Using multi-group confirmatory factor analysis (MCFA) and multiple-indicator-multiple-cause (MIMIC) to investigate group difference in the context of the second-order factor model with either the unparceled or parceled data had never been thoroughly examined. The present study investigated (1) the difference of MCFA and MIMIC in terms of Type I error rate and power when testing the mean difference of the higher-order latent factor (delta kappa) in a second-order confirmatory factor analysis (CFA) model; and (2) the impact of data parceling on the test of (delta kappa) between groups by using the two approaches. The methods were introduced, including the design of the models, the design of Monte Carlo simulation, the calculation of empirical Type I Error and empirical power, the two parceling strategies, and the adjustment of the random error variance. The results suggested that MCFA should be favored when the compared groups were when the different group sizes were paired with the different generalized variances, and MIMIC should be favored when the groups were balanced (i.e., have equal group sizes) in social science and education disciplines. This study also provided the evidence that parceling could improve the power for both MCFA and MIMIC when the factor loadings were low without bringing bias into the solution when the first-order factors were collapsed. However, parceling strategies might not be necessary when the factor loadings were high. The results also indicated that the two approaches were equally favored when domain representative parceling strategy was applied.

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In this thesis, I present my study on the impact of multi-group network structure on the performance of consensus building strategies, and the preliminary mathematical formulation of the problem on improving the performance of the National Airspace system (NAS) through long-term investment. The first part of the thesis is concerned with a structural approach to the consensus building problem in multi-group distributed sensor networks (DSNs) that can be represented by bipartite graph. Direct inference of the convergence behavior of consensus strategies from multi-group DSN structure is one of the contributions of this thesis. The insights gained from the analysis facilitate the design and development of DSNs that meet specific performance criteria. The other part of the thesis is concerned with long-term planning and development of the NAS at a network level, by formulating the planning problem as a resource allocation problem for a flow network. The network-level model viewpoint on NAS planning and development will give insight to the structure of future NAS and will allow evaluation of various paradigms for the planning problem.

A generalization of multigroup energy condensation theory has been developed. The new method generates a solution within the few-group framework which exhibits the energy spectrum characteristic of a many-group transport solution, without the computational time usually associated with such solutions. This is accomplished by expanding the energy dependence of the angular flux in a set of general orthogonal functions. The expansion leads to a set of equations for the angular flux moments in the few-group framework. The 0th moment generates the standard few-group equation while the higher moment equations generate the detailed spectral resolution within the few-group structure. It is shown that by carefully choosing the orthogonal function set (e.g., Legendre polynomials), the higher moment equations are only coupled to the 0th-order equation and not to each other. The decoupling makes the new method highly competitive with the standard few-group method since the computation time associated with determining the higher moments become negligible as a result of the decoupling. The method is verified in several 1-D benchmark problems typical of BWR configurations with mild to high heterogeneity.

Intelligence testing has had a relatively long and controversial history, beginning with what is generally considered the first formal measure of intelligence, the Binet-Simon Scales (1916). Questions regarding possible cultural bias in these measures arose virtually simultaneously (e.g. Burt, 1921; Stern, 1914). Over the course of the twentieth and early twenty-first centuries, an abundance of intelligence measures have been developed, with many of them having several revisions, but the issue of test bias remains an important one, both in the professional literature and in the popular press (Reynolds & Lowe, 2009). A current intelligence measure in use, the Differential Ability Scales, Second Edition (DAS-II, Elliott, 2007), is a test with growing popularity for assessment of children and youth, not only for its ease of use, but also for its appeal to young children and its nonverbal composite (among other things). Consequently, it is essential that there be empirical evidence supporting the use of the DAS-II as an appropriate measure of cognitive abilities for children of varying backgrounds. The test publishers conducted extensive research with a representative sample during test development in an effort to ensure that the measure met adequate reliability and validity criteria; however, the issue of test bias, particularly regarding cultural or racial/ethnic groups, was not explicitly addressed. This issue was raised and examined with the original DAS by Keith, Quirk, Schartzer, and Elliott (1999), but with the significant changes made from the first edition to the second, there is no guaranty that the evidence from the earlier would necessarily apply to the latter. The current study investigated whether the DAS-II demonstrates systematic construct bias toward children and youth of any of four ethnic groups: Black, Hispanic, Asian, and White. Multi-group confirmatory factor analysis using data from the DAS-II standardization sample was used to assess whether criteria for increasingly strict levels of invariance were met across groups. Outcomes of this research contribute to an existing body of literature on test bias, as well as provide evidence regarding cross-group construct validity in the DAS-II. Ultimately the results of this study can be used to evaluate the appropriateness of the DAS-II for clinical use with certain ethnic groups and will help to emphasize further the importance of exploring these issues with all standardized tests. / text

This thesis which consists of four papers is concerned with estimation methods in factor analysis and structural equation models. New estimation methods are proposed and investigated. In paper I an approximation of the penalized maximum likelihood (ML) is introduced to fit an exploratory factor analysis model. Approximated penalized ML continuously and efficiently shrinks the factor loadings towards zero. It naturally factorizes a covariance matrix or a correlation matrix. It is also applicable to an orthogonal or an oblique structure. Paper II, a simulation study, investigates the properties of approximated penalized ML with an orthogonal factor model. Different combinations of penalty terms and tuning parameter selection methods are examined. Differences in factorizing a covariance matrix and factorizing a correlation matrix are also explored. It is shown that the approximated penalized ML frequently improves the traditional estimation-rotation procedure. In Paper III we focus on pseudo ML for multi-group data. Data from different groups are pooled and normal theory is used to fit the model. It is shown that pseudo ML produces consistent estimators of factor loadings and that it is numerically easier than multi-group ML. In addition, normal theory is not applicable to estimate standard errors. A sandwich-type estimator of standard errors is derived. Paper IV examines properties of the recently proposed polychoric instrumental variable (PIV) estimators for ordinal data through a simulation study. PIV is compared with conventional estimation methods (unweighted least squares and diagonally weighted least squares). PIV produces accurate estimates of factor loadings and factor covariances in the correctly specified confirmatory factor analysis model and accurate estimates of loadings and coefficient matrices in the correctly specified structure equation model. If the model is misspecified, robustness of PIV depends on model complexity, underlying distribution, and instrumental variables.

This research focuses on modelling reflectors in typical material testing reactors (MTRs). Reflectors present some challenges to the usual approach to full-core calculational models. Diffusion theory is standardly used in full-core calculations and is known to be inaccurate in regions where the flux is anisotropic, for example within the reflectors. Thus, special consideration should be given to reflector models. In this research, normalised generalised equivalence theory is used to homogenise cross-sections and calculate equivalent nodal parameters and albedo boundary conditions for the reflector surrounding a typical MTR reactor. Various studies have shown that equivalence theory can be used to accurately generate equivalent nodal parameters for the core and reflector regions of large reactors, such as pressurised and boiling water reactors, in one dimension and for two neutron energy groups. This has not been tested for smaller reactors where leakage, environment sensitivity and multi-group spectrum dependency are much larger. The SAFARI-1 MTR reactor is modelled in this work. A thirty day operational cycle is simulated for this reactor, using the nodal diffusion code MGRAC. NGET reflector equivalent nodal parameters are calculated using the codes NEWT and EQUIVA. The impact of different reflector models are evaluated, based on their effect on the core power, flux distribution, reactivity and neutron leakage over the duration of the operational cycle. It is found that homogenisation introduces some environment dependencies in the reflector parameters, particularly in the corners of the reactor core. In full-core calculations, the reflector parameters show some sensitivity to the in-core reflector structures, but not the fuel composition. A practical reflector model for SAFARI-1 is proposed, which proves that NGET equivalence theory can be used for multi-group reflector modelling in a small MTR reactor. This approach to reflector modelling simplifies the core model, increases the accuracy of a diffusion calculation, and increases the efficiency (shorter calculational time and better convergence behaviour) of computer simulations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

This research focuses on modelling reflectors in typical material testing reactors (MTRs). Reflectors present some challenges to the usual approach to full-core calculational models. Diffusion theory is standardly used in full-core calculations and is known to be inaccurate in regions where the flux is anisotropic, for example within the reflectors. Thus, special consideration should be given to reflector models. In this research, normalised generalised equivalence theory is used to homogenise cross-sections and calculate equivalent nodal parameters and albedo boundary conditions for the reflector surrounding a typical MTR reactor. Various studies have shown that equivalence theory can be used to accurately generate equivalent nodal parameters for the core and reflector regions of large reactors, such as pressurised and boiling water reactors, in one dimension and for two neutron energy groups. This has not been tested for smaller reactors where leakage, environment sensitivity and multi-group spectrum dependency are much larger. The SAFARI-1 MTR reactor is modelled in this work. A thirty day operational cycle is simulated for this reactor, using the nodal diffusion code MGRAC. NGET reflector equivalent nodal parameters are calculated using the codes NEWT and EQUIVA. The impact of different reflector models are evaluated, based on their effect on the core power, flux distribution, reactivity and neutron leakage over the duration of the operational cycle. It is found that homogenisation introduces some environment dependencies in the reflector parameters, particularly in the corners of the reactor core. In full-core calculations, the reflector parameters show some sensitivity to the in-core reflector structures, but not the fuel composition. A practical reflector model for SAFARI-1 is proposed, which proves that NGET equivalence theory can be used for multi-group reflector modelling in a small MTR reactor. This approach to reflector modelling simplifies the core model, increases the accuracy of a diffusion calculation, and increases the efficiency (shorter calculational time and better convergence behaviour) of computer simulations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

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