Biplots: qualititative data

A previous paper, Biplots: Quantitative data, dealt exclusively with biplots for quantitative data. This paper is mainly concerned with qualitative data or data in the form of counts. Qualitative data can be nominal or ordinal, and it is usually reported in a coded numerical form. In the analysis of qualitative data, many methods can be grouped as quantification methods (e.g., categorical principal component analysis, correspondence analysis, multiple correspondence analysis, homogeneity analysis): transforming qualities into quantitative values that may then be treated with quantitative methods. All the features of quantitative biplots are found in qualitative biplots, but calibrated interpolation axes become labeled category‐level points and calibrated prediction axes become prediction regions. Interpretation remains in terms of distance, inner products, and sometimes area. WIREs Comput Stat 2016, 8:82–111. doi: 10.1002/wics.1377

[1]  Casper J. Albers,et al.  Visualising interactions in bi- and triadditive models for three-way tables , 2017 .

[2]  John C. Gower,et al.  Biplots: quantitative data , 2015 .

[3]  John C. Gower,et al.  The analysis of distance of grouped data with categorical variables: Categorical canonical variate analysis , 2014, J. Multivar. Anal..

[4]  Casper J. Albers,et al.  A contribution to the visualisation of three-way arrays , 2014, J. Multivar. Anal..

[5]  Michael C. Hout,et al.  Multidimensional Scaling , 2003, Encyclopedic Dictionary of Archaeology.

[6]  John C. Gower,et al.  Understanding Biplots: Gower/Understanding Biplots , 2011 .

[7]  P. Kroonenberg.  Applied Multiway Data Analysis , 2008 .

[8]  John C. Gower,et al.  A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis , 2006, Comput. Stat. Data Anal..

[9]  Snigdhansu Chatterjee,et al.  Procrustes Problems , 2005, Technometrics.

[10]  John C. Gower,et al.  The geometry of biplot scaling , 2004 .

[11]  B. L. Roux,et al.  Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis , 2004 .

[12]  ten Josephus Berge,et al.  Review of: J.C. Gower & G.B. Dijksterhuis: Procrustes Problems, Oxford University Press. , 2004 .

[13]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[14]  K. Ruben Gabriel,et al.  Goodness of fit of biplots and correspondence analysis , 2002 .

[15]  J C Gower.  The role of constraints in determining optimal scores. , 1998, Statistics in medicine.

[16]  Fred A. van Eeuwijk,et al.  MULTIPLICATIVE INTERACTION IN GENERALIZED LINEAR MODELS , 1995 .

[17]  M. Greenacre.  Correspondence analysis in practice , 1993 .

[18]  B. Francis,et al.  Algorithmic approaches for fitting bilinear models. , 1992 .

[19]  J. Gower.  FISHER'S OPTIMAL SCORES AND MULTIPLE CORRESPONDENCE ANALYSIS , 1990 .

[20]  A. Gifi,et al.  NONLINEAR MULTIVARIATE ANALYSIS , 1990 .

[21]  B. Flury.  Common Principal Components and Related Multivariate Models , 1988 .

[22]  M. Greenacre.  Correspondence analysis of multivariate categorical data by weighted least-squares , 1988 .

[23]  Jan L. A. van Rijckevorsek,et al.  Component and correspondence analysis: dimension reduction by functional approximation , 1988 .

[24]  J. Gower,et al.  Metric and Euclidean properties of dissimilarity coefficients , 1986 .

[25]  Sidney Addelman,et al.  trans-Dimethanolbis(1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionato)zinc(II) , 2008, Acta crystallographica. Section E, Structure reports online.

[26]  Forrest W. Young,et al.  Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features , 1976 .

[27]  M. J. R. Healy,et al.  An approach to the scaling of categorized attributes , 1976 .

[28]  O. L. Davies,et al.  Design and analysis of industrial experiments , 1954 .

[29]  L. Guttman,et al.  The Quantification of a class of attributes : A theory and method of scale construction , 1941 .

[30]  M. Kendall.  Statistical Methods for Research Workers , 1937, Nature.