Item Response Theory (IRT) Models, like the one parameter, two parameters, or normal Ogive, have been discussed for many years. These models represent a rich area of investigation due to their complexity as well as the large amount of data collected in relationship to model parameter estimation. Here we propose a new way of looking at IRT models using I-projections and duality. We use convex optimization methods to derive these models. The Kullback-Leibler divergence is used as a metric and specific constraints are proposed for the various models. With this approach, the dual problem is shown to be much easier to solve than the primal problem. In particular when there are many constraints, we propose the application of a projection algorithm for solving these types of problems. We also consider re-framing the problem and utilizing a decomposition algorithm to solve for parameters as well. Both of these methods will be compared to the Rasch and 2-Parameter Logistic models using established computer software where estimation of model parameters are done under Maximum Likelihood Estimation framework. We will also compare the appropriateness of these techniques on multidimensional item response data sets and propose new models with the use of I-projections.

The focus of this project is on the employment of reader response theory, methodology and strategy in the development of poetry units for grades nine through twelve for university-bound students. The purpose of the project is to introduce teachers to various reader-response theories, demonstrate how a curriculum may be designed using the transactional reader-response methodology, and provide units of study which are founded on the transactional theory and methodology, and also support the expectations for students established in the various Ministry documents. / Thesis / Master of Arts in Teaching (MAT)

The presented thesis is devoted to the field of organic light emitting diodes (OLEDs). Time-dependent Kohn-Sham density functional theory (TDDFT) is applied in order to eludicate optical properties such as fluorescence and phosphorescence for some of the most important materials. The accuracy of TDDFT is evaluated with respect to the calculated absorption and emission spectra for commonly used light emitting polymers. A continuation of this work is devoted to Polyfluorene as this polymer has proven to be very promising. In this study the chain length dependence of its singlet and triplet excited states is analyzed as well as the excited state structures. Understanding the phosphorescence mechanism of tris(2-phenylpyridine)Iridium is of importance in order to interpret the high efficiency of OLEDs containing these specimens. The mechanism is analyzed by calculating the electric transition dipole moments by means of TDDFT using quadratic response functions. As not only the optical properties are essential for effective devices, electron transfer properties are addressed. The electron transfer capability of the sulfur and nitrogen analogues of Oxadiazole is evaluated through their internal reorganization energy. / <p>QC 20101109</p>

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The purpose of this research was to investigate the relation between measurement bias at the item level (differential item functioning, dif) and predictive bias at the test score level. Dif was defined as a difference in the probability of getting a test item correct for examinees with the same ability but from different subgroups. Predictive bias was defined as a difference in subgroup regression intercepts and/or slopes in predicting a criterion. Data were simulated by computer. Two hypothetical subgroups (a reference group and a focal group) were used. The predictor was a composite score on a dimensionally complex test with 60 items. Sample size (35, 70, and 105 per group), validity coefficient (.3 or .5), and the mean difference on the predictor (0, .33, .66, and 1 standard deviation, sd) and the criterion (0 and .35 sd) were manipulated. The percentage of items showing dif (0%, 15%, and 30%) and the effect size of dif (small = .3, medium = .6, and large = .9) were also manipulated. Each of the 432 conditions in the 3 x 2 x 4 x 2 x 3 x 3 design was replicated 500 times. For each replication, a predictive bias analysis was conducted, and the detection of predictive bias against each subgroup was the dependent variable. The percentage of dif and the effect size of dif were hypothesized to influence the detection of predictive bias; hypotheses were also advanced about the influence of sample size and mean subgroup differences on the predictor and criterion. Results indicated that dif was not related to the probability of detecting predictive bias against any subgroup. Results were inconsistent with the notion that measurement bias and predictive bias are mutually supportive, i.e., the presence (or absence) of one type of bias is evidence in support of the presence (or absence) of the other type of bias. Sample size and mean differences on the predictor/criterion had direct and indirect effects on the probability of detecting predictive bias against both reference and focal groups. Implications for future research are discussed.

Cooperative interactions permeate through nature, bringing about emergent behavior and complexity. Using a simple cooperative model, I illustrate the mean field dynamics that occur at the critical point of a second order phase transition in the framework of Langevin equations. Through this formalism I discuss the response, both linear and nonlinear, to external forces. Emphasis is placed on how information is transferred from one individual to another in order to facilitate the collective response of the cooperative network to a localized perturbation. The results are relevant to a wide variety of systems, ranging from nematic liquid crystals, to flocks and swarms, social groups, and neural networks.

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