abstract: Researchers who conduct longitudinal studies are inherently interested in studying individual and population changes over time (e.g., mathematics achievement, subjective well-being). To answer such research questions, models of change (e.g., growth models) make the assumption of longitudinal measurement invariance. In many applied situations, key constructs are measured by a collection of ordered-categorical indicators (e.g., Likert scale items). To evaluate longitudinal measurement invariance with ordered-categorical indicators, a set of hierarchical models can be sequentially tested and compared. If the statistical tests of measurement invariance fail to be supported for one of the models, it is useful to have a method with which to gauge the practical significance of the differences in measurement model parameters over time. Drawing on studies of latent growth models and second-order latent growth models with continuous indicators (e.g., Kim & Willson, 2014a; 2014b; Leite, 2007; Wirth, 2008), this study examined the performance of a potential sensitivity analysis to gauge the practical significance of violations of longitudinal measurement invariance for ordered-categorical indicators using second-order latent growth models. The change in the estimate of the second-order growth parameters following the addition of an incorrect level of measurement invariance constraints at the first-order level was used as an effect size for measurement non-invariance. This study investigated how sensitive the proposed sensitivity analysis was to different locations of non-invariance (i.e., non-invariance in the factor loadings, the thresholds, and the unique factor variances) given a sufficient sample size. This study also examined whether the sensitivity of the proposed sensitivity analysis depended on a number of other factors including the magnitude of non-invariance, the number of non-invariant indicators, the number of non-invariant occasions, and the number of response categories in the indicators. / Dissertation/Thesis / Doctoral Dissertation Psychology 2016

Os modelos para dados categorizados ordinais são extensões dos Modelos Lineares Generalizados e suas suposições e inferências são fundamentadas por esta classe de modelos. Os Modelos de Logitos Cumulativos, em que a função de ligação é constituída de probabilidades acumuladas, são muito utilizados para este tipo de variável, sendo uma de suas simplificações, os Modelos de Chances Proporcionais, em que para todas as covaríaveis no modelo há um crescimento linear nas razões de chances, porém, neste caso, é necessária a verificação da suposição de paralelismo. Outros modelos como o Modelo de Chances Proporcionais Parciais, o Modelo de Categorias Adjacentes e o Modelo Logito de Razão Contínua também podem ser utilizados. Em diversos estudos deste tipo, é necessário a utilização de modelos mistos, seja pelo tipo de um fator ou a dependência entre observações da variável resposta. Objetivou-se, neste trabalho, o estudo de modelos para variável resposta ordinal com a inclusão de um ou mais efeitos aleatórios. Esses modelos são ilustrados com a utilização de dados reais de análise sensorial, cuja variável resposta é constituída de uma escala ordinal e deseja-se saber dentre duas variedades de tomates desidratados (Italiano e Sweet Grape), qual teve melhor aceitação pelos consumidores. Nesse experimento os provadores avaliaram uma única vez cada uma das variedades, sendo as repetições constituídas pelas avaliações dadas por diferentes provadores. Nesse caso, é necessária a inclusão de um efeito aleatório por provador, para que o modelo consiga capturar as diferenças entre esses provadores não treinados. O Modelo de Chances Proporcionais ajustou-se de maneira satisfatória aos dados, podendo-se fazer uso das estimativas de probabilidades e razões de chances para a interpretação dos resultados e concluindo-se que o sabor da variedade Sweet Grape foi o que mais agradou os provadores, independente do sexo. / Models for ordinal categorical data are extensions of the Generalized Linear Models and their assumptions and inferences are based on this class of models. The Cumulative Logit Models in wich the link function consists of accumulated probabilities are more used for this type of variable, with one of its simplifications are the Proportional Odds Model, in wich for all covariates in the model there is a linear growth in odds ratios, but in this case, checking the parallelism assumption is required. Other models such as the Partial Proportional Odds Model, the Adjacent-Categories Logits and Continuation-Ratio Logits model can also be used. In several of such studies, the use of mixed models is required, either by type of factor or dependence between the response variable observations. The aim of this work is studying models for ordinal variable response with the inclusion of one or more random effects. These models are illustrated by using real data of sensory analysis, the response variable consists of an ordinal scale and we want to know from two varieties of dried tomatoes, Italian and Sweet Grape, which had better acceptance by consumers. In this experiment, the panelists evaluated each variety once, and the repetitions constituted by the ratings given by different tasters. In this case, the inclusion of a random effect by taster is required so that the model can capture the difference between these untrained tasters. The Proportional Odds Model fitted satisfactorily to the data and it is possible to make use of the estimates of probabilities and odds ratios for the interpretation of results and concluding that the taste of the variety Sweet Grape was the one that most pleased the tasters regardless of sex.

Ph.D. students are an integral part of the tertiary education system. Encouragement for doctoral programs and their students is very important because they are the ones who will participate in research projects in the future and they will contribute to society as a whole. The majority of scholarships for Ph.D. students comes from public sources. An important question to be asked is whether the scholarships are sufficient to finance Ph.D. studies and whether there are differences in the amount depending on gender, field of study or region. This thesis aims to answer these questions by applying statistical methods to the results of the survey DOKTORANDI 2014.

Point estimation of several association parameters in categorical data are presented. Typically, a constant is added to the frequency counts before the association measure is computed. We will study the accuracy of these adjusted point estimators based on frequentist and Bayesian methods respectively. In particular, amended estimators for the ratio of independent Poisson rates, relative risk, odds ratio, and the ratio of marginal binomial proportions will be examined in terms of bias and mean squared error.

This research paper focuses on fraud detection in the financial industry using Generative Adversarial Networks (GANs) in conjunction with Uni and Multi Variate Bayesian Model with Shrinkage Priors (BMSP). The problem addressed is the need for accurate and advanced fraud detection techniques due to the increasing sophistication of fraudulent activities. The methodology involves the implementation of GANs and the application of BMSP for variable selection to generate synthetic fraud samples for fraud detection using the augmented dataset. Experimental results demonstrate the effectiveness of the BMSP GAN approach in detecting fraud with improved performance compared to other methods. The conclusions drawn highlight the potential of GANs and BMSP for enhancing fraud detection capabilities and suggest future research directions for further improvements in the field.

Η παρούσα διπλωματική εργασία ασχολείται με πολυδιάστατα κατηγορικά δεδομένα όπως αυτά προκύπτουν από συλλογή μέσω ερωτηματολογίων. Για να αναλυθεί όμως ένα ερωτηματολόγιο το οποίο περιλαμβάνει πλήθος ερωτήσεων-μεταβλητών και να εξάγουμε ορισμένα χρήσιμα συμπεράσματα θα πρέπει, πρώτα από όλα να γίνει η κατάλληλη κωδικοποίηση των δεδομένων. Χρησιμοποιώντας στατιστικές τεχνικές και μεθόδους κατάλληλες για κατηγορικά δεδομένα μπορούμε πιο εύκολα να μελετήσουμε τις σχέσεις μεταξύ των μεταβλητών. Για τον σκοπό αυτό, παρουσιάζουμε και αναλύουμε τη θεωρία της Παραγοντικής Ανάλυσης των Αντιστοιχιών και της Πολλαπλής Παραγοντικής Ανάλυσης των Αντιστοιχιών. Ύστερα, αναλύουμε τα αποτελέσματα που δίνουν οι μέθοδοι όταν τις χρησιμοποιήσουμε για την ανάλυση του ερωτηματολογίου. Τα συμπεράσματα που προκύπτουν έχουν ιδιαίτερο ενδιαφέρον. Η δυναμικότητα των μοντέλων αυτών παρουσιάζεται μέσα από μία εφαρμογή από τον χώρο των κοινωνικών επιστημών σε θέματα που αφορούν τα σχολεία και τους μαθητές της Πρωτοβάθμιας εκπαίδευσης. Στις μεθόδους αυτές δίνεται έμφαση κυρίως στα γραφικά αποτελέσματα αλλά και στις εκτιμήσεις των σκορ των κατηγοριών των μεταβλητών. Όλα τα παραπάνω τα συγκρίνουμε κριτικά μεταξύ τους στη θεωρία και στη πράξη έτσι ώστε ο ενδιαφερόμενος αναγνώστης να κατανοήσει περισσότερο τις μεθόδους αυτές και να αποκομίσει όσο το δυνατόν περισσότερες πληροφορίες που θα τον βοηθήσουν για την εφαρμογή τους. / This dissertation deals with multivariate categorical data of a raw data set produced by a questionnaire designed for a research purpose. However, in order to analyze a questionnaire and extract some fruitful results, that includes a great number of questions-variables, we must first impose a structure on it especially on situations this specific structure is missing. Whenever the structure is imposed, by using statistical techniques and methods designed for categorical data, we can then study more efficiently the relations among the variables in concern for further analyses. The capacity of these models is presented through an application from the social sciences on issues concerning schools and pupils in primary education. The analysis on a smaller subset is further explored by describing the issues of Correspondence Analysis, and Multiple Correspondence Analysis. With these methods, we focus on the interpretation of the results on the graphical displays of the data but also on the estimated category scores of the variables. The above methods described in this dissertation and the results after implementing them are all critically compared with each other at each chapter. This gives to the interesting reader the possibility to fully understand them and to obtain additional information on their implementation.

The importance of simultaneous consideration of forms and functions in youth measures of aggressive behavior is well established. Competing models have presented these highly interrelated constructs as either independent (e.g., reactive or overt) or paired factors (e.g., reactive and overt). The current study examines these models in the context of assessing the viability of a new self-report measure, the Peer Conflict Scale – 20 Item Version. Confirmatory factor analyses were conducted on PCS 20 responses from 1,048 school-age youth living in the Gulf Coast region. Both models significantly improved upon one or two-factor alternatives, and demonstrated partial invariance across gender and grade. The models showed comparable levels of fit to the data, though some loadings for the independent factors model were non-significant. Results encourage use of the PCS 20 across research settings and developmental contexts, while also demonstrating the viability of a paired factors model of aggression.

Estudos em que a resposta de interesse é uma variável categorizada são bastante comuns nas mais diversas áreas da Ciência. Em muitas situações essa resposta é composta por mais de duas categorias não ordenadas, denominada então de uma variável politômica nominal, e em geral o objetivo do estudo é associar a probabilidade de ocorrência de cada categoria aos efeitos de variáveis explicativas. Ademais, existem tipos especiais de estudos em que os dados são coletados diversas vezes para uma mesma unidade amostral ao longo do tempo, os estudos longitudinais. Estudos assim requerem o uso de modelos estatísticos que considerem em sua formulação algum tipo de estrutura que suporte a dependência que tende a surgir entre observações feitas em uma mesma unidade amostral. Neste trabalho são abordadas duas extensões do modelo de logitos generalizados, usualmente empregado quando a resposta é politômica nominal com observações independentes entre si. A primeira consiste de uma modificação das equações de estimação generalizadas para dados nominais que se utiliza de razões de chances locais para descrever a dependência entre as observações da variável resposta politômica ao longo dos diversos tempos observados. Este tipo de modelo é denominado de modelo marginal. A segunda proposta abordada consiste no modelo de logitos generalizados com a inclusão de efeitos aleatórios no preditor linear, que também leva em conta uma dependência entre as observações. Esta abordagem caracteriza o modelo de logitos generalizados misto. Há diferenças importantes inerentes às interpretações dos modelos marginais e mistos, que são discutidas e que devem ser levadas em consideração na escolha da abordagem adequada. Ambas as propostas são aplicadas em um conjunto de dados proveniente de um experimento da área agronômica realizado em campo, conduzido sob um delineamento casualizado em blocos com esquema fatorial para os tratamentos. O experimento foi acompanhado ao longo de seis estações do ano, caracterizando assim uma estrutura longitudinal, sendo a variável resposta o tipo de vegetação observado no campo (touceiras, plantas invasoras ou espaços vazios). Os resultados encontrados são satisfatórios, embora a dependência presente nos dados não seja tão caracterizada; por meio de testes como da razão de verossimilhanças e de Wald diversas diferenças significativas entre os tratamentos foram encontradas. Ainda, devido às diferenças metodológicas das duas abordagens, o modelo marginal baseado nas equações de estimação generalizadas mostra-se mais adequado para esses dados. / Studies where the response is a categorical variable are quite common in many fields of Sciences. In many situations this response is composed by more than two unordered categories characterizing a nominal polytomous outcome and, in general, the aim of the study is to associate the probability of occurrence of each category to the effects of variables. Furthermore, there are special types of study where many measurements are taken over the time for the same sampling unit, called longitudinal studies. Such studies require special statistical models that consider some kind of structure that support the dependence that tends to arise from the repeated measurements for the same sampling unit. This work focuses on two extensions of the baseline-category logit model usually employed in cases when there is a nominal polytomous response with independent observations. The first one consists in a modification of the well-known generalized estimating equations for longitudinal data based on local odds ratios to describe the dependence between the levels of the response over the repeated measurements. This type of model is also known as a marginal model. The second approach adds random effects to the linear predictor of the baseline-category logit model, which also considers a dependence between the observations. This characterizes a baseline-category mixed model. There are substantial differences inherent to interpretations when marginal and mixed models are compared, what should be considered in the choice of the most appropriated approach for each situation. Both methodologies are applied to the data of an agronomic experiment installed under a complete randomized block design with a factorial arrangement for the treatments. It was carried out over six seasons, characterizing the longitudinal structure, and the response is the type of vegetation observed in field (tussocks, weeds or regions with bare ground). The results are satisfactory, even if the dependence found in data is not so strong, and likelihood-ratio and Wald tests point to several differences between treatments. Moreover, due to methodological differences between the two approaches, the marginal model based on generalized estimating equations seems to be more appropriate for this data.

This dissertation has three consecutive topics. First, we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. The index is also applicable when both variables are continuous. Second, we develop a sufficient variable selection procedure based on the new measure in a large p small n setting. Our approach incorporates marginal information between each predictor and the response as well as joint information among predictors. As a result, our method is more capable of selecting all truly active variables than marginal selection methods. Furthermore, our procedure can handle both continuous and discrete responses with mixed-type predictors. We establish the sure screening property of the proposed approach under mild conditions. Third, we focus on a model-free sufficient dimension reduction approach using the new measure. Our method does not require strong assumptions on predictors and responses. An algorithm is developed to find dimension reduction directions using sequential quadratic programming. We illustrate the advantages of our new measure and its two applications in high dimensional data analysis by numerical studies across a variety of settings.

Spatially explicit ecological models rely on spatially exhaustive data layers that have scales appropriate to the ecological processes of interest. Such data layers are often categorical raster maps derived from high-resolution, remotely sensed data that must be scaled to a lower spatial resolution to make them compatible with the scale of ecological analysis. Statistical functions commonly used to aggregate categorical data are majority-, nearest-neighbor- and random-rule. For heterogeneous landscapes and large scaling factors, however, use of these functions results in two critical issues: (1) ignoring large portions of information present in the high-resolution grid cells leads to high and uncontrolled loss of information in the scaled dataset; and (2) maintaining classes from the high-resolution dataset at the lower spatial resolution assumes validity of the classification scheme at the low-resolution scale, failing to represent recurring mixes of heterogeneous classes present in the low-resolution grid cells. The proposed new scaling algorithm resolves these issues, aggregating categorical data while simultaneously controlling for information loss by generating a non-hierarchical, representative, classification system valid at the aggregated scale. Implementing scaling parameters, that control class-label precision effectively reduced information loss of scaled landscapes as class-label precision increased. In a neutral-landscape simulation study, the algorithm consistently preserved information at a significantly higher level than the other commonly used algorithms. When applied to maps of real landscapes, the same increase in information retention was observed, and the scaled classes were detectable from lower-resolution, remotely sensed, multi-spectral reflectance data with high accuracy. The framework developed in this research facilitates scaling-parameter selection to address trade-offs among information retention, label fidelity, and spectral detectability of scaled classes. When generating high spatial resolution land-cover maps, quantifying effects of sampling intensity, feature-space dimensionality and classifier method on overall accuracy, confidence estimates, and classifier efficiency allowed optimization of the mapping method. Increase in sampling intensity boosted accuracies in a reasonably predictable fashion. However, adding a second image acquired when ground conditions and vegetation phenology differed from those of the first image had a much greater impact, increasing classification accuracy even at low sampling intensities, to levels not reached with a single season image.