Understanding Biplots

Understanding Biplots

Volumn , Issue , 2010, Pages 1-463

  Gower, John ^a   Lubbe, Sugnet ^b   le Roux, Niël ^c  

^a OPEN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF CAPE TOWN   (South Africa)

^c STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85133741692     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470973196     Document Type: Book

References (89)

1. Aldrich, C., Gardner, S. and le Roux, N.J. (2004) Monitoring of metallurgical process plants by using biplots. American Institute of Chemical Engineers Journal, 50, 2167-2186.
2. Bailey, R.A. and Gower, J.C. (1990) Approximating a symmetric matrix. Psychometrika, 55, 665-675.
3. Baraitser, A.M. and Obholzer, A. (1981) Cape Country Furniture. Cape Town: Struik.
4. Barbezat, D.A. and Hughes, J.W. (2005) Salary structure effects and the gender pay gap in academia. Research in Higher Education, 46, 621-640.
5. Bayer, A.E. and Astin, H.E. (1975) Sex differentials in the academic reward system. Science, 188, 796-802.
6. Benzécri, J.-P. (1973) L’Analyse des Données (2 volumes). Paris: Dunod.
7. Blackman, J.A., Bingham, J. and Davidson, J.L. (1978) Response of semi-dwarf and conventional winter wheat varieties to the application of nitrogen fertilizer. Journal of Agricultural Science, Cambridge, 90, 543-550.
8. Blasius, J., Eilers, P.H.C. and Gower, J.C. (2009) Better biplots. Computational Statistcs and Data Analysis, 53, 3145-3158.
9. Borg, I. and Groenen, P.J.F. (2005) Modern Multidimensional Scaling (2nd edition). New York:Springer.
10. Botha, A. (1977) Herkoms van die Kaapse Stoel. Cape Town: A.A. Balkema.
11. Bradu, D. and Gabriel, K.R. (1978) The biplot as a diagnostic tool for models of two-way tables. Technometrics, 20, 47-68.
12. Burden, M., Gardner, S., le Roux, N.J. and Swart, J.P.J. (2001) Ou-Kaapse meubels en stinkhoutidentifikasie:moontlikhede met kanoniese veranderlike-analise en bistippings. South African Journal of Cultural History, 15, 50-73.
13. Clarke, C.R.E., Morris, A.R., Palmer, E.R., Barnes, R.D., Baylis, W.B.H., Burley, J., Gourlay, I.D., O’Brien, E., Plumptre, R.A. and Quilter, A.K. (2003) Effect of Environment on Wood Density and Pulp Quality of Five Pine Species Grown in Southern Africa. Tropical Forestry Papers No 43. Oxford: Oxford Forestry Institute, Department of Plant Sciences, University of Oxford.
14. Constantine, A.G. and Gower, J.C. (1978) Graphical representation of asymmetry. Applied Statistics, 27, 297-304.
15. Cook, R.D. and Weisberg, S. (1982) Residuals and Influence in Regression. London:Chapman & Hall.
16. Cox, T.F. and Cox, M.A. (2001) Multidimensional Scaling (2nd edition). Boca Raton, FL:Chapman & Hall/CRC.
17. Cramér, H. (1946) Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press.
18. De Leeuw, J. (1977) Applications of convex analysis to multidimensional scaling. In J.R. Barra et al. (eds), Recent Developments in Statistics, pp. 133-145. Amsterdam: North Holland.
19. Eckart, C. and Young, G. (1936) The approximation of one matrix by another of lower rank. Psychometrika, 1, 211-218.
20. Eilers, P.H.C. and Goeman, J.J. (2004) Enhancing scatterplots with smoothed densities. Bioinformatics, 20, 623-628.
21. Fang, K.T., Kotz, S. and Ng, K.W. (1990) Symmetric Multivariate and Related Distributions. Boca Raton, FL: Chapman & Hall/CRC.
22. Flury, B. (1988) Common Principal Components and Related Multivariate Models. New York:John Wiley & Sons, Inc.
23. Flury, B. (1997) A First Course in Multivariate Statistics. New York: Springer.
24. Gabriel, K.R. (1971) The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453-467.
25. Gabriel, K.R. (2002) Goodness of fit of biplots and correspondence analysis. Biometrika, 89, 423-436.
26. Gardner, S., le Roux, N.J., Rypstra, T. and Swart, J.P.J. (2005) Extending a scatterplot for displaying group structure in multivariate data: a case study. ORiON, 21, 111-124.
27. Gardner-Lubbe, S., le Roux, N.J. and Gower, J.C. (2008) Measures of fit in principal component and canonical variate analyses. Journal of Applied Statistics, 35, 947-965.
28. Gifi, A. (1990) Nonlinear Multivariate Analysis. Chichester: John Wiley & Sons, Ltd.
29. Goldberg, K.M. and Iglewicz, B. (1992) Bivariate extensions of the boxplot. Technometrics, 34, 307-320.
30. Good, P. (2000) Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses (2nd edition). Berlin: Springer-Verlag.
31. Gordon, N., Morton, T. and Braden, I. (1974) Is there discrimination by sex, race and discipline? American Economic Review, 64, 419-427.
32. Gower, J.C. (1968) Adding a point to vector diagrams in multivariate analysis. Biometrika, 55, 582-585.
33. Gower, J.C. (1977) The analysis of asymmetry and orthogonality. In J.R. Barra et al. (eds), Recent Developments in Statistics, pp. 109-123. Amsterdam: North Holland.
34. Gower, J.C. (1982) Euclidean distance geometry. Mathematical Scientist, 7, 1-14.
35. Gower, J.C. (1990) Three dimensional biplots. Biometrika, 77, 773-785.
36. Gower, J.C. (1992) Generalized biplots. Biometrika, 79, 475-493.
37. Gower, J.C. (1993) The construction of neighbour-regions in two dimensions for prediction with multi-level categorical variables. In O. Opitz, B. Lausen and R. Klar (eds), Information and classification: Concepts-Methods-Applications. Proceedings 16th Annual conference of the Gesellschaft f ür Klassifikation, Dortmund, April 1992, pp. 174-189. Heidelberg:Springer.
38. Gower, J.C. (2004) The geometry of biplot scaling. Biometrika, 91, 705-714.
39. Gower, J.C. (2006) Divided by a common language: Analyzing and visualizing two-way arrays. In M. Greenacre and J. Blasius (eds), Multiple Correspondence Analysis and Related Methods, pp. 77-106. Boca Raton, FL: Chapman & Hall/CRC.
40. Gower, J.C. (2008) Asymmetry analysis: The place of models. In K. Shigemasu et al. (eds), New Trends in Psychometrics, pp. 69-78. Tokyo: Universal Academy Press.
41. Gower, J.C. and Dijksterhuis, G.B. (2004) Procrustes Problems. Oxford: Oxford University Press.
42. Gower, J.C. and Hand, D.J. (1996) Biplots. London: Chapman & Hall.
43. Gower, J.C. and Harding, S. (1988) Nonlinear biplots. Biometrika, 75, 445-455.
44. Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5-48.
45. Gower, J.C. and Ngouenet, R.F. (2005) Nonlinearity effects in multidimensional scaling. Journal of Multivariate Analysis. 94, 344-365.
46. Gower, J.C., Meulman, J.J. and Arnold, G.M. (1999) Non-metric linear biplots. Journal of Classification, 16, 181-196.
47. Gower, J.C., Groenen, P.J.F. and Van de Velden, M. (2010) Area biplots. Journal of Computational and Graphical Statistics, 19, 46-61.
48. Green, P.J. (1985) Peeling data. In S. Kotz and N.L. Johnson (eds), Encyclopedia of Statistical Science, Volume 6, pp. 660-664. New York: John Wiley & Sons, Inc.
49. Greenacre, M.J. (1984) Theory and Applications of Corresepondence Analysis. London: Academic Press.
50. Greenacre, M.J. (1988) Correspondence analysis of multivariate categorical data by weighted least squares. Biometrika, 75, 457-467.
51. Greenacre, M.J. (2007) Correspondence Analysis in Practice (2nd edition). Boca Raton, FL:Chapman & Hall/CRC.
52. Heiser, W.J. and De Leeuw, J. (1977) How to use SMACOF-1. Research Report. Leiden: Department of Data Theory, University of Leiden.
53. Hills, M. (1969) On looking at large correlation matrices. Biometrika, 56, 249-253.
54. Hirschfeld, H.O. (1935) A connection between correlation and contingency. Proceedings of the Cambridge Philosophical Society, 31, 520-524.
55. Hyndman, R.J. (1996) Computing and graphing highest density regions. American Statistician, 50, 120-126.
56. Jolliffe, I.T. (2002) Principal Component Analysis (2nd edition). New York: Springer.
57. Jorion, P. (1997) Value at Risk. New York: McGraw-Hill.
58. Kempton, R.A. (1984) The use of biplots in interpreting variety by environment interactions. Journal of Agricultural Science, Cambridge, 103, 123-135.
59. Krzanowski, W.J. (2004) Biplots for multifactorial analysis of distance. Biometrics, 60, 517-524.
60. Lawley, D.N. and Maxwell, A.E. (1971) Factor Analysis as a Statistical Method (2nd edition). London: Butterworths.
61. Le Roux, B. and Rouanet, H. (2004) Geometric Data Analysis: From Correspondence Analysis to Structured Data. Dordrecht: Kluwer.
62. Le Roux, N.J. and Gardner, S. (2005) Analysing your multivariate data as a pictorial: a case for applying biplot methodology? International Statistical Review, 73, 365-387.
63. Liu, R.Y., Parelius, J.M. and Singh, K. (1999) Multivariate analysis by data depth: descriptive statistics, graphics and inference. Annals of Statistics, 27, 783-858.
64. McNabb, R. and Wass, V. (1997) Male-female salary differentials in British universities. Oxford Economic Papers, New Series, 49, 328-343.
65. Pison, G., Struyf, A. and Rousseeuw, P.J. (1999) Displaying a clustering with CLUSPLOT. Computational Statistics and Data Analysis, 30, 381-392.
66. R Development Core Team (2009) R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. http://www.R-project.org
67. Rao, C.R. (1952) Advanced Statistical Methods in Biometric Research. New York: John Wiley & Sons, Inc.
68. Rothkopf, E.Z. (1957) A measure of stimulus similarity and errors in some paired-associate learning. Journal of Experimental Psychology, 53, 94-101.
69. Rousseeuw, P.J. and Ruts, I. (1997) The bagplot: a bivariate box-and-whiskers plot. Technical report. Antwerp: Department of Mathematics and Computer Science, Universitaire Instelling Antwerpen. http://win-www.uia.ac.be/u/statis/
70. Rousseeuw, P.J., Ruts, I. and Tukey, J.W. (1999) The bagplot: a bivariate boxplot. American Statistician, 53, 382-387.
71. Ruts, I. and Rousseeuw, P.J. (1996) Computing depth contours of bivariate point clouds. Computational Statistics and Data Analysis, 23, 153-168.
72. Scott, D.W. (1992) Multivariate Density Estimation. New York: John Wiley & Sons, Inc.
73. Shepard, R, N. and Carroll, J.D. (1966). Parametric representation of nonlinear data structures. In P.R. Krishnaiah (ed.), Multivariate Analysis, pp. 561-592. New York: Academic Press.
74. Silvey, S.D., Titterington, D.N. and Torsney, B. (1978) An algorithm for optimal designs on a finite design space. Communications in Statistics: Theory and Methods, A7, 1379-1389.
75. Swart, J.P.J. (1980) Non-destructive wood sampling methods from living trees: a literature survey. IAWA Bulletin. 1-2, 42.
76. Swart, J.P.J. (1985) ʼn Sistematies-houtanatomiese ondersoek van die Lauracea in Suidelike Afrika. Unpublished MSc thesis, Department of Wood Science, Stellenbosch University, South Africa.
77. Swart, J.P.J. and Van der Merwe, J.J.M. (1980) Embuia-Ocotea porosa en nie Phoebe porosa nie. South African Forestry Journal, 114, 75.
78. Titterington, D.N. (1976) Algorithms for computing D-optimal design on finite design spaces. In Proceedings of the 1976 Conference on Information Science and Systems, pp. 213-216. John Hopkins University, Baltimore, MD.
79. Toutkoushian, R.K. (1998) Racial and marital status differences in faculty pay. Journal of Higher Education, 69, 513-541.
80. Toutkoushian, R.K. (1999) The status of academic women in the 1990s: no longer outsiders, but not yet equals. The Quarterly Review of Economics and Finance, 39, 679-698.
81. Underhill, L.G. (1990) The coefficient of variation biplot. Journal of Classification, 7, 41-56.
82. Van Blerk, S.P. (2000) Generalising Biplots and its Applications in S-Plus. Unpublished MComm thesis, Department of Statistics and Actuarial Science, Stellenbosch University, South Africa.
83. Van der Berg, S., Wood, L. and le Roux, N. (2002). Differentiation in black education. Development Southern Africa, 19, 289-306.
84. Venables, W.N. and Ripley, B.D. (2002) Modern Applied Statistics with S (4th edition). New York:Springer.
85. Walters, I.S. and le Roux, N.J. (2008) Monitoring gender remuneration inequalities in academia using biplots. OriON, 24, 49-73.
86. Ward, M. (2001) The gender salary gap in British academia. Applied Economics, 33, 1669-1681.
87. Warman, C., Woolley, F. and Worswick, C. (2006) The evolution of male-female wages differentials in Canadian universities: 1970-2001. Queen’s Economics Department Working Paper No. 1099. Department of Economics, Queen’s University.
88. Wurz, S., le Roux, N.J., Gardner, S. and Deacon, H.J. (2003) Discriminating between the end products of the earlier Middle Stone Age sub-stages at Klasies River using biplot methodology. Journal of Archaeological Science, 30, 1107-1126.
89. Zani, S., Riani, M. and Corbellini, A. (1998) Robust bivariate boxplots and multiple outlier detection. Computational Statistics and Data Analysis, 28, 257-270.