Rosaria Lombardo

University of Campania "Luigi Vanvitelli"

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Eric J. Beh

University of Wollongong

José G. Clavel

Universidad de Murcia

Shizuhiko Nishisato

University of Toronto

Ida Camminatiello

University of Campania "Luigi Vanvitelli"

Pieter M. Kroonenberg

Leiden University

Rens van de Schoot

Utrecht University

Valentin Amrhein

University of Basel

J Perezgonzalez

Massey University

Fernando Marmolejo‐Ramos

University of South Australia

Tonghui Wang

Jilin Medical University

Cooperative Institutions

University of Naples Federico II

University of Campania "Luigi Vanvitelli"

Istituti di Ricovero e Cura a Carattere Scientifico

MultiMedica

University of Salerno

New Mexico State University

Federico II University Hospital

Consejo Nacional de Investigaciones Científicas y Técnicas

Centre National de la Recherche Scientifique

ASL Roma

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Mathematical Preliminaries

Behaviormetrics (2021)

Shizuhiko Nishisato Eric J. Beh Rosaria Lombardo José G. Clavel

10.1007/978-981-16-2470-4_2

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Pearson's chi‐squared statistic

Wiley series in probability and statistics (2014)

Eric J. Beh Rosaria Lombardo

It is important to highlight the importance of Pearson's chi-squared statistic, analogous measures, and their role in the correspondence analysis of a contingency table. It is also the central measure of association around which the classical approach to correspondence analysis is based. This chapter describes some of the key contributions to the development of association for categorical data that have arisen. Many of these measures are considered for the adaptation of correspondence analysis. In many practical situations, just like with numerical variables, categorical variables may be structured so that some are predictor variables and others are response variables. In these cases, Pearson's chi-squared statistic is no longer appropriate to assess the association. Instead, the Goodman–Kruskal tau index may be considered. The chapter describes this statistic which lies at the heart of the nonsymmetrical correspondence analysis.

Contingency table

Categorical variable

Statistic

Correspondence analysis

10.1002/9781118762875.ch02

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The Evaluation of Venture-Backed IPOs – Certification Model versus Adverse Selection Model, Which Does Fit Better?

Studies in classification, data analysis, and knowledge organization (2008)

Francesco Gangi Rosaria Lombardo

Adverse selection

Sample (material)

10.1007/978-3-540-78246-9_60

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Citations (3)

Multiple and multiway correspondence analysis

Wiley Interdisciplinary Reviews Computational Statistics (2019)

Eric J. Beh Rosaria Lombardo

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 “flattening,” stacking or by some other means; doing so leads to simple or multiple correspondence analysis. Although such a transformation does not always preserve some of the truly multivariate nature of the association. Therefore one may instead adopt the less common multiway correspondence analysis. This paper will briefly explore the development, literature, and possible research opportunities of multiple and multiway correspondence analysis. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction Data: Types and Structures > Categorical Data

Correspondence analysis

Categorical variable

Contingency table

Multiple correspondence analysis

Table (database)

Flattening

10.1002/wics.1464

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Citations (16)

Bootstrap selection of Multivariate Additive PLS Spline models

Decision Support Systems (2008)

Jean-François Durand A. Faraj Rosaria Lombardo

Spline (mechanical)

Source

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Visualising Departures from Symmetry and Bowker’s X2 Statistic

Symmetry (2022)

Eric J. Beh Rosaria Lombardo

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 investigate how similar, or different, the variable is between the two time points or cohorts and so a study of the departure from symmetry of the variable is important. In this paper, we present a method of visualising any departures from symmetry using correspondence analysis. Typically, correspondence analysis uses Pearson’s chi-squared statistic as the foundation for all of its numerical and visual features. In the case of studying the symmetry of a variable, Bowker’s chi-squared statistic, presented in 1948, provides a simple numerical means of assessing symmetry. Therefore, this paper shall discuss how a correspondence analysis can be performed to study the symmetry (or lack thereof) of a categorical variable when Bowker’s statistic is considered. The technique presented here provides an extension to the approach developed by Michael Greenacre in 2000.

Categorical variable

Statistic

Contingency table

Completeness (order theory)

10.3390/sym14061103

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Citations (7)

Simple Ordinal Correspondence Analysis

Wiley series in probability and statistics (2021)

Eric J. Beh Rosaria Lombardo

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 variant of correspondence analysis can be performed for row and column variables that both consist of ordered categories. It describes an alternative strategy to the generalised singular value decomposition. While both variables, Month and Temperature, are ordinal, often such a feature is ignored and the contingency table is analysed using the classical approach to correspondence analysis which assumes that the variables are nominal. The chapter describes how ordered categorical variables are incorporated into a simple correspondence analysis and discusses the role of these scores for assessing differences in the mean and variation of the set of row (or column) profiles.

Contingency table

Categorical variable

Correspondence analysis

Table (database)

Multiple correspondence analysis

10.1002/9781119044482.ch4

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Principal Surfaces Constrained Analysis

Studies in classification, data analysis, and knowledge organization (1999)

Rosaria Lombardo Gerarda Tessitore

Representation

10.1007/978-3-642-60126-2_24

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Clustering as an Alternative

Behaviormetrics (2021)

Shizuhiko Nishisato Eric J. Beh Rosaria Lombardo José G. Clavel

Contingency table

Table (database)

Dimensionless quantity

10.1007/978-981-16-2470-4_6

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Citations (2)

Manipulating the alpha level cannot cure significance testing

David Trafimow Valentin Amrhein Corson N. Areshenkoff Carlos Barrera-Causil Eric J. Beh

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 testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p -value threshold of .05, .01, .005, or anything else, is not acceptable.

Significance testing

Statistical Inference

Multiple comparisons problem

Value (mathematics)

10.7287/peerj.preprints.3411

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Citations (7)