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Associate Professor Eric Beh

Associate Professor

School of Mathematical and Physical Sciences (Statistics)

Career Summary

Biography

The primary focus of my research is on correspondence analysis, in particular the case where categorical variables consist of ordinal responses; this is often the case in many social and scientific studies - such variable structures may form part of (for example) responses from questionnaires and surveys. Correspondence analysis is a statistical procedure (often linked to the family of multivariate data analysis techniques) that allows for a graphical summary of the association between two or more categorical variables. While investigating the theoretical properties of correspondence analysis, I have paid particular attention to ordinal contingency tables. My work with ordinal categorical data also extends to partitioning quantities commonly used to measure the extent to which two (and more generally multiple) categorical variables are associated. In particular, such partitions have been applied to the Pearson chi-squared statistic (for symmetrically related variables) and the Goodman-Kruskal tau index, Marcotorchino index and the Gray-William indices (all used for asymmetrically associated variables). Other work I have undertaken, in collaboration with my colleagues, has resulted in an iterative free (direct) procedure for estimating the linear-by-linear association term commonly included in ordinal log-linear models. Work is currently being developed to look at the properties of these direct procedures and their extension to more general cases. I have also been very interested in ecological inference - a technique used to identify the behaviour of individual/cellular level data when only aggregate data is available. In particular, I am interested in the properties of a single 2x2 contingency table where the cells of the table are unknown or missing.

Research Expertise
My research interests cover the broad statistical topic of categorical data analysis, with particular emphasis on the mathematical development and application of correspondence analysis, measures of bivariate and multivariate association, log-linear models and ecological inference. The primary focus of my research is on correspondence analysis, in particular the case where categorical variables consist of ordinal responses; this is often the case in many social and scientific studies - such variable structures may form part of (for example) responses from questionnaires and surveys. Correspondence analysis is a statistical procedure (often linked to the family of multivariate data analysis techniques) that allows for a graphical summary of the association between two or more categorical variables. While investigating the theoretical properties of correspondence analysis, I have paid particular attention to ordinal contingency tables. My work with ordinal categorical data also extends to partitioning quantities commonly used to measure the extent to which two (and more generally multiple) categorical variables are associated. In particular, such partitions have been applied to the Pearson chi-squared statistic (for symmetrically related variables) and the Goodman-Kruskal tau index, Marcotorchino index and the Gray-William indices (all used for asymmetrically associated variables). Other work I have undertaken, in collaboration with my colleagues, has resulted in an iterative free (direct) procedure for estimating the linear-by-linear association term commonly included in ordinal log-linear models. Work is currently being developed to look at the properties of these direct procedures and their extension to more general cases. I have also been very interested in ecological inference - a technique used to identify the behaviour of individual/cellular level data when only aggregate data is available. In particular, I am interested in the properties of a single 2x2 contingency table where the cells of the table are unknown or missing. 

Collaborations
My research interests cover the broad statistical topic of categorical data analysis, with particular emphasis on the mathematical development and application of correspondence analysis, measures of bivariate and multivariate association, log-linear models and ecological inference. I am actively engaged in collaborations with national and international researchers including * Professor Luigi D'Ambra, University of Naples, Italy * Professor Thomas B. Farver, University of California - Davis, USA * Associate Professor Rosaria Lombardo, Second University of Naples, Italy * Dr Biagio Simonetti, University of Sannio, Italy * Professor John Rayner, University of Newcastle * Professor Derek Smith, University of Newcastle * Dr Clovia Holdsworth, University of Newcastle

Qualifications

  • Doctor of Philosophy, University of Wollongong
  • Bachelor of Mathematics (Honours), University of Wollongong

Keywords

  • Categorical Data Analysis
  • Correspondence Analysis
  • Ecological Inference
  • Measures of Association
  • Statistics

Fields of Research

Code Description Percentage
080299 Computation Theory and Mathematics not elsewhere classified 15
140399 Econometrics not elsewhere classified 15
010499 Statistics not elsewhere classified 70

Professional Experience

UON Appointment

Title Organisation / Department
Associate Professor University of Newcastle
School of Mathematical and Physical Sciences
Australia
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (6 outputs)

Year Citation Altmetrics Link
2016 Beh EJ, Lombardo R, An Introduction to Correspondence Analysis, Wiley, Chichester, UK, ~200 (2016)
2014 Beh EJ, Lombardo R, Correspondence Analysis: Theory, Methods and New Strategies, John Wiley & Sons, Chichester, England, 592 (2014) [A1]
Citations Scopus - 2
2011 Beh EJ, Park LAF, Russell KG, Proceedings of the Fourth Annual ASEARC Conference, University of Wollongong Press, University of Wollongong, 91 (2011)
2011 Beh EJ, Park LAF, Russell KG, Proceedings of the Fourth Annual ASEARC Conference, University of Wollongong Press, University of Wollongong, 91 (2011)
2005 Beh EJ, Clark RG, Rayner, Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong Press, University of Wollongong, 185 (2005)
Co-authors John Rayner
2005 Beh EJ, Clark RG, Rayner, Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong Press, University of Wollongong, 185 (2005)
Co-authors John Rayner
Show 3 more books

Chapter (3 outputs)

Year Citation Altmetrics Link
2015 Beh EJ, Cheema SA, Tran, Hudson I, 'Adjustment to the aggregate association index to minimize the impact of large samples', Advances in Latent Variables, Springer, Switzerland 241-251 (2015)
Co-authors Irene Hudson
2014 Beh EJ, Tran D, Hudson I, Moore L, 'Clustering of stratified aggregated data using the aggregate association index: Analysis of New Zealand voter turnout (1893 ¿ 1919)', Analysis and Modeling of Complex Data in Behavioral and Social Sciences, Springer, Heidelberg 21-28 (2014) [B1]
DOI 10.1007/978-3-319-06692-9_3
Co-authors Irene Hudson
2004 Steel DG, Beh EJ, Chambers RL, 'The information in aggregate data', Ecological Inference: New Methodological Strategies, Cambridge University Press 51-68 (2004)

Ecological inference attempts to draw conclusions concerning individual-level relationships using data in the form of aggregates for groups in the population. The groups are often... [more]

Ecological inference attempts to draw conclusions concerning individual-level relationships using data in the form of aggregates for groups in the population. The groups are often geographically defined. A fundamental statistical issue is how much information aggregate data contain concerning the relationships and parameters that we are trying to estimate. The information affects the standard errors of estimates as well as the power of any tests of hypothesis. It also affects the ability to tell, from the aggregate data, which different models under consideration are supported by the data. In this chapter likelihood-based methods are considered. We show in general how aggregation affects the information matrix associated with the maximum likelihood estimates compared with the case when individual-level data are available. Hypothesis testing using aggregate data is also considered. We apply this general approach to ecological inference in the case of several 2 by 2 tables and show how the information is affected by aggregation. Tests of the hypothesis that the parameters are constant across the groups are developed using aggregate data. We also consider how the addition of a small number of individual-level data obtained from a sample, ignoring the groups, increases the information concerning the parameters. The theory is illustrated through an example.

DOI 10.1017/CBO9780511510595.004
Citations Scopus - 14

Journal article (64 outputs)

Year Citation Altmetrics Link
2015 Lombardo R, Beh EJ, Kroonenberg PM, 'Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials', Psychometrika, (2015)

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... [more]

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 characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display¿the polynomial biplot.

DOI 10.1007/s11336-015-9448-y
2015 Beh EJ, Lombardo R, 'Confidence regions and approximate p-values for classical and non symmetric correspondence analysis', Communications in Statistics - Theory and Methods, 44 95-114 (2015)

Recently, a procedure was developed for constructing 100(1-a)% confidence ellipses for points in a low-dimensional plot obtained from performing classical correspondence analysis.... [more]

Recently, a procedure was developed for constructing 100(1-a)% 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-values of each of the points in this space. Such features enable the researcher to determine the statistical significance of a category to the association structure between the categorical variables being analyzed. They also reflect the information contained in dimensions higher than those that typically allow for a visual inspection of the association structure.

DOI 10.1080/03610926.2013.768665
2015 Beh EJ, Lombardo R, 'Confidence Regions and Approximate p-values for Classical and Non-Symmetric Correspondence Analysis', Communications in Statistics - Theory and Methods, 44 95-114 (2015) [C1]
DOI 10.1080/03610926.2013.768665
2015 Beh EJ, 'Applied Categorical and Count Data Analysis', Australian and New Zealand Journal of Statistics, 164-165 (2015)
2014 D'Ambra L, Beh EJ, Camminatiello I, 'Cumulative Correspondence Analysis of Two-Way Ordinal Contingency Tables', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 43 1099-1113 (2014) [C1]
DOI 10.1080/03610926.2012.670356
Citations Scopus - 1
2013 Beh EJ, Tran D, Hudson IL, 'A reformulation of the aggregate association index using the odds ratio', Computational Statistics and Data Analysis, 68 52-65 (2013) [C1]

Since its inception in the 1950s the odds ratio has become one of the most simple and popular measures available for analysing the association between two dichotomous variables. S... [more]

Since its inception in the 1950s the odds ratio has become one of the most simple and popular measures available for analysing the association between two dichotomous variables. Since the direction and magnitude of the association can be captured in such a simple measure, its impact has been felt throughout much of scientific research, in particular in epidemiology and clinical trials. Despite this, its applicability for analysing aggregate data has rarely been considered. In this paper we shall express a new measure of association (the aggregate association index, or AAI), in terms of the classic odds ratio. The advantage of doing so is that we are able to explore the use of the odds ratio in a context for which it was not originally intended, and that is for the analysis of a 2×2 table where only the aggregate data is known. © 2013 Published by Elsevier B.V. All rights reserved.

DOI 10.1016/j.csda.2013.06.009
Citations Scopus - 1
Co-authors Irene Hudson
2013 Rayner JCW, Thas O, Pipelers P, Beh EJ, 'Calculating bivariate orthonormal polynomials by recurrence', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 55 15-24 (2013) [C1]
DOI 10.1111/anzs.12011
Citations Scopus - 1
Co-authors John Rayner
2012 Smith DR, Beh EJ, 'Measuring 'risk' in occupational health studies: Standard methods and some alternatives for epidemiological research', Industrial Health, 50 463-465 (2012) [C3]
Citations Scopus - 2Web of Science - 2
Co-authors Derek Smith
2012 Beh EJ, 'Exploratory multivariate analysis by example using R [Book review]', Journal of Applied Statistics, 39 1381-1382 (2012) [C3]
DOI 10.1080/02664763.2012.657409
2012 Beh EJ, 'Simple correspondence analysis using adjusted residuals', Journal of Statistical Planning and Inference, 142 965-973 (2012) [C1]
Citations Scopus - 3Web of Science - 2
2012 Beh EJ, 'Biplots in Practice', JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY, 175 1073-1074 (2012) [C3]
DOI 10.1111/j.1467-985X.2012.01069_5.x
2012 Beh EJ, 'Biplots in practice [Book Review]', Journal of the Royal Statistical Society Series A -Statistics in Society, 175 1073-1074 (2012) [C3]
DOI 10.1111/j.1467-985X.2012.01069_5.x
2012 Beh EJ, Lombardo R, 'A genealogy of correspondence analysis', Australian & New Zealand Journal of Statistics, 54 137-168 (2012) [C1]
Citations Scopus - 1
2012 Beh EJ, Farver TB, 'The box-cox transformation and non-iterative estimation methods for ordinal log-linear models', Australian & New Zealand Journal of Statistics, 54 475-484 (2012) [C1]
2012 Beh EJ, Holdsworth CI, 'A visual evaluation of a classification method for investigating the physicochemical properties of Portuguese wine', Current Analytical Chemistry, 8 205-217 (2012) [C1]
Citations Scopus - 2
Co-authors Clovia Holdsworth
2012 Beh EJ, Farver TB, 'A numerical evaluation of the classification of Portuguese red wine', Current Analytical Chemistry, 8 218-223 (2012) [C1]
Citations Scopus - 2
2012 Smith DR, Beh EJ, 'Asbestos Kills - No Matter How You Cut the Data', ARCHIVES OF ENVIRONMENTAL & OCCUPATIONAL HEALTH, 67 187-188 (2012) [C3]
DOI 10.1080/19338244.2012.675791
Co-authors Derek Smith
2012 Duy T, Beh EJ, Smith DR, 'Real-World Occupational Epidemiology, Part 3: An Aggregate Data Analysis of Selikoff's "20-Year Rule"', ARCHIVES OF ENVIRONMENTAL & OCCUPATIONAL HEALTH, 67 243-248 (2012) [C1]
DOI 10.1080/10937404.2012.678766
Co-authors Derek Smith
2012 Tran DT, Beh EJ, Smith DR, 'Real-world occupational epidemiology, Part 3: An aggregate data analysis of Selikoff's '20-year rule'', Archives of Environmental & Occupational Health, 67 243-248 (2012) [C1]
Citations Scopus - 2Web of Science - 2
Co-authors Derek Smith
2012 Smith DR, Beh EJ, 'Asbestos kills - No matter how you cut the data', Archives of Environmental & Occupational Health, 67 187-188 (2012) [C3]
Citations Scopus - 3Web of Science - 3
Co-authors Derek Smith
2012 Beh EJ, Farver TB, 'A computational study assessing maximum likelihood and noniterative methods for estimating the linear-by-linear parameter for ordinal log-linear models', ISRN Computational Mathematics, 396831 (2012) [C1]
DOI 10.5402/2012/396831
2012 Beh EJ, Farver TB, 'On estimating the linear-by-linear parameter for ordinal log-linear models: A computational study', ISRN Computational Mathematics, 340415 (2012) [C1]
DOI 10.5402/2012/340415
2011 Beh EJ, Smith DR, 'Real World Occupational Epidemiology, Part 2: A Visual Interpretation of Statistical Significance', ARCHIVES OF ENVIRONMENTAL & OCCUPATIONAL HEALTH, 66 245-248 (2011) [C1]
DOI 10.1080/19338244.2011.564235
Citations Web of Science - 4
Co-authors Derek Smith
2011 Beh EJ, Smith DR, 'Real world occupational epidemiology, part 2: A visual interpretation of statistical significance', Archives of Environmental & Occupational Health, 66 245-248 (2011) [C1]
DOI 10.1080/19338244.2011.564235
Citations Scopus - 5Web of Science - 4
Co-authors Derek Smith
2011 Smith DR, Beh EJ, 'Occupational Epidemiology in the Real World: Irving Selikoff, Odds Ratios, and Asbestosis', Archives of Environmental and Occupational Health, 66 63-64 (2011) [C3]
DOI 10.1080/19338244.2010.533044
Citations Scopus - 5Web of Science - 6
Co-authors Derek Smith
2011 Beh EJ, Smith DR, 'Real world occupational epidemiology part 1: Odds ratios, relative risk, and asbestosis', Archives of Environmental and Occupational Health, 66 119-123 (2011) [C1]
DOI 10.1080/19338244.2011.564233
Citations Scopus - 8Web of Science - 7
Co-authors Derek Smith
2011 Smith DR, Beh EJ, 'Hirayama, passive smoking and lung cancer: 30 years on and the numbers still don't lie', Public Health, 125 179-181 (2011) [C3]
DOI 10.1016/j.puhe.2011.02.008
Citations Scopus - 6Web of Science - 6
Co-authors Derek Smith
2011 Lombardo R, Beh EJ, D'Ambra A, 'Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials', Journal of Applied Statistics, 38 2119-2132 (2011) [C1]
DOI 10.1080/02664763.2010.545118
Citations Scopus - 1
2011 Beh EJ, D'Ambra L, Simonetti B, 'Correspondence analysis of cumulative frequencies using a decomposition of Taguchi's statistic', Communications in Statistics -Theory and Methods, 40 1620-1632 (2011) [C1]
DOI 10.1080/03610921003615880
Citations Scopus - 2Web of Science - 1
2011 Beh EJ, Simonetti B, 'Investigating the European perception of food using moments obtained from non-symmetrical correspondence analysis', Journal of Statistical Planning and Inference, 141 2953-2960 (2011) [C1]
Citations Scopus - 1
2011 Beh EJ, Lombardo R, Simonetti B, 'A European perception of food using two methods of correspondence analysis', Food Quality and Preference, 22 226-231 (2011) [C1]
Citations Scopus - 6Web of Science - 4
2011 Beh EJ, 'Review: Understanding Biplots by John Gower, Sugnet Gardner-Lubbe and Niel Le Roux', Australian & New Zealand Journal of Statistics, 53 493-494 (2011) [C3]
2011 Beh EJ, 'Review: Biplots in Practice, by Michael Greenacre', Australian & New Zealand Journal of Statistics, 53 389-391 (2011) [C3]
2010 Beh EJ, 'The aggregate association index', Computational Statistics and Data Analysis, 54 1570-1580 (2010) [C1]
DOI 10.1016/j.csda.2010.01.006
Citations Scopus - 3Web of Science - 4
2010 Lombardo R, Beh EJ, 'Simple and multiple correspondence analysis for ordinal-scale variables using orthogonal polynomials', Journal of Applied Statistics, 37 2101-2116 (2010) [C1]
DOI 10.1080/02664760903247692
Citations Scopus - 3Web of Science - 2
2010 Simonetti B, Beh EJ, D'Ambra L, 'The analysis of dependence for three way contingency tables with ordinal variables: A case study of patient satisfaction', Journal of Applied Statistics, 37 91-103 (2010) [C1]
DOI 10.1080/02664760802653552
Citations Scopus - 1
2010 Beh EJ, 'Elliptical confidence regions for simple correspondence analysis', Journal of Statistical Planning and Inference, 140 2582-2588 (2010) [C1]
DOI 10.1016/j.jspi.2010.03.018
Citations Scopus - 6Web of Science - 3
2010 Hudson IL, Moore L, Beh EJ, Steel DG, 'Ecological inference techniques: An empirical evaluation using data describing gender and voter turnout at New Zealand elections, 1893-1919', Journal of the Royal Statistical Society Series A: Statistics in Society, 173 185-213 (2010) [C1]
DOI 10.1111/j.1467-985X.2009.00609.x
Citations Scopus - 2Web of Science - 5
Co-authors Irene Hudson
2010 Beh EJ, Farver TB, 'AN EVALUATION OF NON-ITERATIVE METHODS FOR ESTIMATING THE LINEAR-BY-LINEAR PARAMETER OF ORDINAL LOG-LINEAR MODELS (vol 51, pg 335, 2009)', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 52 241-242 (2010) [C3]
DOI 10.1111/j.1467-842X.2010.00579.x
2009 Gauci VJ, Beckhouse AG, Lyons V, Beh EJ, Rogers PJ, Dawes IW, Higgins VJ, 'Zinc starvation induces a stress response in Saccharomyces cerevisiae that is mediated by the Msn2p and Msn4p transcriptional activators', FEMS Yeast Research, 9 1187-1195 (2009) [C1]
DOI 10.1111/j.1567-1364.2009.00557.x
Citations Scopus - 4Web of Science - 3
2009 Rayner JC, Beh EJ, 'Towards a better understanding of correlation', Statistica Neerlandica, 63 324-333 (2009) [C1]
DOI 10.1111/j.1467-9574.2009.00425.x
Citations Scopus - 4Web of Science - 4
Co-authors John Rayner
2009 Beh EJ, D'Ambra L, 'Some interpretative tools for non-symmetric correspondence analysis', Journal of Classification, 26 55-76 (2009) [C1]
DOI 10.1007/s00357-009-9025-0
Citations Scopus - 7Web of Science - 4
2009 Rayner JC, Beh EJ, 'Components of Pearson's statistic for at least partially ordered m-way contingency tables', Journal of Applied Mathematics and Decision Sciences, 2009 1-9 (2009) [C1]
DOI 10.1155/2009/980706
Citations Scopus - 4
Co-authors John Rayner
2009 Beh EJ, Farver TB, 'An evaluation of non-iterative methods for estimating the linear-by-linear parameter of ordinal log-linear models', Australian and New Zealand Journal of Statistics, 51 335-352 (2009) [C1]
DOI 10.1111/j.1467-842X.2009.00549.x
Citations Scopus - 6Web of Science - 7
2008 Beh EJ, 'Simple correspondence analysis of nominal-ordinal contingency tables', Journal of Applied Mathematics & Decision Sciences, 2008 (2008) [C1]
DOI 10.1155/2008/218140
Citations Scopus - 5
2008 Amenta P, Simonetti B, Beh EJ, 'Single ordinal correspondence analysis with external information', Asian Journal of Mathematics and Statistics, 1 34-42 (2008) [C1]
DOI 10.3923/ajms.2008.34.42
2008 Beh EJ, 'Correspondence analysis of aggregate data: The 2x2 table', Journal of Statistical Planning and Inference, 138 2941-2952 (2008) [C1]
DOI 10.1016/j.jspi.2007.11.004
Citations Scopus - 5Web of Science - 6
2007 Beh EJ, Simonetti B, D'Ambra L, 'Partitioning a non-symmetric measure of association for three-way contingency tables', JOURNAL OF MULTIVARIATE ANALYSIS, 98 1391-1411 (2007) [C1]
DOI 10.1016/j.jmva.2007.01.011
Citations Scopus - 12Web of Science - 6
2007 Lombard R, Beh EJ, D'Ambra L, 'Non-symmetric correspondence analysis with ordinal variables using orthogonal polynomials', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 52 566-577 (2007) [C1]
DOI 10.1016/j.csda.2006.12.040
Citations Scopus - 21Web of Science - 13
2006 Peiris S, Beh EJ, 'Where statistics teaching can go wrong', CAL-laborate, 15 21-23 (2006) [C1]
2005 D'Ambra L, Beh EJ, Amenta P, 'Catanova for two-way contingency tables with ordinal variables using orthogonal polynomials', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 34 1755-1769 (2005) [C1]
DOI 10.1081/STA-200066325
Citations Scopus - 18Web of Science - 14
2005 Beh EJ, 'S-PLUS code for simple and multiple correspondence analysis', COMPUTATIONAL STATISTICS, 20 415-438 (2005) [C1]
DOI 10.1007/BF02741306
Citations Scopus - 4Web of Science - 1
2005 Beh EJ, Simonetti B, D'Ambra L, 'Three way ordinal NSCA analysis of patient satisfaction evaluation', Statistica & Applicazioni, 3 21-28 (2005)
2004 Beh EJ, 'Simple correspondence analysis: A bibliographic review', INTERNATIONAL STATISTICAL REVIEW, 72 257-284 (2004) [C1]
Citations Scopus - 38Web of Science - 35
2004 Beh EJ, 'S-PLUS code for ordinal correspondence analysis', COMPUTATIONAL STATISTICS, 19 593-612 (2004) [C1]
Citations Scopus - 3
2004 Beh EJ, Davy PJ, 'A non-iterative alternative to ordinal log-linear models', Journal of Applied Mathematics & Decision Science, 7 1-20 (2004) [C1]
DOI 10.1155/S1173912604000057
2004 Beh EJ, Davy PJ, 'A non-iterative alternative to ordinal log-linear models', Journal of Applied Mathematics and Decision Sciences, 8 67-86 (2004)

Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The... [more]

Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fitting and re-fitting to search for the best model. Another advantage is that quadratic and higher order effects can readily be included, in contrast to conventional log-linear models which incorporate linear terms only. The focus of the discussion is the application of the new parameter estimation technique to multi-way contingency tables with at least one ordered variable. This will also be done by considering singly and doubly ordered two-way contingency tables. It will be shown by example that the resulting parameter estimates are numerically similar to corresponding maximum likelihood estimates for ordinal log-linear models. Copyright© 2004, Lawrence Erlbaum Associates, Inc.

Citations Scopus - 9
2001 Beh EJ, 'Confidence circles for correspondence analysis using orthogonal polynomials', Journal of Applied Mathematics and Decision Sciences, 5 35-45 (2001) [C1]

An alternative approach to classical correspondence analysis was developed in [3] and involves decomposing the matrix of Pearson contingencies of a contingency table using orthogo... [more]

An alternative approach to classical correspondence analysis was developed in [3] and involves decomposing the matrix of Pearson contingencies of a contingency table using orthogonal polynomials rather than via singular value decomposition. It is especially useful in analysing contingency tables which are of an ordinal nature. This short paper demonstrates that the confidence circles of Lebart, Morineau and Warwick (1984) for the classical approach can be applied to ordinal correspondence analysis. The advantage of the circles in analysing a contingency table is that the researcher can graphically identify the row and column categories that contribute or not to the hypothesis of independence. Copyright© 2001, Lawrence Erlbaum Associates, Inc.

Citations Scopus - 7
2001 Beh EJ, 'Partitioning Pearson's chi-squared statistic for singly ordered two-way contingency tables', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 43 327-333 (2001) [C1]
DOI 10.1111/1467-842X.00179
Citations Scopus - 17Web of Science - 12
1999 Beh EJ, 'Correspondence analysis of ranked data', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 28 1511-1533 (1999) [C1]
DOI 10.1080/03610929908832370
Citations Scopus - 7Web of Science - 2
1999 Beh EJ, Davy PJ, 'Partitioning Pearson's chi-squared statistic for a partially ordered three-way contingency table', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 41 233-246 (1999) [C1]
DOI 10.1111/1467-842X.00077
Citations Scopus - 17Web of Science - 12
1998 Beh EJ, 'A comparative study of scores for correspondence analysis with ordered categories', BIOMETRICAL JOURNAL, 40 413-429 (1998) [C1]
DOI 10.1002/(SICI)1521-4036(199808)40:4<413::AID-BIMJ413>3.0.CO;2-V
Citations Scopus - 21Web of Science - 16
1998 Beh EJ, Davy PJ, 'Partitioning Pearson's chi-squared statistic for a completely ordered three-way contingency table', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 40 465-477 (1998) [C1]
DOI 10.1111/1467-842X.00050
Citations Scopus - 21Web of Science - 16
1997 Beh EJ, 'Simple Correspondence analysis of ordinal cross-classifications using orthogonal polynomials', Biometrical Journal, 39 589-613 (1997) [C1]
Citations Scopus - 32Web of Science - 27
Show 61 more journal articles

Conference (43 outputs)

Year Citation Altmetrics Link
2014 Tran D, Beh E, Hudson IL, 'Generalising Aggregate Association Index.its Connection With Odds Ratio And Association Measurements', Australian Statistical Conference. Abstracts, Sydney, NSW (2014) [E3]
Co-authors Irene Hudson
2014 Zafar S, Cheema S, Beh EJ, Hudson I, 'Some asymptotic properties of the non-iterative estimates of linear-by-linear association parameter', Abstracts Australian Statistical Conference in conjunction with the Institute of Mathematical Statistics Annual Meeting, Sydney (2014) [E3]
Co-authors Irene Hudson
2014 Tran D, Beh EJ, Hudson I, 'Generalising the aggregate association index: Its connection with the odds ratio and other common association measurements', Abstracts of Australian Statistical Conference in conjunction with the Institute of Mathematical Statistics Annual Meeting, Sydney (2014) [E3]
Co-authors Irene Hudson
2014 Cheema S, Beh EJ, Hudson I, 'Adjustment to the aggregate association index for large samples', Abstracts of the Australian Statistical Conference in conjunction with the Institute of Mathematical Statistics Annual Meeting, Sydney (2014) [E3]
Co-authors Irene Hudson
2014 Hudson IL, Cheema SA, Beh EJ, 'Adjustment to the aggregate association index for large samples', -, Sydney, NSW. Australia (2014) [E3]
Co-authors Irene Hudson
2014 Zafar S, Cheema S, Beh EJ, Hudson IL, 'Some Asymptotic Properties Of Non-iterative Estimates Of Linear-by-linear Association Parameter', Sixth Annual ASEARC Conference, University of Wollongong, NSW. Australia (2014) [E3]
Co-authors Irene Hudson
2013 Hudson IL, Cheema SA, Beh EJ, 'On issues concerning the assessment of information contained in aggregate data using the F-test', Proceedings of Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) 2013 conference, University of Newcastle, NSW, Australia (2013) [E3]
Co-authors Irene Hudson
2013 Zafar S, Beh EJ, Hudson IL, 'An overview of estimation for ordinal log-linear models', Proceedings of Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) 2013 conference, University of Newcastle, NSW, Australia (2013) [E3]
Co-authors Irene Hudson
2013 Tran DT, Beh E, Hudson I, 'Geographically clustering New Zealand electorates in the 1893 general election using data describing gender and voter turnout: an application of the Aggregate Association Index', Proceedings of the 49th ANZIAM Conference, Newcastle, NSW (2013) [E3]
Co-authors Irene Hudson
2013 Hudson IL, Beh EJ, Cheema S, Tran D, 'Adjusting the aggregate association index for large samples', Advances in Latent Variables: Proceedings of SIS 2013 Statistical Conference, Brescia, Italy (2013) [E1]
Co-authors Irene Hudson
2013 Beh EJ, Zafar S, Cheema S, Hudson IL, 'A Study of Bias for Non-Iterative Estimates of the Linear-by-Linear Association Parameter from the Ordinal Log-Linear Models', Advances in Latent Variables: Proceedings of the SIS 2013 Statistical Conference, Brescia, Italy (2013) [E1]
Co-authors Irene Hudson
2013 Hudson IL, Zafar S, Cheema SA, Beh EJ, Hudson SA, Abell AD, 'Linking ordinal log-linear models with Correspondence Analysis: an application to estimating drug-likeness in the drug discovery process', MODSIM2013, 20th International Congress on Modelling and Simulation, Adelaide, SA (2013) [E1]
Co-authors Irene Hudson
2013 Hudson IL, Tran D, Beh EJ, 'The Aggregate Association Index and its links with common measurements of association in a 2x2 table: An Analysis of Early NZ gendered voting data', MODSIM2013, 20th International Congress on Modelling and Simulation, Adelaide, South Australia (2013) [E1]
Co-authors Irene Hudson
2013 Hudson IL, Cheema SA, Beh EJ, 'On issues concerning the assessment of information contained in aggregate data using the F-statistics', MODSIM2013, 20th International Congress on Modelling and Simulation, Adelaide, SA (2013) [E1]
Co-authors Irene Hudson
2013 Beh EJ, Lombardo R, Guerrero L, 'Non-symmetric three-way correspondence analysis to analyse text data in a food context', Advances on Latent Variables - Methods, Models and Applications, Brescia, Italy (2013)
2012 Cheema SA, Beh EJ, Hudson IL, 'The aggregate informative index', Handbook. Australian Statistical Conference, Adelaide, SA (2012) [E3]
Co-authors Irene Hudson
2012 Tran DT, Beh EJ, Hudson IL, Moore L, 'Investigating the Aggregate Association Index for analysing voter turnout at New Zealand elections 1893-1920', Handbook. Australian Statistical Conference, Adelaide, SA (2012) [E3]
Co-authors Irene Hudson
2012 Zafar S, Beh EJ, Hudson IL, 'An overview of estimation for ordinal log-linear models', Handbook. Australian Statistical Conference, Adelaide, SA (2012) [E3]
Co-authors Irene Hudson
2012 Tran DT, Beh EJ, Hudson IL, 'The Aggregate Association Index and its Application in the 1893 New Zealand Election', Proceedings of the Fifth Annual ASEARC Conference: Looking to the Future, Wollongong, NSW (2012) [E1]
Co-authors Irene Hudson
2012 Beh EJ, Tran DT, Hudson IL, Moore L, 'The Aggregate Association Index and its extensions', Analysis and Modelling of Complex Data in Behavioural and Social Sciences, Anacapri, Italy (2012) [E3]
Co-authors Irene Hudson
2012 Lombardo R, Ringrose T, Beh EJ, 'Bootstrap confidence regions in classical and ordered multiple correspondence analysis', Analysis and Modelling of Complex Data in Behavioural and Social Sciences, Anacapri, Italy (2012) [E3]
2012 Camminatiello I, Beh EJ, D'Ambra L, 'A unified approach to simple correspondence analysis', Stochastic Modeling Techniques and Data Analysis, Crete (2012)
2011 Beh EJ, 'The odds ratio and aggregate data: The 2x2 contingency table', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference, Parramatta, NSW (2011) [E1]
2011 Beh EJ, Park L, Russell K, 'Conference editors', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference, Parramatta, NSW (2011) [E4]
2010 Beh EJ, Simonetti B, 'A few moments for non-symmetrical correspondence analysis: A European perception of food', AGROSTAT 2010: Proceedings of the 11th European Symposium on Statistical Methods for the Food Industry, Benevento, Italy (2010) [E1]
2009 Beh EJ, 'A few moments for simple correspondence analysis', ASEARC: Proceedings of the Third Annual ASEARC Research Conference, Newcastle, NSW (2009) [E1]
2009 Lombardo R, Beh EJ, 'Simple and multiple ordered correspondence analysis to evaluate customer satisfaction', ASEARC: Proceedings of the Third Annual ASEARC Research Conference, Newcastle, NSW (2009) [E1]
2008 Beh EJ, Lombardo R, Simonetti B, 'Model based methods for performing multi-way non-symmetric correspondence analysis', MTISD2008 - Methods, Models and Information Technologies for Decision Support Systems, Salento, Italy (2008)
2007 Mirto L, Thorpe GW, Beh EJ, Dawes IW, Higgins VJ, 'The age old mystery of aging ¿ a genome-wide functional analysis in Saccharomyces cerevisiae', Yeast, Melbourne (2007)
2006 Beh EJ, Simonetti B, D'Ambra L, 'The analysis of dependence for three way tables with ordinal variables in food industry evaluation', 9emes Journees Agro-Industrie et Methodes Statistiques, University of Sannio, Italy (2006)
2006 Beh EJ, Amenta P, Simonetti B, 'Single ordinal correspondence analysis with external information', 9emes Journees Agro-Industrie et Methodes Statistiques, University of Sannio, Italy (2006)
2006 D'Ambra L, Simonetti B, Beh EJ, 'A dimensional reduction method for ordinal three-way contingency table', COMPSTAT 2006: Proceedings in Computational Statistics, Rome, ITALY (2006)
DOI 10.1007/978-3-7908-1709-6_21
2005 Donegan K, Beh EJ, Murray P, 'Using correspondence analysis to detect or verify similar questions in a survey', Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong (2005)
2005 Beh EJ, 'A very brief history of correspondence analysis', Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong (2005)
2005 Beh EJ, D'Ambra L, 'Correspondence analysis as an explorative tool', Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong (2005)
2005 Beh EJ, 'Detecting outliers using correspondence analysis', Proceedings of the 55th Session of the International Statistical Institute, Sydney, Australia (2005)
2005 hudson I, Moore L, Beh EJ, Steel DG, 'Gendered counts of historical voting in New Zealand, 1893 - 1919: A rigorous statistical ecological (EI) approach', Proceedings of the 55th Session of the International Statistical Institute, Sydney, Australia (2005)
Co-authors Irene Hudson
2005 Beh EJ, D'Ambra L, Lombardo R, 'Decomposing Goodman-Kruskal's tau for ordinal categorical variables', Proceedings of the 55th Session of the International Statistical Institute, Sydney, Australia (2005)
2005 Donegan K, Beh EJ, Murray P, 'Using correspondence analysis to detect or verify similar questions in a survey', Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong (2005)
2005 Beh EJ, 'A very brief history of correspondence analysis', Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong (2005)
2005 Beh EJ, D'Ambra L, 'Correspondence analysis as an explorative tool', Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong (2005)
2003 Beh EJ, 'Coding categorical data for simple correspondence analysis', Current Research on Modelling, Data Mining and Quantitative Techniques, University of Western Sydney (2003)
2003 Davy PD, Rayner JCW, Beh EJ, 'Generalised correlations and Simpson's paradox', Current Research on Modelling, Data Mining and Quantitative Techniques, University of Western Sydney (2003)
Co-authors John Rayner
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Software (1 outputs)

Year Citation Altmetrics Link
2014 Lombardo Rosaria, Beh EJ, 'R Package ¿CAvariants¿', 1 (2014) [G1]

Thesis / Dissertation (1 outputs)

Year Citation Altmetrics Link
1999 Beh EJ, Correspondence Analysis Using Orthogonal Polynomials, University of Wollongong (1999)
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Grants and Funding

Summary

Number of grants 1
Total funding $5,000

Click on a grant title below to expand the full details for that specific grant.


20101 grants / $5,000

Advances in Categorical Data Analysis$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Associate Professor Eric Beh
Scheme New Staff Grant
Role Lead
Funding Start 2010
Funding Finish 2010
GNo G1000623
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed1
Current3

Total current UON EFTSL

PhD2.15

Current Supervision

Commenced Level of Study Research Title / Program / Supervisor Type
2013 PhD Quantification of the Extent of Association Between Dichotomous Variables Using Aggregate Data
Statistics, Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
2011 PhD The Aggregate Association Index and its Extensions in Ecological Inference and Correspondence Analysis
Statistics, Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
2011 PhD Non-Iterative Estimation Methods for Ordinal Log-Linear Models
Statistics, Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor

Past Supervision

Year Level of Study Research Title / Program / Supervisor Type
2015 PhD An Investigation of the Prevalence, Correlates and Potential Intervention Strategies for Musculoskeletal Disorders among School Teachers in Botswana
Public Health, Faculty of Health and Medicine, The University of Newcastle
Co-Supervisor
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Associate Professor Eric Beh

Position

Associate Professor
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Statistics

Contact Details

Email eric.beh@newcastle.edu.au
Phone 4921 5113
Fax (02) 4921 6898

Office

Room V130
Building Mathematics
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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