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Master of Science / Department of Statistics / Gary L. Gadbury / This report presents an analysis of data resulting from a lipidomics experiment. The experiment sought to determine the changes in the lipidome of big bluestem prairie grass when exposed to stressors. The two stressors were drought (versus a watered condition) and a rust infection (versus no infection), and were whole plot treatments arranged in a 2 by 2 factorial. A split plot treatment factor was the position on a sampled leaf (top half versus bottom half). In addition, samples were analyzed at different times, representing a blocking factor. A total of 110 samples were used and, for each sample, concentrations of 137 lipids were obtained. Many lipids were not detected for certain samples and, in some cases, a lipid was not detected in most samples. Thus, each lipid was analyzed separately using a modeling strategy that involved a combination of mixed effects linear models and a categorical analysis technique, with the latter used for certain lipids to determine if a pattern of observed zeros was associated with the treatment condition(s). In addition, p-values from tests of fixed effects in a mixed effect model were computed three different ways and compared. Results in general show that the drought condition has the greatest effect on the concentrations of certain lipids, followed by the effect of position on the leaf. Of least effect on lipid concentrations was the rust condition.

Master of Science / Department of Statistics / Nora Bello / Ordered categorical responses are frequently encountered in many disciplines. Examples of interest in agriculture include quality assessments, such as for soil or food products, and evaluation of lesion severity, such as teat ends status in dairy cattle. Ordered categorical responses are characterized by multiple categories or levels recorded on a ranked scale that, while apprising relative order, are not informative of magnitude of or proportionality between levels. A number of statistically sound models for ordered categorical responses have been proposed, such as logistic regression and probit models, but these are commonly underutilized in practice. Instead, the ordinary least squares linear regression model is often employed with ordered categorical responses despite violation of basic model assumptions. In this study, the inferential implications of this approach are investigated using a simulation study that evaluates robustness based on realized Type I error rate and statistical power. The design of the simulation study is motivated by applied research cases reported in the literature. A variety of plausible scenarios were considered for simulation, including various shapes of the frequency distribution and different number of categories of the ordered categorical response. Using a real dataset on frequency of antimicrobial use in feedlots, I demonstrate the inferential performance of ordinary least squares linear regression on ordered categorical responses relative to a probit model.

Although there is a wealth of knowledge on categorization in infancy, there are still many unanswered questions about the nature of category representation in infancy. For example, it is yet unclear whether categories in infancy have well-defined boundaries or what knowledge about species categories young infants have before entering the lab. Using a morphing technique, we linearly altered the proportion of cat versus dog in images and observed how infants reacted to contrasts between pairs of images that either did or did not cross over the categorical boundary. This was done while equating between-category and within-category similarity. Results indicate that infants’ pre-existing categories of cats and dogs are discrete and mutually exclusive. Experiment 2 found that inversion caused a disruption in processing by 6.5- but not 3.5- month-old infants, indicating a developmental change in category representation. These findings demonstrate a propensity to dichotomize early in life that could have implications for social categorizations, such as race and gender. Furthermore, this work extends previous knowledge of infant categorical perception by demonstrating a priori knowledge of familiar species categories and the boundaries between them.

This study aims to examine teachers' views on special adaptation againt behavioral problems with pupils in the elementary schools' lower grades. In addition, there is and interest in how teachers motivate their didactic choices in the classroom with theese students. A qualitative study was done by using semi-structured interviews which were customized according to the aim. The respondents' answers were then analyzed based on the research found in this study. In order to present the results we have created three themes, each one based on the issues raised in our study. The result shows that there are different perspectives in understanding behavioral problems. Furthermore, the results present that there is a difference in teachers' way of describing these problem situations depending on which perspective teachers adopt.

As terrorism continues to evolve, can we better understand when a terrorist group will utilize mass violence as opposed to targeted violence? Jeff Goodwin argues that by understanding societal factors, we can predict when a terrorist organization will choose selective or categorical terrorism. But, can we rely on these societal factors alone or can other factors allow for a more complex understanding? After testing each of the variables and additional factors against three case studies, it became apparent that Goodwin’s theory could be utilized to better understand when a terrorist organization will utilize selective versus categorical terrorism. Additionally, the presence or absence of a culture of honor may also predict the type of violence a terrorist organization will utilize. I propose that future research examine the relationship between target and violence type and a culture of honor.

>Magister Scientiae - MSc / Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category which provides a basis for categorical study of topology. We show that they are equivalent to the categorical neighbourhood operators and house the closure and interior operators. The natural notion of strict morphism with respect to a topogenous order is shown to capture the known ones in the settings of closure, interior and neighbourhood operators.

In social and economic studies many of the collected variables are measured on a nominal scale, often with a large number of categories. The definition of categories can be ambiguous and different classification schemes using either a finer or a coarser grid are possible. Categorization has an impact when such a variable is included as covariate in a regression model: a too fine grid will result in imprecise estimates of the corresponding effects, whereas with a too coarse grid important effects will be missed, resulting in biased effect estimates and poor predictive performance. To achieve an automatic grouping of the levels of a categorical covariate with essentially the same effect, we adopt a Bayesian approach and specify the prior on the level effects as a location mixture of spiky Normal components. Model-based clustering of the effects during MCMC sampling allows to simultaneously detect categories which have essentially the same effect size and identify variables with no effect at all. Fusion of level effects is induced by a prior on the mixture weights which encourages empty components. The properties of this approach are investigated in simulation studies. Finally, the method is applied to analyse effects of high-dimensional categorical predictors on income in Austria.

A preliminary study of the feasibility of using categorical variables in discriminant function analysis was performed. Data including both continuous and categorical variables were used and predictive results examined. The discriminant function techniques were found to be robust enough to include the use of categorical variables. Some problems were encountered with using the trace criterion for selecting the most discriminating variables when these variables are categorical. No monotonic relationship was found to exist between the trace and the number of correct predictions. This study did show that the use of categorical variables does have much potential as a statistical tool in classification procedures. (50 pages)