Research Article Volume 4 Issue 10

Comparison between Simple Correspondence Analysis and Canonical Correspondence Analysis: Application in Public Health

Estefania J Guevara1, Melba L Vertel2* and Daniel E Tamara1

1 Department of Mathematics and Statistics, Faculty of Exact and Natural Sciences, National University of Colombia, Manizales, Colombia
2Department of Mathematics, Faculty of Education and Sciences, University of Sucre, Sincelejo, Colombia

*Corresponding Author: Melba L Vertel, Department of Mathematics, Faculty of Education and Sciences, University of Sucre, Sincelejo, Colombia.

Received: July 29, 2022; Published: September 28, 2022


The main objective of this work is to methodologically compare simple correspondence analysis (ACS) and canonical correspondence analysis (ACC) applied to frequency tables. A theoretical presentation of the weighted principal component analysis (PCA) is made under the "French school of data". The comparison of the two methods refers to putting them in parallel, since they do not point to exactly the same methodological objectives; properties, common and different elements of the methods are presented and illustrated with the example of Urbina and Londoño (2003). This analysis methodology is presented with an application in public health based on the work of Iriarte., et al. (2012). To execute the statistical techniques, the R software, the ade4 and FactoClass packages are used.

Keywords: Multivariate Data Analysis; Simple Correspondence Analysis; Canonical Analysis of Correspondences; Public Health; Statistical Language R


  1. Mendenhall W. “Statistics for administration and economics, Vol. III, I beroamerica, Mexico City” (1981).
  2. Spiegel M and D Murray. “Statistics, Vol. VII, Mc Graw Hill, Mexico City” (1991).
  3. Canavos G. “Probability and Statistics: Applications and Methods, Mc. Graw Hill” (1992).
  4. Walpole R and R Myers. “Probability and Statistics, Mc Graw Hill” (1997).
  5. Montgomery D and Runger C. “Probability and Statistics applied to Engineering, Mc. Graw Hill” (1996).
  6. Weimer P. “Statistics, CECSA” (1999).
  7. Martínez C. “Estadística y Muestreo, segunda edn, ECOE, Universidad Nacional de Colombia, Bogotá” (2004).
  8. Lebart L., et al. “Statisitique exploratoire multidimension, Dunod, Paris” (1995).
  9. Lebart L., et al. “Statistical data processing, Barcelona, Marcombo” (2000).
  10. Escofier B and J Pagès. “Single and multiple factor analysis. Objectives, methods and interpretation, University of the Basque Country, Bilbao” (1988-1998).
  11. Cabarcas G and C Pardo. “Multivariate statistical methods in social research, Cursillo, Statistics Symposium - Santa Marta. National University”. Department of Statistics (2001).
  12. Dray SyD. “Elèments d'interface entre analyses multivariées, systèmes d'information geographique et observations écologiques, PhD thesis, Universite Claude Bernard - Lyon 1 (2003).
  13. Chessel DyA and Dufour. “The ade4-package: implementing the duality diagram for ecologists”. Journal of Statistical Software 22 (2007): 1-20.
  14. Greenacre M. “Correspondence Analysis in Practice, 2nd edition, Chapman and Hall/CRC (2007).
  15. Pardo CE. “Euclidean geometry in statistics: methods in main axes, Department of Statistics, National University of Colombia, Bogotá”. Conference for the V Conference on Mathematics, Statistics and Didactics. Pedagogical and Technological University of Colombia (2008).
  16. Pardo CE and PDel Campo. “Combination of factorial methods and cluster analysis in R: the FactoClass package”. Revista Colombiana de Estadística 30 (2007).
  17. Díaz L and M Morales. “Statistical analysis of categorical data, master's thesis, Faculty of Sciences, Department of Statistics, National University of Colombia (2010).
  18. Husson F., et al. “Exploratory Multivariate Analysis by Example Using R, Chapman and Hall/CRC computer science y data analysis (2011).
  19. Hirschfeld HO. “A connection between correlation and contingency, Proceedings of the Cambridge Philosophical Society”. Mathematical and Physical Sciences 31 (1935): 520-524.
  20. Fisher R. “The precision of discriminant functions”. Annals of Eugenics 10 (1940): 422-429.
  21. Guttman L. “The quantification of a class of attributes: A theory and method of scale construction”. Social Science Research Council, New-York (1941): 319-348.
  22. Hayashi C. “On the quantification of qualitative data from the mathematic statistical point of view”. Annals of the Institute of Statistical Mathematics 2 (1950): 35-47.
  23. Nishisato S. “Analysis of Categorical Data: Dual Scaling and its Applications, University of Toronto Press, London (1980).
  24. Williams E. “Use of scores for the analysis of association in contingency tables”. Biometrika 39 (1952): 274-289.
  25. Hill M. “Reciprocal averaging: an eigenvector method of ordination”. Journal of Ecology 61 (1973): 237-249.
  26. Hill M. “Correspondence analysis: A neglected multivariate method. applied statistics”. Journal of the Royal Statistical Society Series C 23 (1974): 340-354.
  27. Benzecri J. “Statistical analysis as a tool to make patterns emerge from data, dans Watanabe S., ed”. Methodologies of Pattern Recognition (1969): 35-60.
  28. Cailliez F and yJ Pagès. “Introduction à l'analyse des données, SMASH, 9 rue Duban 75016 Paris”. (1976): 616.
  29. Tenenhaus M and YF Young. “An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data”. Psychometrika 50 (1985): 91-119.
  30. Escoufier Y. “The duality diagram: a means of better practical applications, Legendre. and L. Legendre, editors”. Development in numerical ecology, Springer Verlag, Berlin, Germany (1987): 139-156.
  31. Fine J. “Introduction to multidimensional data analysis from examples, Brochure, PRESTA: Programme de recherche et a'enseignement en statistique appliquée, Sao Carlos (1996).
  32. Fernández P. “The use of simple correspondence analysis (ACS) as an aid in the interpretation of data in archaeology. A case study”. Anthropological Bulletin, Universidad de Los Andes 55 (2002): 687-713 (2002).
  33. Becué M., et al. “Multiple factor analysis for contingency tables: study of mortality in the autonomous communities of Spain, National Congress of Statistics and Operations Research, Lleida 8 to 11 April (2003).
  34. Vertel M and CE Pardo. “Comparison between canonical correspondence analysis and multiple factor analysis in tables of continuous frequencies-variables, Master's Thesis, National University of Colombia, Faculty of Sciences”. Department of Statistics, Bogotá (2010).
  35. Ter-Braak C. “Canonical correspondence analysis: A new technique for multivariate direct gradient analysis”. Ecology (1986): 65.
  36. Chessel D., et al. “Propriétés the canonical analysis of correspondences; an illustration in hydrobiology”. Revue Statistique Appliquée4 (1987): 55-72.
  37. Lebreton J., et al. “Principal component and correspondence analyses with respect to instrumental variables: an overview of their role in studies of structure-activity and species-environment relationships”. Applied Multivariate Analysis in SAR and Environmental Studies (1991): 85-114.
  38. Dolédec S and YD Chessel. “Recent developments in linear ordination methods for environmental sciences”. Advances in Ecology, India 1 (1991): 133-155.
  39. Birks H and H Austin. “An annotated bibliography of canonical correspondence analysis and related constrained ordination methods, Botanical Institute, Norway”. All-Gaten 41, N-5007 Bergen, Bunch, K.J., Heneghan (1994).
  40. Pavoine S and YA Dufour. “Canonical correspondence analysis, a standard in ecology, CARME 2003: International Conference on Correspondence Analysis and Related Methods (2003): 63-64.
  41. Urbina J and M Londoño. “Distribution of the herpeto-fauna community associated with four areas with different degrees of disturbance on Gorgona Island, Colombian Pacific”. Revista de la Academia Colombiana de Ciencias 27 (2003): 105-112.
  42. Iriarte I., et al. “Seroprevalencia a leptospira spp patógeno en rodentes del área urbana de la ciudad de Sincelejo, Sucre, Memorias: XXII Simposio de Estadística UNAL”. Faculty of Sciences. Department of Statistics, Bucaramanga (2012).
  43. Castellar A., et al. “Identification of leptospira interrogans in a population of rodents from two localities of the municipality of sincelejo, degree work, University of Sucre (2012).
  44. Perez A., et al. “Identification of leptospira interrogans by polymerase chain reaction (pcr) in a population of rodents in the municipality of sincelejo, Degree work, University of Sucre” (2013).
  45. R Development Core Team T: “A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2007).
  46. et al. “Coexistence and Dynamical Connections between Hyperchaos and Chaos in the4D Rössler System: A Computer-Assisted Proof”. SIAM Journal of Applied Dynamical Systems1 (2016): 356-390.


Citation: Melba L Vertel., et al. “Comparison between Simple Correspondence Analysis and Canonical Correspondence Analysis: Application in Public Health".Acta Scientific Computer Sciences 4.10 (2022): 74-81.


Copyright: © 2022 Melba L Vertel., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


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