This thesis consists of four papers that deal with several aspects of the measurement of model fit for categorical data. In all papers, special attention is paid to situations with sparse data. The first paper concerns the computational burden of calculating Pearson's goodness-of-fit statistic for situations where many response patterns have observed frequencies that equal zero. A simple solution is presented that allows for the computation of the total value of Pearson's goodness-of-fit statistic when the expected frequencies of response patterns with observed frequencies of zero are unknown. In the second paper, a new fit statistic is presented that is a modification of Pearson's statistic but that is not adversely affected by response patterns with very small expected frequencies. It is shown that the new statistic is asymptotically equivalent to Pearson's goodness-of-fit statistic and hence, asymptotically chi-square distributed. In the third paper, comprehensive simulation studies are conducted that compare seven asymptotically equivalent fit statistics, including the new statistic. Situations that are considered concern both multinomial sampling and factor analysis. Tests for the goodness-of-fit are conducted by means of the asymptotic and the bootstrap approach both under the null hypothesis and when there is a certain degree of misfit in the data. Results indicate that recommendations on the use of a fit statistic can be dependent on the investigated situation and on the purpose of the model test. Power varies substantially between the fit statistics and the cause of the misfit of the model. Findings indicate further that the new statistic proposed in this thesis shows rather stable results and compared to the other fit statistics, no disadvantageous characteristics of the fit statistic are found. Finally, in the fourth paper, the potential necessity of determining the goodness-of-fit by two sided model testing is adverted. A simulation study is conducted that investigates differences between the one sided and the two sided approach of model testing. Situations are identified for which two sided model testing has advantages over the one sided approach.

As in society in general, exclusion of individuals takes place in the school system. Even though schools – according to the curriculum – are supposed to cherish diversity, many children are left outside of the community formed during school activities. In order to gain knowledge of how schools can prevent and inhibit exclusion, this work aims to study how the problem is interpreted and managed. The study included six pedagogues: three pre-school teachers and three 1–7th grade teachers. Using a qualitative method with interviews, I have examined whether there is a difference between the two groups’ of interpretation and management of exclusion.In the analysis, the relational and categorical perspectives are used. The study shows, among other things, that the pre-school teachers are more categorical in their interpretation of exclusion than the 1–7th grade teachers. In spite of this, the pre-school teachers emphasize – to a greater extent than the 1–7th grade teachers – that the school’s social dimensions have a strong impact on their work. The study also shows that the 1–7th grade teachers have a more individualized approach to their work against exclusion. Further, the study shows that the work against exclusion of school children is mostly practised on individual- and group level, and that the particular school in this study lacks an official and joint approach for inclusion.

It is widely accepted that color is perceived categorically. Categorical perception of color can be defined as the tendency to discriminate colors that are from different categories easier, quicker and more accurately than colors that are from the same category. The present study investigated whether brain activity patterns verifies the concept of categorical color perception, an instantiation of top-down influences on low-level perception. Participants performed a color discrimination task on color pairs. Three categories of color pairs are defined in the green-blue region as follows. One of the pairs was specified as cross-category pair by choosing one color from green side of the green-blue boundary and the other color from blue side. The other two pairs were featured as within-category pairs by choosing two shades of green for within-green pair and two shades of blue for within-blue pair. Crucially, the pairs varied only in hue dimension and the physical distance between each of three pairs was set to 10 degrees in CIE LCh space. Pairs on the screen are displayed adjacently or with gaps in between, to further investigate the effect of space in color discrimination. Correct responses, reaction times and fMRI BOLD signals are recorded. Behavioral findings yielded a decrementing pattern from green to blue region challenging the prediction of categorical perception argument that performance is better at green-blue boundary than both within green and blue regions. Behavioral findings also indicated that adjacent display of colors facilitated color discrimination when compared to display of colors with spatial gaps. Brain activity patterns indicated that separate neural processes might underlie these distinct behavioral differences. Although standardized with respect to the color metric, the three categories of our experiment might have involved differences with respect to difficulty levels and memory requirements. Brain activity differences reported in the within-green condition versus cross-category condition are focused on Frontal Eye Fields and Fusiform Gyrus, which is seem to be modulated by Frontal Eye Field activity / increased activation in these regions is related to enhanced visual performance and higher scores, which is consistent with significantly better performance in within-green discrimination than cross-category discrimination. For the same contrast, Parahippocampal Gyrus and Precuneus activations suggest better visual recall and behavioral improvement due to more efficient maintenance in spatial working memory for within-green discrimination than cross-category discrimination. Brain activity differences reported in the within-blue condition versus cross-category condition is focused on Superior Temporal Gyrus, which is involved in color discrimination having the role of color memory. When within-green and within-blue conditions are compared, there was differential activation in the Fusiform Gyrus, and this is the only brain activity which might be attributed to a categorical effect. This comparison also yielded activity in Medial Frontal and Superior Frontal regions concerning more confident perceptual decisions and improved performance on within-green discrimination than within-blue discrimination. In addition, spatial separation of stimuli entailed more cognitive resources to color discrimination than adjacent stimuli as suggested by Cuneus and Lingual Gyrus activations. Overall, to the best of our knowledge our study is the first to investigate the neural framework for color perception, which revealed that color perception might involve several complex sub-processes that activate memory and attention.

One of the oldest and most fundamental problems in statistics is the analysis of cross-classified data called contingency tables. Analyzing contingency tables is typically a question of association - do the variables represented in the table exhibit special dependencies or lack thereof? The statistical models which best capture these experimental notions of dependence are the categorical conditional independence models; however, until recent discoveries concerning the strongly algebraic nature of the conditional independence models surfaced, the models were widely overlooked due to their unwieldy implicit description. Apart from the inferential question above, this thesis asks the more basic question - suppose such an experimental model of association is known, how can one incorporate this information into the estimation of the joint distribution of the table? In the traditional parametric setting several estimation paradigms have been developed over the past century; however, traditional results are not applicable to arbitrary categorical conditional independence models due to their implicit nature. After laying out the framework for conditional independence and algebraic statistical models, we consider three aspects of estimation in the models using the minimum Euclidean (L2E), minimum Pearson chi-squared, and minimum Neyman modified chi-squared distance paradigms as well as the more ubiquitous maximum likelihood approach (MLE). First, we consider the theoretical properties of the estimators and demonstrate that under general conditions the estimators exist and are asymptotically normal. For small samples, we present the results of large scale simulations to address the estimators' bias and mean squared error (in the Euclidean and Frobenius norms, respectively). Second, we identify the computation of such estimators as an optimization problem and, for the case of the L2E, propose two different methods by which the problem can be solved, one algebraic and one numerical. Finally, we present an R implementation via two novel packages, mpoly for symbolic computing with multivariate polynomials and catcim for fitting categorical conditional independence models. It is found that in general minimum distance estimators in categorical conditional independence models behave as they do in the more traditional parametric setting and can be computed in many practical situations with the implementation provided.

<p>The thesis develops nonparametric Bayesian models to handle incomplete categorical variables in data sets with high dimension using the framework of multiple imputation. It presents methods for ignorable missing data in cross-sectional studies, and potentially non-ignorable missing data in panel studies with refreshment samples.</p><p>The first contribution is a fully Bayesian, joint modeling approach of multiple imputation for categorical data based on Dirichlet process mixtures of multinomial distributions. The approach automatically models complex dependencies while being computationally expedient. </p><p>I illustrate repeated sampling properties of the approach</p><p>using simulated data. This approach offers better performance than default chained equations methods, which are often used in such settings. I apply the methodology to impute missing background data in the 2007 Trends in International Mathematics and Science Study.</p><p>For the second contribution, I extend the nonparametric Bayesian imputation engine to consider a mix of potentially non-ignorable attrition and ignorable item nonresponse in multiple wave panel studies. Ignoring the attrition in models for panel data can result in biased inference if the reason for attrition is systematic and related to the missing values. Panel data alone cannot estimate the attrition effect without untestable assumptions about the missing data mechanism. Refreshment samples offer an extra data source that can be utilized to estimate the attrition effect while reducing reliance on strong assumptions of the missing data mechanism. </p><p>I consider two novel Bayesian approaches to handle the attrition and item non-response simultaneously under multiple imputation in a two wave panel with one refreshment sample when the variables involved are categorical and high dimensional. </p><p>First, I present a semi-parametric selection model that includes an additive non-ignorable attrition model with main effects of all variables, including demographic variables and outcome measures in wave 1 and wave 2. The survey variables are modeled jointly using Bayesian mixture of multinomial distributions. I develop the posterior computation algorithms for the semi-parametric selection model under different prior choices for the regression coefficients in the attrition model. </p><p>Second, I propose two Bayesian pattern mixture models for this scenario that use latent classes to model the dependency among the variables and the attrition. I develop a dependent Bayesian latent pattern mixture model for which variables are modeled via latent classes and attrition is treated as a covariate in the class allocation weights. And, I develop a joint Bayesian latent pattern mixture model, for which attrition and variables are modeled jointly via latent classes.</p><p>I show via simulation studies that the pattern mixture models can recover true parameter estimates, even when inferences based on the panel alone are biased from attrition. </p><p>I apply both the selection and pattern mixture models to data from the 2007-2008 Associated Press/Yahoo News election panel study.</p> / Dissertation

The purpose of this study is to examine concepts of freedom and evil, and to clarify their relation in terms of Kant&rsquo / s moral philosophy. In this study, I firstly examine Kant&rsquo / s understanding of freedom and the problems that this understanding leads to. I also discuss how the concept of freedom can be reconciled with the concept of evil expressed in the form of &ldquo / propensity to evil&rdquo / . Additionally, I attempt to show the significance of the notion of evil for Kant&rsquo / s moral theory. Evil is one of the most criticized concepts of Kant&rsquo / s philosophy and it is considered as inconsistent with his earlier thoughts by his contemporaries. Kant claims that the &ldquo / propensity to evil&rdquo / is universal to all of human race, but it does not mean that human beings are actually evil. They become good or evil with their free will (Willk&uuml / r). In this study, I propose that Kant&rsquo / s understanding of evil is a concept that helps to conceive one&rsquo / s own freedom in terms of Kant&rsquo / s morality. I also try to show that in spite of its similarities with the Christian doctrine of &ldquo / original sin&rdquo / , Kant&rsquo / s conception of evil should not be considered as a religious issue / it is a matter of freedom as the extension of his moral theory and his earlier thoughts. Kant&rsquo / s earlier works do not seem to be sufficient for comprehending his moral thoughts. Therefore, it can be proposed that with the introduction of the concept of evil in the Religion within the Limits of Reason, the missing part of Kant&rsquo / s moral theory is completed.

Turkish speakers differentiate the blue region of color spectrum into mavi (blue) and lacivert (dark blue) / whereas non-Turkish speakers in this study had only one color term in the blue region. The present study aimed to explore the predictions of the Linguistic Relativity Hypothesis. Operationally, Categorical Perception (CP) effects were used. In Experiment 1, Turkish speakers performed a naming task to determine an average category boundary between mavi and lacivert. In Experiment 2, both Turkish and non-Turkish speakers&rsquo / color-difference detection thresholds were estimated on the average boundary as well as within the mavi and lacivert categories. The thresholds were also estimated in the green region, in which both groups had only one color term. 2-TAFC method, which eliminates the effects of memory or labeling and isolates the perceptual processes, was used to estimate the thresholds. Turkish speakers, and not non-Turkish speakers, were predicted to show CP effects only in the blue region: thresholds should be lower on the boundary than within-category. The result revealed that Turkish speakers&rsquo / color-difference detection thresholds were lower than those of non-Turkish speakers both in the blue and the green regions. The difference in the green region does not rule out the LRH. It is possible that this difference resulted from the limitations of the study. Finally, in Experiment 3, Turkish speakers&rsquo / thresholds were also estimated on their individual boundaries. The patterns of the thresholds revealed by Experiment 3 were similar to the pattern of the thresholds in Experiment 2.

Children at risk for reading problems also have difficulty perceiving critical differences in speech sounds (Breier et al., 2004; Edwards, Fox, & Rogers, 2003; de- Gelder & Vroomen, 1998). These children rely more heavily on context than the acoustic qualities of sound to facilitate word reading. Dialect use, such as African American English (AAE) may influence literacy development in similar ways. Dialect use has been shown to affect speech sound processing and can even result in spelling errors (Kohler, et al., in press). The purpose of this study is to determine if children who speak AAE process cues indicative of final consonant voicing differently than children who speak a more mainstream dialect of English. Twenty-six typically developing children in grades K-2 who spoke either AAE or a more mainstream American English dialect participated. The speech stimuli consisted of nonsense productions of vowel + plosive consonant. These stimuli were systematically altered by changing the vowel and stop-gap closure duration simultaneously, which resulted in the final consonant changing from a voiced consonant, like “ib”, to a voiceless consonant, like “ip”. Two tasks were developed: a continuum task where the child had to indicate when the stimuli changed in voicing and a same-different task which involved determining if two stimuli were identical in voicing or not. No significant differences between groups were found for dialect use or grade for the same/different task. In the continuum task, chi-square analyses revealed significant differences in response patterns attributable to dialect and grade. In addition, a significant consonant by speaker interaction was found for mean ratings. Correlations between mean continuum rating and phonological awareness composites were not significant. In conclusion, it was evident that children who speak AAE present with differences in their perception of final consonants in VC nonsense syllables. This finding suggests the dialect speakers may be using different cues to make judgments regarding the speech signal, or that the speakers of AAE have a less mature ability to extract fine phonetic detail due to the influence of their dialect (Baran & Seymour, 1979). More research is warranted to determine the exact role that dialect plays.

This paper presents and evaluates an algorithm to translate a dependency treebank into a Combinatory Categorial Grammar (CCG) lexicon. The dependency relations between a head and a child in a dependency tree are exploited to determine how CCG categories should be derived by making a functional distinction between adjunct and argument relations. Derivations for an English (CoNLL08 shared task treebank) and for an Italian (Turin University Treebank) dependency treebank are performed, each requiring a number of preprocessing steps. In order to determine the adequacy of the lexicons, dubbed DepEngCCG and DepItCCG, they are compared via two methods to preexisting CCG lexicons derived from similar or equivalent sources (CCGbank and TutCCG). First, a number of metrics are used to compare the state of the lexicon, including category complexity and category growth. Second, to measures the potential applicability of the lexicons in NLP tasks, the derived English CCG lexicon and CCGbank are compared in a sentiment analysis task. While the numeric measurements show promising results for the quality of the lexicons, the sentiment analysis task fails to generate a usable comparison. / text

People use facial appearance to infer the social attributes of others. A primary indicator of facial attractiveness is prototypicality (the proximity of an object to its categorical central tendency); faces and objects closer to the central tendency are judged as more attractive. Perceptual fluency theory suggests that cognitive processing speed directly generates positive affect. This dissertation examined the relationships among attractiveness, prototypicality, and affective response in faces and non-face objects across adult and 8-year-old participants using a reaction time (RT) paradigm. RT predicted positive affect and disgust responses to facial stimuli. Of particular note are the series of complementary findings suggesting that reaction to unattractive faces may be both quantitatively (i.e., longer RT latencies) and qualitatively (i.e., judged to be less typical) different from high and medium attractive faces. These findings may help explain how appearance-based stereotypes are formed and maintained. / text