FABIO RAPALLO

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Il libro presenta le principali metodologie statistiche per l'analisi di dati multivariati con particolare attenzione alle basi matematiche

In recent literature a new combinatorial algorithm for the selection of robust fractional factorial designs has been introduced. In this work we analyze the application of this algorithm in the case of ordered factors.

In this work we define log-linear models to compare several square contingency tables under the quasi-independence or the quasi-symmetry model, and the relevant Markov bases are theoretically characterized. Through Markov bases, an exact test to evaluate if two or more tables fit a common model is introduced. Two real-data examples illustrate...

Given 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.

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The 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 $2 imes 2$ tables based on the aberrations. With a simple simulation study, we compare its performance with the...

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In this work, we present the results of several simulations on main-effect factorial designs. The goal of such simulations is to investigate the connections between the D-optimality of a design and its geometric structure. By means of a combinatorial object, namely the circuit basis of the model matrix, we show that it is possible to define a...

We consider binary Orthogonal Arrays and we analyze the aberrations of the fractions obtained by the deletion of p = 1;2 or 3 design points. Some explicit formulae are given for p = 1 and some examples are presented in the other cases.

In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We code the s levels of a factor with the s-th roots of the unity. We focus on the notion of regular fraction in the complex coding, called C-regularity. We introduce methods to check whether a given symmetric orthogonal array can...

We consider a recently developed algebraic criterion to check whether a fraction is saturated or not for a given model. Such criterion is based on combinatorial algebraic objects, namely the circuit basis of the design matrix of the model. We show on a case study how to use indicator functions of the circuits to classify saturated fractions....

In this work we consider the weighted kappa as a measure of rater agreement for ordinal variables, and we use a simulated annealing algorithm to find the maximum agreement configuration. The proposed algorithm allow us to show, through some examples, that the maximum agreement depends strongly on the choice of the weighting scheme.

The aim of this work is to highlight some interesting connections between contingency tables analysis and design of experiments. In particular, we consider two-way tables in correspondence to two-factor designs. We provide a condition that characterizes the estimability of the independence model for all saturated fractions.

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In this work, we analyze the connection between contingency table analysis and copulas in a discrete framework. We focus on the impact of structural zeros on the general theory presented by Geenens (2020) based on a new idea of copula models for discrete variables. Through examples, we investigate the pros and cons of applying the theory...

We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors. Here, we focus on three-way binary tables and show that, even in such a simple case, the situation is quite...

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