Produces a biplot from a set of variates (S.A. Harding).
Options
PRINT = string tokens |
Printed output from the analysis (singular, scores); default * i.e. no output |
|---|---|
GRAPHICS = string token |
What sort of graphics to use (lineprinter, highresolution); default high |
WINDOW = scalar |
Window number for the graph; default 3 |
SCREEN = string token |
Whether to clear the screen before plotting or to continue plotting on the old screen (clear, keep); default clea |
METHOD = string token |
Type of analysis required (principalcomponent, variate, diagnostic); default prin |
STANDARDIZE = string tokens |
Whether to centre the configurations (at the origin), and/or to normalize them (to unit sum of squares) prior to analysis (centre, normalize); default cent, norm |
LABELS = factor or text |
Labels to identify the points for the individuals |
VLABELS = factor or text |
Labels to identify the points for the variates |
NDIMENSIONS = scalar |
Number of dimensions to save with COORDINATES and VCOORDINATES; default 2 |
Parameters
DATA = pointers |
Each pointer contains a set of variates to be analysed |
|---|---|
COORDINATES = matrices |
Used to store the scores for the individuals |
VCOORDINATES = matrices |
Used to store the scores for the variates |
Description
BIPLOT produces a graphical representation of the relationships between data units and variates, as described by Gabriel (1971).
The data for the procedure consist of a set of variates, contained in a pointer specified by the DATA parameter. The data may be centred at the origin and/or normalized before plotting, by setting the STANDARDIZE option. The variates must not contain any missing values, nor should they be restricted. The values of the variates remain unaltered on exit from the procedure. The METHOD option allows the user to select which form of the biplot is to be plotted: principal component, variate, or diagnostic biplot.
Printed output is controlled by the option PRINT with settings: singular to print the singular values, and scores to print the scores. By default, nothing is printed.
The GRAPHICS option controls whether the biplot is plotted in high-resolution or line-printer styles; or setting GRAPHICS=* suppresses the plot. The WINDOW option specifies the window to use for a high-resolution plot (default 3), and the SCREEN option controls whether or not to clear the screen first (default clear).
Results from the analysis can be saved using the parameters COORDINATES and VCOORDINATES. The structures specified for these parameters need not be declared in advance. The number of dimensions that are saved is specified by the NDIMENSIONS option; default 2.
Options: PRINT, GRAPHICS, WINDOW, SCREEN, METHOD, STANDARDIZE, LABELS, VLABELS, NDIMENSIONS.
Parameters: DATA, COORDINATES, VCOORDINATES.
Method
The biplot (Gabriel, 1971) is a graphical representation of the relationships between n individuals and between p variates. If these variates are arranged as a matrix X (n × p), the singular value decomposition of X ( X = U S V ′ ) is used to express the least-squares approximation to X in two dimensions in the form X2 = A B ′, where X2 is (n × 2); A (n × 2) and B (p × 2) are given by the first two columns of ( U Sr ) and ( V S(1-r) ) respectively. The matrices A and B give the coordinates of the row and column markers, and the constant r can be set to either 0, 0.5, or 1 to obtain the form of the biplot requested by the METHOD option.
Action with RESTRICT
The variates must not be restricted.
References
Gabriel, K.R. (1971). The biplot graphic display of matrices with application to pricipal component analysis. Biometrika, 58, 453.
Gower, J.C. and Digby, P.G.N. (1981). Expressing Complex Relationships in Two Dimensions. In: Interpreting Multivariate Data (ed. V. Barnett). Wiley, New York.
See also
Procedures: DBIPLOT, CABIPLOT, CRBIPLOT, CRTRIPLOT.
Commands for: Multivariate and cluster analysis, Graphics.
Example
CAPTION 'BIPLOT example'; STYLE=meta VARIATE [NVALUES=20] v[1...7] READ v[] 4.0 11.0 4.0 28.0 31.0 17.0 21.0 5.0 11.0 5.0 29.0 30.0 16.0 21.0 7.0 9.0 6.0 25.0 30.0 17.0 23.0 3.0 9.0 5.0 28.0 32.0 12.0 15.0 5.0 15.0 6.0 29.0 34.0 18.0 21.0 3.0 10.0 5.0 23.0 27.0 17.0 20.0 3.0 10.0 7.0 24.0 28.0 18.0 21.0 3.0 13.0 7.0 29.0 34.0 18.0 21.0 3.0 10.0 5.0 26.0 21.0 17.0 28.0 5.0 10.0 6.0 26.0 30.0 16.0 23.0 7.0 9.0 5.0 26.0 30.0 16.0 23.0 4.0 11.0 8.0 27.0 31.0 17.0 22.0 3.0 12.0 6.0 26.0 31.0 18.0 24.0 4.0 11.0 7.0 26.0 31.0 18.0 23.0 6.0 10.0 9.0 28.0 31.0 21.0 27.0 4.0 12.0 9.0 27.0 32.0 16.0 25.0 5.0 12.0 8.0 29.0 33.0 15.0 22.0 4.0 14.0 6.0 23.0 29.0 16.0 19.0 4.0 10.0 6.0 25.0 29.0 19.0 22.0 3.0 15.0 7.0 25.0 29.0 16.0 19.0 : TEXT [VALUES=va,vb,vc,vd,ve,vf,vg] vlabs BIPLOT [PRINT=singular,scores; VLABELS=vlabs] v