..-
help for ^coranal^                                            (Philippe Van Kerm)
..-

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 for
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 numerical
    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(^#^)^ first
    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 variables
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@

