A Geneaology of Correspondence Analysis: Part 2 - The Variants


Abstract


In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis,
a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analyse
the association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development of
correspondence analysis across all areas of research.

DOI Code: 10.1285/i20705948v12n2p542

Keywords: Correspondence analysis, dual scaling, optimal scaling, reciprocal averaging, R, history of statistics

References


Beh, E. J. (2001). Partitioning Pearson's chi-squared statistic for singly ordered two-way contingency tables. The Australian and New Zealand Journal of Statistics, 43, 327 -333.

Best, D. J. and Rayner, J. C. W. (1996). Nonparametric analysis for doubly ordered two-way contingency tables. Biometrics, 52, 1153 - 1156.

Braga, J., Chabadel, O., Sonan, N.K. and Gueramy, A. (2005). Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions.

International Journal of Legal Medicine, 119, 260 - 274.

Carrol, J. D., Green, P. E. and Schaer, C. M. (1986). Interpoint distance comparisons in correspondence analysis. Journal of Marketing Research, 23, 271 - 280.

Carrol, J. D., Green, P. E. and Schaer, C. M. (1987). Comparing interpoint distances in correspondence analysis: A clarication. Journal of Marketing Research, 24, 445 -

Carrol, J. D., Green, P. E. and Schaer, C. M. (1989). Reply to Greenacre's commentary on the Carroll-Green-Schaer scaling of two-way correspondence analysis solutions.

Journal of Marketing Research, 26, 366 - 368.

De Tibeiro, J. J. S. and Murdoch, D. J. (2010). Correspondence analysis with incomplete

paired data using Bayesian imputation. Bayesian Analysis, 5, 519 - 532.

Egger, J., Gall, M., Wallner, J., Boechat, P., Hann, A., Li, X., Chen, X. and Schmalstieg, D. (2017). HTC Vive MeVisLab integration via OpenVR for medical applications.

PLoS ONE, 12(3): e0173972, 14 pages.

Freeman, M. F. and Tukey, J. W. (1950). Transformations related to the angular and square root. Annals of Mathematical Statistics, 21, 607-611.

Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58, 453 - 467.

Gi, A. (1990). Nonlinear Multivariate Analysis Wiley.

Goodman, L. A. and Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49, 732 - 764.

Gray, L.N. and Williams, J.S. (1981). Goodman and Kruskal b multiple and partial analogs. Proceedings of the Social Statistics Section, 10, 50 - 62.

Greenacre, M. (2010). Biplots in Practice. Bilbao: Fundacion BBVA.

Greenacre, M. J. (1984). Theory and Applications of Correspondence Analysis. London: Academic Press.

Greenacre, M. J. (1989). The Carroll-Green-Schaer scaling in correspondence analysis: a theoretical and empirical appraisal. Journal of Marketing Research, 26, 358 - 365.

Electronic Journal of Applied Statistical Analysis 51

Hilfert, T. and Konig, M. (2016). Low-cost virtual reality environment for engineering and construction. Visualization in Engineering, 4(2), 18 pages.

Kendall, D. G. (1971). Seriation. In Mathematics in the Archaeological and Historical Sciences, eds. F. R. Hodson, D. G. Kendall, P. Tauti, pp. 215 - 252, University Press.

Kroonenberg, P. M. (2008). Applied Multiway Data Analysis. Chichester: Wiley.

Krishnam, A., Williams, L. J., Mcintosh, A. R. and Abdi, H. (2011). Partial Least Squares (PLS) methods for neuroimaging: A tutorial and review. NeuroImage, 56,

- 475.

Lancaster, (1953). A reconciliation of 2, considered from metrical and enumerative aspects. Sankya, 13, 1 - 10.

Lombardo, R. (2011). Three-way association measure decompositions: the Delta index. Journal of Statistical Planning and Inference, 141, 1789 - 1799.

Merchant, Z., Goetz, E. T., Cifuentes, L., Keeney-Kennicutt, W. and Davis, T. J. (2014).

Eectiveness of virtual reality-based instruction on students' learning outcomes in K-12 and higher education: A meta-analysis. Computers & Education, 70, 29 - 40.

Marcotorchino, F. (1985). Utilisation des Comparaisons par Paires en Statistique des Contingencies: Partie III. Report F081, Etude du Centre Scientique, IBM, France.

Moglia, A., Ferrari, V., Morelli, L., Ferrari, M., Mosca, F. and Cuschieri, A. (2016). A systematic review of virtual reality simulators for robot-assisted surgery. European

Urology, 69, 1065 - 1080.

Nenadic, O. and Greenacre, M. (2007). Correspondence analysis in R, with two- and three-dimensional graphics: The ca package. Journal of Statistical Software, 20(3), 13

pages.

Niehorster, D. C., Li, L. and Lappe, M. (2017). The accuracy and precision of position and orientation tracking in the HTC Vive virtual reality system for scientic research.

i-Perception, May-June 2017, 1 - 13.

Nishisato, S. (1994). Elements of Dual Scaling: An Introduction to Practical Data Analysis. Hillsdale, N. J.: Lawrence Erlbaum Associates.

Nishisato, S. (2007). Multidimensional Descriptive Non-Linear Analysis. London: Chapman & Hall/CRC.

Rayner, J. C. W. and Best, D. J. (2000). Analysis of singly ordered two-way contingency tables. Journal of Applied Mathematics & Decision Sciences, 4, 83 - 98.

Tenenhaus, M. and Young, F. (1985). An analysis and synthesis of multiple correspondence

analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data. Psychometrika, 50, 91 - 119.

Taguchi, G. (1966). Statistical Analysis. Tokyo: Maruzen. (In Japanese).

Taguchi, G. (1974). A new statistical analysis for clinical data, the accumulating analysis, in contrast with the chi-square test. Saishin Igaku, 29, 806 - 813.

Tucker, L.R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279-311.

Van Der Heijden, P. G. M. and De Leeuw, J. (1985). Correspondence analysis used complementary to loglinear analysis. Psychometrika, 50, 429 - 447.

Van Der Heijden, P. G. M., De Falguerolles, A. and De Leeuw, J. (1989). A combined approach to contingency table analysis using correspondence analysis and log-linear

analysis. Applied Statistics, 38, 249 - 292.

Velev, D. and Zlateva, P. (2017). Virtual reality challenges in education and training. International Journal of Learning and Teaching, 3, 33 - 37.

Weber, A. (1929). The Theory of Location of Industry Chicago University Press.

Whittaker, R. H. (1967). Gradient analysis of vegetation. Biological Review, 42, 207 -264.


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