1,721,057 research outputs found
Mixture versus loglinear models in contingency table analysis
No full textWe study here two different approaches to model a cluster structure in contingency tables. From a classical independence model, we consider an additional pattern structure given by a family of subsets of cells where we allow a specific mean parameter. We encode such structure through mixture models and loglinear models, and we compare the algebraic equations defining these classes of models. We discuss some examples, and we characterize the models in some special cases
Comparison of contingency tables under quasi-symmetry
No full textIn this work we define a test to compare several square contingency tables under the quasi-symmetry model. Working within the class of log-linear models, we present a suitable model and an exact test to verify if two or more tables fit a common quasi-symmetry model. The exact test is then defined through classical tools of Algebraic Statistics, namely the computation of a Markov basis and the application of a MCMC algorithm
Exact inference and conditioning structures for Cohen's kappa with algebraic algorithms
No full textIn questo lavoro presentiamo un algoritmo per l'inferenza esatta sull'indice kappa di Cohen nel caso multivariato. Tale algoritmo è basato su tecniche di Algebra Commutativa che permettono di campionare efficientemente dallo spazio delle tabelle di contingenza multidimensionali con margini fissati. Forniamo inoltre alcune osservazioni sulla struttura del condizionamento e sull'uso delle differenti versioni dell'indice kappa utili in molte applicazioni a problemi di rater agreement multivariato
Mixture versus loglinear models in contingency table analysis
No full textWe study here two different approaches to model a cluster structure in contingency tables. From a classical independence model, we consider an additional pattern structure given by a family of subsets of cells where we allow a specific mean parameter. We encode such structure through mixture models and loglinear models, and we compare the algebraic equations defining these classes of models. We discuss some examples, and we characterize the models in some special cases
Aberration for the analysis of two-way contingency tables
No full textThe aberrations are quantities usually computed in the context of Factorial Experiments. In this work, we introduce the use of the aberrations in the framework of contingency table analysis, and we propose a test of independence for 2×2
tables based on the aberrations. With a simple simulation study, we compare its
performance with the well known chi-square test and Fisher’s exact tes
Comparison of contingency tables under quasi-symmetry
No full textIn this work we define a test to compare several square contingency tables under the quasi-symmetry model. Working within the class of log-linear models, we present a suitable model and an exact test to verify if two or more tables fit a common quasi-symmetry model. The exact test is then defined through classical tools of Algebraic Statistics, namely the computation of a Markov basis and the application of a MCMC algorithm
Robustness of Fractional Factorial Designs through Circuits
Full text linkGiven a model, we define the robustness of an experimental design as a function of the number of estimable minimal sub-fractions of it. We show how the circuit basis of the design matrix can be used to see if a minimal fraction is estimable or not and we describe an algorithm for finding robust fractions
On the aberrations of mixed level orthogonal arrays with removed runs
No full textGiven an orthogonal array we analyze the aberrations of the sub-fractions which are obtained by the deletion of some of its points. We provide formulae to compute the Generalized Word-Length Pattern of any sub-fraction. In the case of the deletion of one single point, we provide a simple methodology to find which the best sub-fractions are according to the Generalized Minimum Aberration criterion. We also study the effect of the deletion of 1, 2 or 3 points on some examples. The methodology does not put any restriction on the number of levels of each factor. It follows that any mixed level orthogonal array can be considered
Circuits for robust designs
Full text linkThis paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix named circuit basis. This representation turns out to be an appropriate way to study the optimality criteria referred to as robustness: the sensitivity of the design to the removal of design points. Exploiting the combinatorial properties of the circuit basis, we show that high values of robustness are obtained by avoiding small circuits. Many examples are given, from classical combinatorial designs to two-level factorial designs including interactions. The complexity of the circuit representations is useful because the large range of options they offer, but conversely requires the use of dedicated software. Suggestions for speed improvement are made
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