Simple Correspondence Analysis ------------------------------
^coranal^ var1 var2 [^if^ exp] [^in^ range] ^[^weight^],^[^d(^#^) q(^#^)^ > ^as^ymmetric]
^aweight^s and ^fweight^s are allowed; see help @weights@.
To reset problem-size limits, see help @matsize@.
Description -----------
The command ^coranal^ produces numerical results as well as graphical outputs f > or simple correspondence analyses. The computation algorithm draws most largely on Blasius and Greenacre [2].
Options -------
^d(^#^)^ specifies the number of dimensions to be considered (for both numerica > l and graphical displays). If ^d(0)^ is specified, then ^coranal^ provides no > graphical display and returns the numerical output for all non-trivial dimensions. For maps to be readable, # must be set larger than 1. Furthermore, consistent maps can only be obtained by specifying # lower than or equal to the number of underlying non-trivial dimensions. Default # is 0. ^q(^#^)^ specifies a quality of representation threshold (0<#<=1). It restricts the mappings to points satisfying the condition that their quality of representation (sum of contributions of principal axes) in the ^d(^#^)^ fir > st dimensions is higher than or equal to #. Rejected points are still mapped but symbolized by a dot.
^as^ymmetric specifies that the joint displays of var1 and var2 are to be presented in the form of asymmetric maps (both variables are taken as vertices consecutively). By default, symmetric maps are displayed.
Remarks and Restrictions ------------------------
- var1 and var2 must be numeric variables. No string variables are allowed.
- Internally using the @tabulate@ command, var1 (or var2) can take on a maximum of 300 values and var2 (or var1) can take on a maximum of 20 values.
- Beware of the possible aspect ratio distortion of the maps.
Besides,
- In order to obtain easy to read graphs, variables should preferably be labeled. Note that the exact coordinates of the points are located right in the middle of the label name.
- Think of @reshape@ commands to compute simple correspondence analyses on more than two variables (stacked cross-tabulations). Also see @MCA@.
- A trick to apply the analysis directly on already cross-tabulated data is: consider creating in your dataset the two variables analyzed then use the @fillin@ command to obtain an observation for all possible combinations of the two variables. Create then a "fweighting" variable, say fw, containing the observed frequency of each combination and apply @coranal@ to your two variable > s and specify ^[fweight=fw]^ in the command line.
Example -------
.. use "C:\Stata\auto.dta", clear (1978 Automobile Data)
.. coranal rep78 hdroom, d(3) ------------------------------------------------------------------------------
SIMPLE CORRESPONDENCE ANALYSIS
------------------------------------------------------------------------------
Total Inertia : 0.719
Principal Inertias and Percentages :
Inertia Share Cumul Dim1 0.263 0.366 0.366 Dim2 0.226 0.314 0.680 Dim3 0.132 0.184 0.864
hdroom coordinates :
Mass Inertia Dim1 Dim2 Dim3 hdroom:1.5 0.043 0.197 1.479 1.405 0.457 hdroom:2 0.188 0.068 -0.163 0.272 -0.406 hdroom:2.5 0.203 0.060 0.360 -0.372 -0.090 hdroom:3 0.159 0.067 0.336 -0.477 -0.281 hdroom:3.5 0.188 0.095 -0.436 -0.187 0.491 hdroom:4 0.145 0.074 -0.026 0.319 0.241 hdroom:4.5 0.058 0.048 -0.862 0.071 0.174 hdroom:5 0.014 0.111 -1.662 1.661 -1.237
rep78 coordinates :
Mass Inertia Dim1 Dim2 Dim3 rep78:1 0.029 0.176 1.282 1.765 0.070 rep78:2 0.116 0.186 -0.853 0.789 -0.450 rep78:3 0.435 0.099 -0.305 -0.218 0.234 rep78:4 0.261 0.118 0.498 0.119 0.214 rep78:5 0.159 0.140 0.406 -0.493 -0.675
Explained inertia of axis by hdroom :
Dim1 Dim2 Dim3 hdroom:1.5 0.3610 0.3804 0.0687 hdroom:2 0.0190 0.0617 0.2350 hdroom:2.5 0.0997 0.1243 0.0125 hdroom:3 0.0682 0.1606 0.0950 hdroom:3.5 0.1363 0.0293 0.3443 hdroom:4 0.0004 0.0654 0.0635 hdroom:4.5 0.1635 0.0013 0.0133 hdroom:5 0.1520 0.1771 0.1677
Explained inertia of axis by rep78 :
Dim1 Dim2 Dim3 rep78:1 0.1808 0.4002 0.0011 rep78:2 0.3202 0.3198 0.1773 rep78:3 0.1540 0.0918 0.1807 rep78:4 0.2452 0.0163 0.0905 rep78:5 0.0998 0.1721 0.5504
Contributions of principal axes to hdroom :
Dim1 Dim2 Dim3 hdroom:1.5 0.4820 0.4351 0.0460 hdroom:2 0.0738 0.2050 0.4573 hdroom:2.5 0.4396 0.4694 0.0277 hdroom:3 0.2691 0.5428 0.1880 hdroom:3.5 0.3790 0.0697 0.4805 hdroom:4 0.0013 0.1996 0.1135 hdroom:4.5 0.8918 0.0060 0.0365 hdroom:5 0.3622 0.3617 0.2005
Contributions of principal axes to rep78 :
Dim1 Dim2 Dim3 rep78:1 0.2704 0.5126 0.0008 rep78:2 0.4523 0.3869 0.1257 rep78:3 0.4108 0.2097 0.2419 rep78:4 0.5468 0.0311 0.1013 rep78:5 0.1882 0.2780 0.5209
Author ------
Philippe VAN KERM <philippe.vankerm@@fundp.ac.be> University of Namur, Department of Economics Rempart de la Vierge 8 B-5000 Namur, Belgium.
References ----------
[1] Benzecri J.-P. and F. Benzecri (1980) , Analyse des correspondances: expose elementaire, Dunod, Paris.
[2] Blasius J. and M. Greenacre (1994), 'Computation of Correspondence Analysis' in Greenacre M. and J. Blasius (Eds.), Correspondence Analysis in the Social Sciences - Recent Developments and Applications, Academic Press, London.
[3] Greenacre Michael J. (1984), Theory and Applications of Correspondence Analysis, Academic Press, London. [4] Greenacre Michael J. (1993), Correspondence Analysis in Practice, Academic Press, London. [5] Greenacre M. and J. Blasius (Eds.) (1994), Correspondence Analysis in the Social Sciences - Recent Developments and Applications, Academic Press, London.
[6] Greenacre M. and T. Hastie (1987), 'The Geometric Interpretation of Correspondence Analysis', Journal of the American Statistical Association, vol.82(398).
[7] Volle Michel (1985), L'analyse des donnees, 3e ed., Economica.
Also see --------
@mca@, @factor@, @pca@, @canon@, @tabulate@, @matrix@