
Rosaria LombardoUniversity of Campania "Luigi Vanvitelli" · Faculty of Economics
Rosaria Lombardo
Economics Degree- PhD in Computational Statistics
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Introduction
My research focuses on correspondence analysis (CA), association measures and dimension reduction methods for three-way data. Eric J Beh and I have published two Wiley books on CA, the first being a technical, practical, computational and historical look at the topic (2014) and second provides an introductory discussion (2021). With Shizuhiko Nishisato and Jose Clavel, we have also published "Modern Quantification Theory" with Springer (2022)
Additional affiliations
March 2001 - June 2001
January 2007 - December 2012
Publications
Publications (108)
When analysing the association between the ordered categorical variables of a contingency table, orthogonal polynomials derived from the recurrence formulae of Emerson (1968, Biometrics, 24: 695 - 701) have been extensively used. The calculation of such polynomials is somewhat limited because they reflect only the univariate structure of each varia...
This paper presents a theory of contrasts designed for modified Freeman–Tukey (FT) statistics which are derived through square-root transformations of observed frequencies (proportions) in contingency tables. Some modifications of the original FT statistic are necessary to allow for ANOVA-like exact decompositions of the global goodness of fit (GOF...
Power transformations of count data, including cell frequencies of a contingency table, have been well understood for nearly 100 years, with much of the attention focused on the square root transformation. Over the past 15 years, this topic has been the focus of some new insights into areas of correspondence analysis where two forms of power transf...
Using data from the Swedish National Diabetes Register, this study examines the gender disparity among patients with type 1 diabetes who have experienced a specific cardiovascular complication, while exploring the association between their weight variability, age group, and gender. Fourteen cardiovascular complications have been considered. This an...
Recently, Beh and Lombardo (2022, Symmetry, 14, 1103) showed how to perform a correspondence analysis on a two-way contingency table where Bowker’s statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic could be used to visually identify departures from perfect symmetry. Interestingly, Bowker’s statistic is a spe...
Recently, there appeared in this journal (Beh and Lombardo \textbf{2022}, {\it Symmetry}, 14, 1103) a paper that showed how to perform a correspondence analysis on a two-way contingency table where Bowker's statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic can be used to visually identify departures from per...
Using data from the Swedish National Diabetes Register, this study examines the gender disparity among patients with type I diabetes who have experienced a specific cardiovascular complication, while exploring the association between weight variability, age group, and gender. Fourteen cardiovascular complications have been considered. This analysis...
This paper is concerned with the scaling of the row and column categories of a two-way contingency table when applying a power transformation to the elements of the table’s profiles; power transformations have been widely discussed in the correspondence analysis literature. We adopt the method of reciprocal averaging to produce a one-dimensional se...
On 25 September 2015, the United Nations General Assembly adopted the 2030 Agenda for sustainable development, which includes seventeen Sustainable Development Goals, among them the 10th Goal aims to reduce inequalities. Convinced of the importance of this goal, in this paper we propose to study the socio-economic determinants which affect the ineq...
The foundations of correspondence analysis rests with Pearson's chi‐squared statistic. More recently, it has been shown that the Freeman–Tukey statistic plays an important role in correspondence analysis and confirmed the advantages of the Hellinger distance that have long been advocated in the literature. Pearson's and the Freeman–Tukey statistics...
The object of museums is to reflect and respond to the cultural capital inherent in people and achieve their full citizenship potential. New technologies are considered essential to attract new audiences and improve access to museums. There are no current studies linking the application of new technologies in museums to an increase in value creatio...
Sometimes, the same categorical variable is studied over different time periods or across different cohorts at the same time. One may consider, for example, a study of voting behaviour of different age groups across different elections, or the study of the same variable exposed to a child and a parent. For such studies, it is interesting to investi...
For more than 20 years, variants of correspondence analysis have arisen that accommodate for the structure of ordered categorical variables using orthogonal polynomials. When the visual display from this analysis is the biplot, projections linking the origin to the standard coordinate of each category is a common feature. In the case when a column...
Purpose
In the intellectual capital literature, no studies have examined the causal relationship between Italian Fintech companies' performance and intellectual capital, especially the impact of digital industrialization on human capital. This paper aims to fill this gap in measuring human capital efficiency in the Italian Fintech market.
Design/m...
In Chap. chap2, we looked at the geometric aspect of product-moment correlation as the cosine of the angle between two corresponding vectors. In Chap. chap3, we saw the geometry of the contingency table such that each component has a two-dimensional structure. In other words, row variates and column variates associated with one component do not gen...
In Chap. 7, we showed how reciprocal averaging and canonical correlation analysis yield identical row and column scores. Our discussions were centred on the role of row and column profiles, and their centred versions, and so it is these profiles that form the foundation of many scoring techniques concerned with the analysis of categorical variables...
At the heart of visually summarising the association between two categorical variables using techniques such as correspondence analysis is the profile. Simply put, a profile is merely the relative distribution of cell frequencies for a row or column.
This chapter starts with widely observed misuse of Likert scale (LS) in today’s research. Yes, it is about the misuse of this popular method, and someone must speak up now since this misuse is the main cause of what we call “garbage in garbage out”. This phenomenon can be frequently observed in educational, social, psychological, business, politica...
Over half a century of his research career, Nishisato has observed the historical developments of quantification theory. He himself was involved in the heated arguments over the problem of joint graphical display of quantified results, the problem which lasted until recently when he solved it. So, please do allow him to reflect on his personal invo...
One of the fundamental problems in today’s mathematics education is the lack of proper teaching on how to draw a simple graph of scores on, for example, a mathematics test (X1) and an English test (X2). It is reasonable to assume that X1 and X2 are generally correlated (i.e., those who score high on the mathematics test tend to score high on the En...
In Chaps. 7 and 8, our focus has been on describing some of the technical aspects of reciprocal averaging (and canonical correlation analysis), so that one can obtain row and column scores that maximize the association between the variables of a two-way contingency table. The foundations under which, such discussions are laid, rests upon the assump...
Now that we have derived principal coordinates of rows and columns of the contingency table in dual space, we realize that graphical display has the limitation in terms of the number of dimensions it can handle. As an alternative, we will consider dimensionless analysis, that is, analysis which is free from the dimensional considerations. One of th...
In the previous chapter, we gave an overview and application of biplots for numerical data. We described the three types of biplots that one may construct—the row isometric, column isometric, and symmetric biplots—and we demonstrated the utility of the first type by analyzing data from 15 countries around the world and their financial and fiscal re...
We have looked at interesting relations between two representations of the same data, the contingency-table format and the response-pattern format. Although the main objective of quantifying the contingency table is to carry out bi-modal analysis of rows and columns of the table, the contingency table is in some sense not amenable to bi-modal analy...
Visualization techniques represent one of the main pillars in the field of exploratory data analysis. A graphical description of data is often a more preferred option than a numerical one as it is more intuitive and immediate. Boxplots, histograms, and pie charts are familiar forms of data visualization which require only a rudimentary statistical...
The correspondence analysis approach that is described in this chapter is based on the technique described in Beh for a doubly ordered contingency table; where both variables of a two‐way table are ordinal. This approach captures linear and non‐linear sources of association that may exist between the variables. The chapter briefly outlines how this...
This chapter provides an overview of how non‐symmetrical correspondence analysis can be performed on a singly ordered contingency table; that is, a contingency table consisting of one nominal (row/response) variable and one (column/predictor) ordinal variable. For non‐symmetrical correspondence analysis, the key measure of association involves the...
This chapter describes the key mathematical and practical features of correspondence analysis for a two‐way contingency table. In doing so, the technique discusses is referred to as simple correspondence analysis. The chapter focuses on how one may obtain a visual summary of the symmetric association between two nominal categorical variables. It co...
This chapter provides an introduction to how to apply a correspondence analysis to a two‐way contingency table where one variable is treated as a predictor variable and the other variable is treated as a response variable. It explores the key issues of non‐symmetrical correspondence analysis by focusing on this association structure. The discussion...
This chapter describes some common approaches that can be used for simultaneously visualising the association between multiple categorical variables by focusing on the analysis of only three variables. It confines the application of multiple correspondence analysis to the visual summary of the association between three categorical variables, althou...
This chapter confines the discussion of multi‐way correspondence analysis and its application to a three‐way contingency table. It focuses on describing and applying the Tucker3 decomposition as a way to perform multi‐way correspondence analysis on a three‐way contingency table. Pearson's chi squared statistic for a three‐way contingency table cons...
This paper explores climate changes in Italy over the last 30 years. The data come from the European observation gridded dataset and are concerned with the temperature throughout the country. We focus our attention on two Italian regions (Lombardy in northern Italy and Campania in southern Italy) and on two particular years roughly thirty years apa...
In the framework of multi-way data analysis, this paper presents symmetrical and non-symmetrical variants of three-way correspondence analysis that are suitable when a three-way contingency table is constructed from ordinal variables. In particular, such variables may be modelled using general recurrence formulae to generate orthogonal polynomial v...
Description Provides four variants of three-way correspondence analysis (ca): three-way symmetrical ca, three-way non-symmetrical ca, three-way ordered symmetrical ca and three-way ordered non-symmetrical ca.
Traditionally, simple correspondence analysis applied to a two-way contingency table is performed by decomposing a matrix of standardised residuals using singular value decomposition where the sum-of-squares of these residuals gives Pearson’s chi-squared statistic. Such residuals, which are treated as being asymptotically normally distributed, aris...
Deciding on what should be the most suitable reforms of a national judicial system, whether this means reorganising a courts' structure or offering incetives to judges, requires more empirical evidence. The efficiency of the public judicial system is important to any functioning democracy as it affects several aspects of citizens’ life. As a conseq...
This work is copyrighted by Università del Salento, and is licensed under a Creative Commons Attribuzione-Non commerciale-Non opere derivate 3.0 Italia License. For more information see: http://creativecommons.org/licenses/by-nc-nd/3.0/it/ In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Au...
Pearson's chi-square statistic is well established for testing goodness-
of-�t of various hypotheses about observed frequency distributions in contin-
gency tables. A general formula for ANOVA-like decompositions of Pearson's
statistic is given under the independence assumption along with their extensi-
ons to higher-order tables. Mathematically, i...
This paper analyses the non-symmetrical association among some key-words in a food context, given the European countries and gender of participants to a survey. The aim is to understand the meaning of the food concepts traditional and innovation associated to selected key-words in cross-cultural marketing. For studying the association among three c...
Description Provides four variants of three-way correspondence analysis (ca): three-way symmetrical ca, three-way non-symmetrical ca, three-way ordered symmetrical ca and three-way ordered non-symmetrical ca.
This paper provides a composite indicator for comparing the perceived service of satisfac-tion of public transport by residents of a southern Italian city across three time periods spanning 2008–2012. Data were collected from 400 respondents that rated their agreement with 15 attribute-related statements regarding local public transport services. T...
One of the most popular, and versatile, ways of visually analyzing the associating between categorical data is to perform a correspondence analysis on the contingency table that is formed from their cross‐classification. Traditionally the analysis of multiple categorical variables involves transforming such a table into a two‐way form through “flat...
A comprehensive study is conducted on the partition of two common indices for three-way contingency tables under several representative hypotheses about the expected frequencies (hypothesized probabilities). Specifically, the partition of the classical (symmetrical) three-way Pearson index and of the asymmetrical three-way Marcotorchino index are c...
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = .05 to .005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance tes...
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = .05 to .005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance tes...
Traditionally, simple correspondence analysis is performed by decomposing a matrix of standardised residuals using singular value decomposition where the sum-of-squares of these residuals gives Pearson's chi-squared statistic. Such residuals, which are treated as being asymptotically normally distributed, arise by assuming that the cell frequencies...
Traditionally, simple correspondence analysis is performed by decomposing a matrix of standardised residuals using singular value decomposition where the sum-of-squares of these residuals gives Pearson's chi-squared statistic. Such residuals, which are treated as being asymptotically normally distributed , arise by assuming that the cell frequencie...
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significan...
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significan...
For an analysis of the association between two categorical variables that are cross-classified to form a contingency table, graphical procedures have been central to this analysis. In particular, correspondence analysis has grown to be a popular method for obtaining such a summary and there is a great variety of different approaches that one may co...
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science.
Given that blanket and variable alpha levels both are problematic, it is sensible to dispense
with significan...
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = .05 to .005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance tes...
We argue that depending on p-values to reject null hypotheses, including a recent call for changing the canonical alpha level for statistical significance from .05 to .005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable criterion levels both are problematic, it is sensible to dispense...
The pigment spectra and the size structure of phytoplankton communities are considered as informative tools to assess the water quality in the context of the Descriptor 5 (Eutrophication) of the Marine Strategy Framework Directive (2008/56/EC). In this paper we analyse the phytoplankton assemblages in three sectors of the Adriatic Sea, the northern...
Justice court delay is found to be consistently related to pending workload per judge, as well, output per judge (productivity) is found to be strongly related to demand pressure (total available workload) and size of court. The aim of this paper is to investigate among the causes of different performances in courts, highlighting possible anomalies...
This paper presents a description of the R package CAvariants. It performs six variants of correspondence analysis on a two-way contingency table. The main function that shares the same name as the package-CAvariants-allows the user to choose (via a series of input parameters) from six different correspondence analysis procedures. These include the...
The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characte...
The R package, called CAvariants, provides six variants of two-way correspondence analysis (ca):
simple ca, singly ordered ca, doubly ordered ca, non-symmetrical ca,
singly ordered non symmetrical ca, and doubly ordered non symmetrical
ca.
The analysis of the association between the two dichotomous variables of a (Formula presented.) table arises as an important statistical issue in a number of diverse settings, such as in biomedical, medical, epidemiological, pharmaceutical or environmental research. When only the aggregate (or marginal) information is available, the analyst may det...
Three-Way Polynomial Correspondence Analysis for Ordered Contingency Tables
Rosaria Lombardo1 Pieter M. Kroonenberg2 Eric J. Beh3
1Second University of Naples, Economics Department
2Leiden University, Faculty of Social and Behavioural Sciences
3University Drive of Newcastle, School of Mathematical and Physical Sciences.
In this paper we propose th...
Recently, a procedure was developed for constructing 100(1–α)% confidence ellipses for points in a low-dimensional plot obtained from performing classical correspondence analysis. This article reviews the construction of confidence regions for classical and non symmetric correspondence analysis and proposes a simple procedure for determining p-valu...
"Correspondence Analysis: Theory, Practice and New Strategies" examines the key issues of correspondence analysis, and discusses the new advances that have been made over the last 20 years.
The main focus of this book is to provide a comprehensive discussion of some of the key technical and practical aspects of correspondence analysis, and to dem...
Abstract: In this paper we present a way of conducting design of experiments by
Multivariate Additive Partial Least-Squares Splines models, in short MAPLSS. In the
framework of optimal experimental design based on small samples, in order to select
the most informative MAPLSS model, we process an adaptive incremental selection
of observations by a p...
By the early 1990s, the term “data mining” had come to mean the process of finding information in large data sets. In the framework of the Total Quality Management, earlier studies have suggested that enterprises could harness the predictive power of Learning Management System (LMS) data to develop reporting tools that identify at-risk customers/co...
Over the past half a century correspondence analysis has grown from a little known statistical technique designed to graphically depict the association structure of categorical variables that form a contingency table to a very popular tool used in a wide variety of disciplines. Despite this growth, correspondence analysis remains relatively unknown...
In this paper we propose a new strategy to study a dependence problem among qualitative variables, based upon 1) a generalization
of the covariance criterion (Tucker, 1958), 2) a monotone regression in order to preserve the original ordering of categories
on the axis of maximal covariance, and 3) the Partial Least Squares (PLS) approach (Wold, 1966...
Routinely, the multi-response Partial Least-Squares (PLS) is used in regression and classification problems showing good performances in many applied studies. In this paper, we aim to present PLS via spline functions focusing on supervised classification studies and showing how PLS methods historically belongs to L 2 boosting family. The theory of...
Non-symmetric Correspondence analysis is a method increasingly used in place of classical correspondence analysis to portray the asymmetric association of two categorical variables. In this paper we investigate the reliability of graphical displays illustrating variable prediction, by looking at inferential aspects of the sampling variation of the...
When the information given by a panel of judges on wine sensory characteristics is resumed in a three-way table, Y, and the objective is to extract knowledge from a chemical data-set, X, which has a predictive power for wine sensorial variables, the study of the relationships between chemical–physical variables and sensorial data sets is really com...
In situations where the structure of one of the variables of a contingency table is ordered recent theory involving the augmentation of singular vectors and orthogonal polynomials has shown to be applicable for performing symmetric and non-symmetric correspondence analysis. Such an approach has the advantage of allowing the user to identify the sou...
In this paper we describe a general framework to decompose three-way association measures for contingency tables, in particular symmetric and non-symmetric measures will be discussed, like Pearson's index, Marcotorchino's index, whose special case is the Gray–Williams index, and a new non-symmetric one will be proposed, called the Delta index. Afte...
In a recent issue of this journal, Guerrero et al. (2010) studied an interesting data set involving the analysis of consumer-driven associations to the word ‘‘Traditional”, from a food perspective, in six European countries. As part of their analysis, they demonstrated the sources of association between the words studied and the country of origin o...
In the last decade, much effort has been spent on modelling dependence between sensory variables and chemical–physical ones, especially when observed at different occasions/spaces/times or if collected from several groups (blocks) of variables. In this paper, we propose a nonlinear generalization of multi-block partial least squares with the inclus...
In this paper we face off the relationship value management which is a theme in the relationship marketing literature gaining increasing attention in the last decade. The main aim of this study is to evaluate job quality and in particular employees' satisfaction of non-profit enterprises by using, among different exploratory data analysis tools, or...
Correspondence analysis (CA) has gained a reputation for being a very useful statistical technique for determining the nature of association between two or more categorical variables. For simple and multiple CA, the singular value decomposition (SVD) is the primary tool used and allows the user to construct a low-dimensional space to visualize this...
We present an alternative approach to Multiple Correspondence Analysis (MCA) that is appropriate when the data consist of
ordered categorical variables. MCA displays objects (individuals, units) and variables as individual points and sets of category
points in a low-dimensional space. We propose a hybrid decomposition on the basis of the classical...
In this article we develop an extension of categorical analysis of variance for one response and two factors, based on a partitioning of a measure of predictability for three-way contingency tables, known as Gray and Williams's index. At the first instance moment the decomposition of this multiple measure of association in partial association measu...
By the early 1990s, the term "data mining" had come to mean the process of finding information in large data sets. In the framework of the Total Quality Management, earlier studies have suggested that enterprises could harness the predictive power of Learning Management System (LMS) data to develop reporting tools that identify at-risk customers/co...
In the literature, much effort has been put into modeling dependence among variables and their interactions through nonlinear transformations of predictive variables. In this paper, we propose a nonlinear generalization of Partial Least Squares (PLS) using multivariate additive splines. We discuss the advantages and drawbacks of the proposed model,...
This paper suggests a method to generalise principal components analysis by transforming in an adaptive way both original variables and their principal components by nonlinear functions, i.e., B-splines. The main advantage is improving the model fit, taking into account nonlinear relationships, and displaying data in a clearer way via principal sur...