well as an empirical study. The university libraries of the North-West University and Management College of South Africa‟s Business School were used to source reference materials with the aid of a specialised research librarian at the North-West University to assist in the location of the most appropriate sources. Apart from the conclusions based on the results obtained in model development, generalised conclusions include the development of a successful model development methodology and guidance in the use of a number of the statistical techniques. This could greatly assist future researchers in the design of their studies, even outside the discipline of employee engagement. / PhD (Business Administration), North-West University, Potchefstroom Campus, 2015

This study focuses on the development of a validated and confirmed employee engagement measuring model for use by managers and academia. Data was collected from an array of South African managers by employing a structured 5-point Likert scale questionnaire. A total of 260 usable questionnaires could be analysed, signifying a high response rate of 80%. The Statistical Package for Social Sciences software (Version 18, Version 22.0 and AMOS for Windows) was used as the quantitative analytical software. The following statistical techniques were employed to analyse the data, namely the Kaiser-Meyer-Olkin measure of sampling adequacy, Bartlett‟s test of sphericity, Cronbach Alpha reliability coefficients, Exploratory factor analysis, Confirmatory factor analysis and the Pearson correlation coefficient. The development of the Measure Employee Engagement model wielded theoretical and empirical research. The format was structured into four logical stages, hence the presentation of the study in the approved article format. The study covers the following four steps (as per articles): Article one departed by performing a literature study of employee engagement constructs and its measuring criteria. It examined the application of a myriad of models in various application settings to identify the relevant constructs and measuring criteria. From these constructs and criteria, a draft questionnaire was constructed to collect the data on 11 employee engagement constructs. Validation of measuring criteria was performed to ensure that the criteria accurately measure the specific employee engagement construct. The data was also tested for acceptable reliability levels. The second article departs on the validation of the constructs and its measuring criteria, this time as a unified model and not, as performed in Article 1, the construct validation individually. The objective of this article was to simplify the complex model without deterioration of the measuring contribution thereof. This was achieved by employing factor analysis, and after four rounds of eliminating low-loading and dual-loading criteria, the questionnaire was reduced by 25 measuring criteria and seven factors were extracted explaining a favourable 69.75% of the variance. The simplified model was scrutinised to ascertain statistical validity thereof, an objective achieved with flying colours. The inter-correlations between the seven factors were satisfactory, underpinning the validity of the model. The third article focuses on confirming the employee engagement constructs statistically by means of Confirmatory Factor Analysis as well as to determine the goodness of the model fit. The results confirmed that all seven constructs were significant (p<0.05) and important according to the standardised regression weights. Surprisingly, the most important respondent construct Behavioural engagement had the lowest regression weight, while the lower rated Career growth opportunities showed a much higher regression weight – signifying a higher importance and influence on employee engagement. Regarding goodness of model fit, the CFI, RMSEA and Hoelter‟s indices‟ were used. These indices showed that the model as stated above to measure employee engagement is a good fit and that it can be operationalised to be employed in managerial application settings. Article four operationalised the model validated in Articles 2 and 3. The article thus reports on the actual measurement of the different employee engagement constructs as perceived by the respondents. The results showed that the respondents regarded all seven the constructs as important, with Behavioural employment being regarded as the most important one. Career growth opportunities, surprisingly, was rated the least important construct of employee engagement. Correlational analysis indicated that no significant correlation coefficients exist between the demographic variables and the constructs of employee engagement. The study consisted of both a literature study as well as an empirical study. The university libraries of the North-West University and Management College of South Africa‟s Business School were used to source reference materials with the aid of a specialised research librarian at the North-West University to assist in the location of the most appropriate sources. Apart from the conclusions based on the results obtained in model development, generalised conclusions include the development of a successful model development methodology and guidance in the use of a number of the statistical techniques. This could greatly assist future researchers in the design of their studies, even outside the discipline of employee engagement. / PhD (Business Administration), North-West University, Potchefstroom Campus, 2015

<p>The accumulation of high-throughput data from vast sources has drawn a lot attentions to develop methods for extracting meaningful information out of the massive data. More interesting questions arise from how to combine the disparate information, which goes beyond modeling sparsity and dimension reduction. This dissertation focuses on the innovations in the area of heterogeneous data integration.</p><p>Chapter 1 contextualizes this dissertation by introducing different aspects of meta-analysis and model frameworks for high-dimensional genomic data.</p><p>Chapter 2 introduces a novel technique, joint Bayesian sparse factor analysis model, to vertically integrate multi-dimensional genomic data from different platforms. </p><p>Chapter 3 extends the above model to a nonparametric Bayes formula. It directly infers number of factors from a model-based approach.</p><p>On the other hand, chapter 4 deals with horizontal integration of diverse gene expression data; the model infers pathway activities across various experimental conditions. </p><p>All the methods mentioned above are demonstrated in both simulation studies and real data applications in chapters 2-4.</p><p>Finally, chapter 5 summarizes the dissertation and discusses future directions.</p> / Dissertation