Eric J Beh

Eric J Beh
University of Wollongong | UOW · National Institute for Applied Statistics Research Australia

B Maths (Hons), PhD

About

159
Publications
35,575
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1,387
Citations
Introduction
My research focuses on correspondence analysis (CA), association measures and aggregated data. Rosaria Lombardo 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) that consists of technical essays on current practices and new insights.
Additional affiliations
January 2022 - present
Stellenbosch University
Position
  • Extraordinary Professor
January 2022 - present
The University of Newcastle, Australia
Position
  • Honorary Professor (Retired)
December 2021 - present
University of Wollongong
Position
  • Honorary Professorial Fellow
Education
June 1995 - November 1998
University of Wollongong
Field of study
  • Statistics
January 1994
University of Wollongong
Field of study
  • Statistics

Publications

Publications (159)
Book
Full-text available
"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...
Article
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...
Article
Full-text available
Recently (Beh, 2008, JSPI) presented an index that helps to identify how likely two dichotomous categorical variables may be associated given only the aggregate (or marginal) information. Such an index was referred to as the aggregate association index. This paper will further consider some of the issues concerned with that index. These include va...
Article
Over the past few decades correspondence analysis has gained an international reputation as a powerful statistical tool for the graphical analysis of contingency tables. This popularity stems from its development and application in many European countries, especially France, and its use has spread to English speaking nations such as the United Stat...
Article
Confidence regions for simple correspondence analysis allow for the identification of categories that are consistent with independence, and those that are not. This paper describes a procedure for constructing elliptical regions which takes into account the unequal weighting of each of the axes of the plot.
Article
Full-text available
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...
Article
Full-text available
The main goal of this paper is to examine Nobel Prize data by studying the association among the laureate’s country of birth or residence, discipline, time period in which the Nobel Prize was awarded, and gender of the recipient. Multiple correspondence analysis is used as a tool to examine the association between these four categorical variables b...
Conference Paper
Full-text available
This study examines Nobel Prize data by studying the association between the nationality of the laureate, the discipline in which the Nobel Prize was awarded, and the gender of the recipient by maintaining the multi-way structure of the data. A three-way contingency table is formed by simultaneously cross-classifying the three categorical variables...
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
• Species distribution modeling, which allows users to predict the spatial distribution of species with the use of environmental covariates, has become increasingly popular, with many software platforms providing tools to fit such models. However, the species observations used can have varying levels of quality and can have incomplete information,...
Chapter
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...
Chapter
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...
Chapter
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...
Article
Full-text available
We read with great interest the paper “A Systematic Review and Meta‐analysis of Radiofrequency Procedures on Innervation to the Shoulder Joint for relieving Chronic Pain” by Pushparaj and colleagues (2021). This is an excellent and timely systematic assessment of predominately pulsed radiofrequency neurotomy (pRF) of the suprascapular nerve and we...
Article
Full-text available
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...
Article
Full-text available
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...
Code
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.
Article
Full-text available
Objectives The aim of this study was to explore the potential association between (i) the technology features of the applied cognitive technology (ACT) used to support employment-related outcomes for people with intellectual and developmental disabilities and (ii) the cognitive functions. The WHO International Classification of Functioning, Disabil...
Article
Full-text available
The main goal of this study is to examine Nobel Prize data by exploring and studying the association between the Country of the nominated individual (or of the nominated team) and the Discipline in which the Nobel Prize was awarded. The sample studied comprises the eight the most developed countries that received at least one Nobel Prize in the per...
Article
Over the past 50 years, correspondence analysis (CA) has increasingly been used by data analysts to examine the association structure of categorical variables that are cross-classified to form a contingency table. However, the literature has paid little attention to the case where the variables are ordinal. Indeed, Pearson’s chi-squared statistic X...
Preprint
Full-text available
We introduce “matched CA” to study gender differences in (0, 1) symptom indicators. Without numerical statistics, we visually examine the gender differences using a 2-D map. For matched CA, we generate the age-matched table by concatenating female and male contingency tables with the same rank and properties. Matched CA (1) optimally scales the fem...
Chapter
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...
Article
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...
Article
Full-text available
This study investigates the relationship between the consumption of foods and eating locations (home, school/work and others) in British adolescents, using data from the UK National Diet and Nutrition Survey Rolling Program (2008–2012 and 2013–2016). A cross-sectional analysis of 62,523 food diary entries from this nationally representative sample...
Chapter
Correspondence analysis represents the row and column categories of a contingency table as points in a low dimensional space, irrespective of whether the categories are successive or not. In this paper, a scaling method is considered for successive categories that are regarded as a series of boxes (intervals) or numbers defined on a line scale. By...
Article
The demand for a particular product or service is typically associated with different uncertainties that can make them volatile and challenging to predict. Demand unpredictability is one of the managers’ concerns in the supply chain that can cause large forecasting errors, issues in the upstream supply chain and impose unnecessary costs. We investi...
Article
Full-text available
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...
Preprint
Full-text available
The demand for a particular product or service is typically associated with different uncertainties that can make them volatile and challenging to predict. Demand unpredictability is one of the managers' concerns in the supply chain that can cause large forecasting errors, issues in the upstream supply chain and impose unnecessary costs. We investi...
Article
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...
Article
Full-text available
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...
Code
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.
Preprint
Full-text available
Species distribution modelling, which allows users to predict the spatial distribution of species with the use of environmental covariates, has become increasingly popular, with many software platforms providing tools to fit species distribution models. However, the species observations used in species distribution models can have varying levels of...
Article
Full-text available
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...
Article
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...
Presentation
Full-text available
In the study we analyzed gender-matched matrices with a variant of correspondence analysis (CA) called “matched CA”. A two-way contingency table (a 5 age groups x 5 clinical symptom-presence categories) for the male participants and the same 5 x 5 table for the female participants, were concatenated to form a 10 (male/female age groups) x 10 (male/...
Conference Paper
Full-text available
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...
Conference Paper
Gender-specific Study of Cloninger's TCI in relationship to Symptoms of Psychological Distress: an OLLM approach. Extended Ordinary Log-Linear models: Gender specific study of Cloninger's TCI in relationship to Psychological distress The link between personality and depression has long been investigated by researchers in psychological distress. P...
Preprint
Full-text available
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...
Preprint
Full-text available
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...
Poster
Full-text available
Species distribution models are useful tools in ecology. When taxonomists identify distinct species from what was previously believed to be a single species, old species records may be confounded. For rare species, such questions about the identity of species records can restrict efforts to build reliable models. If we have access to observations w...
Article
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...
Preprint
Full-text available
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...
Article
Full-text available
Data aggregation often occurs due to data collection methods or confidentiality laws imposed by government and institutional organisations. This kind of practice is carried out to ensure that an individual's privacy is protected but it results in selective information being distributed. In this case, the availability of only aggregate data makes it...
Article
Full-text available
Calculating the p-value of any test statistic is of paramount importance to all statistically minded researchers across all areas of study. Many, these days, take for granted how the p-value is calculated and yet it is a pivotal quantity in all forms of statistical analysis. For the study of 2x2 tables where dichotomous variables are assessed for a...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Preprint
Full-text available
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...
Article
Research on taste-shape correspondences has focused on one-to-one taste/shape matching tasks. However, foods and drinks tend to involve multiple shapes (or shape attributes) and tastes that co-occur at different moments of our eating experiences. In the present research, we assessed whether food concepts involving more than one taste (e.g., “sweet...
Preprint
Full-text available
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...
Article
This paper presents the application of correspondence analysis (CA) for investigating associations using confidence regions (CRs) with a focus on facilitating mining the data and hypothesis generation. We study the relationship between locations and 'less-healthy' food consumption by UK teenagers. CA allows for a quick visual inspection of the vari...
Chapter
This paper presents the application of correspondence analysis (CA) for investigating associations using confidence regions (CRs) with a focus on facilitating mining the data and hypothesis generation. We study the relationship between locations and "less-healthy" food consumption by UK teenagers. CA allows for a quick visual inspection of the vari...
Article
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...
Conference Paper
"A non-iterative approach to ordinal log-linear models: investigation of log D in drug discovery" In: 31st International Workshop on Statistical Modelling, Editors: Dupuy J-P, Josse K. Statistical Modelling Society, Rennes, France, 4 -8 July, 2016., pp 163-166.
Article
Identification of differentially expressed genes (DEG) in transcriptomic analyses is one of the important tasks to find out significantly activated/deactivated pathways. Outliers and/or the missing values are commonly observed in microarray data; however, most available statistical methods did not deal with these issues and, therefore, their analyt...
Article
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...
Article
Full-text available
This paper presents a comprehensive statistical evaluation of the conductivity performance of PEDOT/PSS films generated at various spin coating speeds (1000 to 5000 rpm) by correspondence analysis (CA), regression and ANOVA models. Poly(3,4-ethylenedioxythiophene) (PEDOT) is a highly conducting insoluble polymer which, when doped with poly(styrene...
Research
Full-text available
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.
Article
Full-text available
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...
Conference Paper
Full-text available
The dual-system estimator, or estimators with a similar underlying set of assumptions and structure, is a widely used approach to estimate the unknown size of a population. Within official statistics its use is linked with population census, while in health applications it is often used to estimate true levels of incidence from imperfect reporting...