Visualization of the Significant Explicative Categories using Catanova Method and Non-Symmetrical Correspondence Analysis for Evaluation of Passenger Satisfaction

ANalysis Of VAriance (ANOVA) is a method to decompose the total variation of the observations into sum of variations due to different factors and the residual component. When the data are nominal, the usual approach of considering the total variation in response variable as measure of dispersion about the mean is not well defined. Light and Margolin (1971) proposed CATegorical ANalysis Of VAriance (CATANOVA), to analyze the categorical data. Onukogu (1985) extended the CATANOVA method to two-way classified nominal data. The components (sums of squares) are, however, not orthogonal. Singh (1996) developed a CATANOVA procedure that gives orthogonal sums of squares and defined test statistics and their asymptotic null distributions. In order to study which exploratory categories are influential factors for the response variable we propose to apply Non-Symmetrical Correspondence Analysis (D'Ambra and Lauro, 1989) on significant components. Finally, we illustrate the analysis numerically, with a practical example

Partially Isometric Immersions and Free Maps

In this paper we investigate the existence of ``partially'' isometric immersions. These are maps f:M->R^q which, for a given Riemannian manifold M, are isometries on some sub-bundle H of TM. The concept of free maps, which is essential in the Nash--Gromov theory of isometric immersions, is replaced here by that of H-free maps, i.e. maps whose restriction to H is free. We prove, under suitable conditions on the dimension q of the Euclidean space, that H-free maps are generic and we provide, for the smallest possible value of q, explicit expressions for H-free maps in the following three settings: 1-dimensional distributions in R^2, Lagrangian distributions of completely integrable systems, Hamiltonian distributions of a particular kind of Poisson Bracket.Comment: 19 pages, 1 figur

Estimating Accidents at Work in European Union

This paper describes safety at work as an issue to be addressed in terms of legislation, with due statistical knowledge of the phenomenon. Through the application of multiple indicators while investigating the rate of homogeneity and non-homogeneity of available data, especially at international level, the concept at study can be analyzed using specific scientific methods. The Total Frequency Rate of accidents could be influenced by a country’s industrial structure. The standardization of industrial structures into NACE divisions or sub-divisions (and not only on an aggregate activity level), has proved very useful as an integral part of the statistical infrastructure used within the European statistical system for producing comparable statistics. Looking at the distribution of the Total Frequency Rates (TFR) of accidents in different world regions, the picture is quite different, as the phenomenon is by no means evenly spread across the globe. Fatalities are proportionately much higher in some regions than in others. Carrying out a country-by-country analysis would in no doubt reveal greater variations. Occupational accidents and work-related diseases in some European countries are twice as high as in some others.We show that the shadow economy has an important impact in outlining an “effective frequency rate of accidents”. In Italy, the impact of an excessive economy and the influence of organized crime in the South, which could alter the basis for reporting work-related accidents and occupational safety performance indicators, has led to the consideration of the actual rate of accidents in Italy slightly higher than the European average

The real time ability of financial and real variables in nowcasting

In this paper we develop an approach to choose the variables useful for the nowcasting (short-term forecasting) of growth rate, that is based on the real time ability of financial and real variables to reproduce reference time series. We assess, for Germany and Italy, the impact of real and financial variables in estimating smoothed gross domestic product (GDP) from 2003 to 2012. In synthesis, the innovation of our work is the one to focus both on a limited number of series both on a large dataset of economic variables, by implementing the dynamic factor model

Dimensionality reduction methods for contingency tables with ordinal variables

Correspondence analysis is a widely used tool for obtaining a graphical representation of the interdependence between the rows and columns of a contingency table, by using a dimensionality reduction of the spaces. The maximum information regarding the association between the two categorical variables is then visualized allowing to understand its nature. Several extensions of this method take directly into account the possible ordinal structure of the variables by using different dimensionality reduction tools. Aim of this paper is to present an unified theoretical framework of several methods of correspondence analysis with ordinal variables

Three-way ordinal non symmetrical correspondence analysis for the evaluation of the patient satisfaction

In some recent articles, emphasis has been given to the partition of the Goodman-Kruskal’s tau index using orthogonal polynomials for the study of the non symmetrical relations in three-way contingency tables. New graphical techniques that consider such a partition and allow for the analysis of asymmetric relationships have been proposed, including three-way ordinal non symmetrical correspondence analysis (Simonetti, 2003). Such a procedure takes into account the presence of an ordinal predictor and response variables. In this paper we demonstrate the applicability of such a technique for the patient satisfaction evaluation

Generalized log odds ratio analysis for the association in two-way contingency table.

The odds ratio is a measure of association used both for the analysis of a contingency table and an contingency table, where I and J are bigger than 2. Nevertheless, the total number of odds ratios to check grows with I and J and several methods have been developed to summarize them. In the present paper we present a general framework for the analysis of the complete set of log odds ratio. Particularly we propose and connect two different methodologies performed on two different data sets. Moreover starting from these methodologies, we focus our attention on the factorial representation of the log odds ratios