This thesis studies the one-factor latent trait model for binary data. In examines the sensitivity of the model when the assumptions about the model are violated, it investigates the information about the prior distribution when the model is estimated semi-parametrically and it also examines the goodness-of-fit of the model using Monte-Carlo simulations. Latent trait models are applied to data arising from psychometric tests, ability tests or attitude surveys. The data are often contaminated by guessing, cheating, unwillingness to give the true answer or gross errors. To study the sensitivity of the model when the data are contaminated we derive the Influence Function of the parameters and the posterior means, a tool developed in the frame of robust statistics theory. We study the behaviour of the Influence Function for changes in the data and also the behaviour of the parameters and the posterior means when the data are artificially contaminated. We further derive the Influence Function of the parameters and the posterior means for changes in the prior distribution and study empirically the behaviour of the model when the prior is a mixture of distributions. Semiparametric estimation involves estimation of the prior together with the item parameters. A new algorithm for fully semiparametric estimation of the model is given. The bootstrap is then used to study the information on the latent distribution than can be extracted from the data when the model is estimated semiparametrically. The use of the usual goodness-of-fit statistics has been hampered for latent trait models because of the sparseness of the tables. We propose the use of Monte-Carlo simulations to derive the empirical distribution of the goodness-of-fit statistics and also the examination of the residuals as they may pinpoint to the sources of bad fit.

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Consider sequential trials comparing two treatments with binary responses. The goal is to derive accurate confidence sets for the treatment difference and the individual success probabilities of the two treatments. We shall begin with the signed-root transformation as a pivot and then apply the approximate theory of Weng and Woodroofe [11] to form accurate confidence sets of these parameters. The explicit correction terms of the pivots are obtained. The simulation studies agree well with the theoretical results.

We present a mixture of latent trait models with common slope parameters (MCLT) for high dimensional binary data, a data type for which few established methods exist. Recent work on clustering of binary data, based on a d-dimensional Gaussian latent variable, is extended by implementing common factor analyzers. We extend the model further by the incorporation of random block effects. The dependencies in each block are taken into account through block-specific parameters that are considered to be random variables. A variational approximation to the likelihood is exploited to derive a fast algorithm for determining the model parameters. The Bayesian information criterion is used to select the number of components and the covariance structure as well as the dimensions of latent variables. Our approach is demonstrated on U.S. Congressional voting data and on a data set describing the sensory properties of orange juice. Our examples show that our model performs well even when the number of observations is not very large relative to the data dimensionality. In both cases, our approach yields intuitive clustering results. Additionally, our dimensionality-reduction method allows data to be displayed in low-dimensional plots. / Early Researcher Award from the Government of Ontario (McNicholas); NSERC Discovery Grants (Browne and McNicholas).

An examination of 14 indexes for determining the number of clusters is conducted on artificial binary data sets being generated according to various design factors. To provide a variety of clustering solutions the data sets are analyzed by different non hierarchical clustering methods. The purpose of the paper is to present the performance and the ability of an index to detect the proper number of clusters in a binary data set under various conditions and different difficulty levels. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

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A análise de dados binários é usualmente feita através da regressão logística, mas esse modelo possui limitações. Modificar a função de ligação da regressão permite maior flexibilidade na modelagem e diversas propostas já foram feitas nessa área. No entanto, não se sabe de nenhum pacote estatístico capaz de estimar esses modelos, o que dificulta sua utilização. O presente trabalho propõe uma implementação em R de quatro modelos de regressão binária com função de ligação paramétrica usando tanto a abordagem frequentista como a Bayesiana. / Binary data analysis is usually conducted with logistic regression, but this model has limitations. Modifying the link function allows greater flexibility in modelling and several proposals have been made on the field. However, to date there are no packages capable of estimating these models imposing some difficulties to utilize them. The present work develops an R implementation of four binary regression models with parametric link functions in both frequentist and Bayesian approaches.

A análise de dados binários é usualmente feita através da regressão logística, mas esse modelo possui limitações. Modificar a função de ligação da regressão permite maior flexibilidade na modelagem e diversas propostas já foram feitas nessa área. No entanto, não se sabe de nenhum pacote estatístico capaz de estimar esses modelos, o que dificulta sua utilização. O presente trabalho propõe uma implementação em R de quatro modelos de regressão binária com função de ligação paramétrica usando tanto a abordagem frequentista como a Bayesiana. / Binary data analysis is usually conducted with logistic regression, but this model has limitations. Modifying the link function allows greater flexibility in modelling and several proposals have been made on the field. However, to date there are no packages capable of estimating these models imposing some difficulties to utilize them. The present work develops an R implementation of four binary regression models with parametric link functions in both frequentist and Bayesian approaches.

Principal components analysis (PCA) has been widely used as a statistical tool for the dimension reduction of multivariate data in various application areas and extensively studied in the long history of statistics. One of the limitations of PCA machinery is that PCA can be applied only to the continuous type variables. Recent advances of information technology in various applied areas have created numerous large diverse data sets with a high dimensional feature space, including high dimensional binary data. In spite of such great demands, only a few methodologies tailored to such binary dataset have been suggested. The methodologies we developed are the model-based approach for generalization to binary data. We developed a statistical model for binary PCA and proposed two stable estimation procedures using MM algorithm and variational method. By considering the regularization technique, the selection of important variables is automatically achieved. We also proposed an efficient algorithm for model selection including the choice of the number of principal components and regularization parameter in this study.

Instead of being out at airports for the sake of testing radar data in Visual Docking Guiding System, one could use emulated radar data to function as real radar data. In this thesis, real radar data processed into binary files are, observed and dissembled to use reverse engineering and in such a way emulate similar binary files. The same software used on real radar data binary files is used to process the emulated ones to detect an object at a certain distance. Using reverse engineering could not on its own result in an emulated radar data binary file. Finally trial and error resulted in a file which gave object detection at a distance of above 21 meters as targeted in this thesis. Furthermore, as future work might be found by targeting other and further distances.