OJS  Vol.5 No.3 , April 2015
A Unified Approach for the Multivariate Analysis of Contingency Tables
Abstract: We present a unified approach to describing and linking several methods for representing categorical data in a contingency table. These methods include: correspondence analysis, Hellinger distance analysis, the log-ratio alternative, which is appropriate for compositional data, and the non-symmetrical correspondence analysis. We also present two solutions working with cummulative frequencies.
Cite this paper: Cuadras, C. and Cuadras, D. (2015) A Unified Approach for the Multivariate Analysis of Contingency Tables. Open Journal of Statistics, 5, 223-232. doi: 10.4236/ojs.2015.53024.

[1]   Cuadras, C.M. (2002) Correspondence Analysis and Diagonal Expansions in Terms of Distribution Functions. Journal of Statistical Planning and Inference, 103, 137-150.

[2]   Cuadras, C.M. and Cuadras, D. (2006) A Parametric Approach to Correspondence Analysis. Linear Algebra and its Applications, 417, 64-74.

[3]   Cuadras, C.M., Cuadras, D. and Greenacre, M. (2006) A Comparison of Different Methods for Representing Categorical Data. Communications in Statistics-Simulation and Computation, 35, 447-459.

[4]   Greenacre, M. (2009) Power Transformations in Correspondence Analysis. Computational Statistics and Data Analysis, 53, 3107-3116.

[5]   Cuadras, C.M. and Fortiana, J. (1996) Weighted Continuous Metric Scaling. In: Gupta, A.K. and Girko, V.L., Eds., Multidimensional Statistical Analysis and Theory of Random Matrices, VSP, The Netherlands, 27-40.

[6]   Cuadras, C.M., Fortiana, J. and Oliva, F. (1997) The Proximity of an Individual to a Population with Applications in Discriminant Analysis. Journal of Classification, 14, 117-136.

[7]   Goodman, L.A. (1993) Correspondence Analysis, Association Analysis, and Generalized Nonindependence Analysis of Contingency Tables: Saturated and Unsaturated Models, and Appropriate Graphical Displays. In: Cuadras, C.M. and Rao, C.R., Eds., Multivariate Analysis: Future Directions 2, Elsevier, Amsterdam, 265-294.

[8]   Beh, E.J. (2004) Simple Correspondence Analysis: A Bibliographic Review. International Statistical Review, 72, 257-284.

[9]   Benzecri, J.-P. (1976) L’Analyse des Donnees. II. L’Analyse des Correspondances. Deuxieme Edition. Dunod, Paris.

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

[11]   Lebart, L. and Saporta, G. (2014) Historical Elements of Correspondence Analysis and Multiple Correspondence Analysis. In: Blasius, J. and Greenacre, M., Eds., Visualization and Verbalization of Data, CRC Press, Taylor & Francis Group, New York, 31-44.

[12]   Cuadras, C.M., Fortiana, J. and Greenacre, M. (2000) Continuous Extensions of Matrix Formulations in Correspondence Analysis, with Applications to the FGM Family of Distributions. In: Heijmans, R.D.H., Pollock, D.S.G. and Satorra, A., Eds., Innovations in Multivariate Statistical Analysis, Kluwer Academic Publishers, Dordrecht, 101-116.

[13]   Cuadras, C.M. (2014) Nonlinear Principal and Canonical Directions from Continuous Extensions of Multidimensional Scaling. Open Journal of Statistics, 4, 132-149.

[14]   Greenacre, M. (2010) Log-Ratio Analysis Is a Limiting Case of Correspondence Analysis. Mathematical Geosciences, 42, 129-134.

[15]   Domenges, D. and Volle, M. (1979) Analyse Factorielle Spherique: Une Exploration. Annales de L’INSEE, 35, 3-84.

[16]   Rao, C.R. (1995) A Review of Canonical Coordinates and an Alternative to Correspondence Analysis Using Hellinger Distance. Questiio, 19, 23-63.

[17]   Beh, E.J. and D’Ambra, L. (2009) Some Interpretative Tools for Non-Symmetrical Correspondence Analysis. Journal of Classification, 26, 55-76.

[18]   Kroonenberg, P.M. and Lombardo, R. (1999) Nonsymmetric Correspondence Analysis: A Tool for Analyzing Contingency Tables with a Dependence Structure. Multivariate Behavioral Research, 34, 367-396.

[19]   Lauro, N. and D’Ambra, L. (1984) L’analyse non symetrique des correspondances. In: Diday, E., Jambu, M., Lebart, L., Pages, J. and Tomassone, R., Eds., Data Analysis and Informatics III, North Holland, Amsterdam, 433-446.

[20]   Aitchison, J. and Greenacre, M. (2002) Biplots of Compositional Data. Applied Statistics, 51, 375-392.

[21]   Greenacre, M. and Lewi, P. (2009) Distributional Equivalence and Subcompositional Coherence in the Analysis of Contingency Tables, Ratio-Scale Measurements and Compositional Data. Journal of Classification, 26, 29-54.

[22]   Greenacre, M. (2008) Dynamic Graphics of Parametrically Linked Multivariate Methods Used in Compositional Data Analysis. Universitat Pompeu Fabra, Barcelona.

[23]   Lewi, P.J. (1976) Spectral Mapping, a Technique for Classifying Biological Activity Profiles of Chemical Compounds. Arzneimittel Forschung—Drug Research, 26, 1295-1300.

[24]   Taguchi, G. (1974) A New Statistical Analysis for Clinical Data, the Accumulating Analysis in Contrast with the Chi-Square Test. Saishin Igaku (The New Medicine), 20, 806-813.

[25]   Nair, V.N. (1987) Chi-Square Type Tests for Ordered Categories in Contingency Tables. Journal of the American Statistical Association, 82, 283-291.

[26]   Beh, E.J., D’Ambra, L. and Simonetti, B. (2011) Correspondence Analysis of Cumulative Frequencies Using a Decomposition of Taguchi’s Statistic. Communications in Statistics-Theory and Methods, 40, 1620-1632.