..-
help for ^mca^ (Philippe Van Kerm)
..-
Multiple Correspondence Analysis
--------------------------------
^mca^ varlist [^if^ exp] [^in^ range] ^[^weight^],^[^d(^#^) q(^#^) n^otrans]
^aweight^s and ^fweight^s are allowed; see help @weights@.
To reset problem-size limits, see help @matsize@.
Description
-----------
The command ^mca^ produces numerical results as well as graphical
representations for multiple correspondence analyses (MCA).
^mca^ actually conducts an adjusted simple correspondence analysis on the Burt
matrix constructed with varlist (i.e. matrix of frequency counts resulting
from all two-way cross-tabulations of the variables in varlist including
the cross-tabulations of each variable with itself). It can be shown that
the total inertia of the Burt matrix is high due to the fitting of the diagonal
sub-matrices. Consequently, a simple correspondence analysis applied to this
matrix usually results in maps of apparently poor quality. As a remedy, if not
otherwise specified (see Options), ^mca^ adjusts the obtained principal
inertias (eigenvalues) following a method suggested by Benzecri and presented
in Greenacre (1984).
The computation algorithm draws most largely on Blasius and Greenacre [2]
and Greenacre [5].
Options
-------
^d(^#^)^ specifies the number of dimensions to be considered (for both numerical
and graphical displays). If ^d(0)^ is specified, then ^mca^ 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.
^n^otrans requests that no adjustments to eigenvalues are to be made.
Remarks and Restrictions
------------------------
- All variables in varlist must be numeric categorical variables. No string
variables are allowed.
- ^mca^ disregards all observations with missing values in any of the variables
in varlist.
- Internally using the @tabulate@ command, the variables in varlist can take on
a maximum of 20 values.
- The points on the outputs are represented by the first five characters of the
variable names followed by _X (where X is the numeric value of each category
composing the considered variable). All variables in varlist must therefore
be distinguishable with the their first 5 characters only. Note that the exact
coordinates of the points are located right in the middle of the label name.
- Beware of the possible aspect ratio distortion of the maps.
Example
-------
.. use "C:\Stata\auto.dta", clear
(1978 Automobile Data)
.. mca foreign hdroom rep78 ,d(3)
------------------------------------------------------------------------------
MULTIPLE CORRESPONDENCE ANALYSIS
------------------------------------------------------------------------------
Total Inertia : 0.431
Principal Inertia Components :
Inertia Share Cumul
Dim1 0.308 0.713 0.713
Dim2 0.060 0.138 0.851
Dim3 0.039 0.090 0.941
Coordinates :
Mass Inertia Dim1 Dim2 Dim3
forei_0 0.232 0.035 -0.387 0.007 -0.016
forei_1 0.101 0.079 0.884 -0.017 0.036
hdroo_1. 0.014 0.025 0.129 1.252 -0.275
hdroo_2 0.063 0.009 -0.156 0.061 0.274
hdroo_2. 0.068 0.036 0.721 -0.077 -0.040
hdroo_3 0.053 0.018 0.568 -0.137 0.012
hdroo_3. 0.063 0.023 -0.498 -0.212 -0.256
hdroo_4 0.048 0.017 -0.422 0.165 -0.050
hdroo_4. 0.019 0.012 -0.745 -0.252 0.041
hdroo_5 0.005 0.015 -1.026 0.149 1.367
rep78_1 0.010 0.024 -0.361 1.360 -0.041
rep78_2 0.039 0.035 -0.752 0.066 0.554
rep78_3 0.145 0.026 -0.336 -0.196 -0.143
rep78_4 0.087 0.022 0.339 0.237 -0.145
rep78_5 0.053 0.055 0.973 -0.150 0.230
Explained inertia of axes :
Dim1 Dim2 Dim3
forei_0 0.1126 0.0002 0.0014
forei_1 0.2574 0.0005 0.0033
hdroo_1. 0.0008 0.3815 0.0282
hdroo_2 0.0050 0.0040 0.1214
hdroo_2. 0.1143 0.0068 0.0028
hdroo_3 0.0558 0.0167 0.0002
hdroo_3. 0.0507 0.0474 0.1059
hdroo_4 0.0279 0.0220 0.0031
hdroo_4. 0.0348 0.0206 0.0008
hdroo_5 0.0165 0.0018 0.2321
rep78_1 0.0041 0.3003 0.0004
rep78_2 0.0710 0.0028 0.3056
rep78_3 0.0531 0.0931 0.0758
rep78_4 0.0326 0.0823 0.0467
rep78_5 0.1634 0.0201 0.0721
Contributions of principal axes :
Dim1 Dim2 Dim3
forei_0 0.9979 0.0003 0.0016
forei_1 0.9979 0.0003 0.0016
hdroo_1. 0.0097 0.9203 0.0445
hdroo_2 0.1622 0.0250 0.4991
hdroo_2. 0.9759 0.0112 0.0031
hdroo_3 0.9357 0.0541 0.0004
hdroo_3. 0.6844 0.1240 0.1807
hdroo_4 0.5021 0.0765 0.0071
hdroo_4. 0.8794 0.1008 0.0026
hdroo_5 0.3352 0.0071 0.5942
rep78_1 0.0532 0.7558 0.0007
rep78_2 0.6304 0.0048 0.3426
rep78_3 0.6317 0.2144 0.1140
rep78_4 0.4584 0.2240 0.0831
rep78_5 0.9072 0.0216 0.0506
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 Michael J. (1994), 'Multiple and Joint Correspondence Analysis'
in Greenacre M. and J. Blasius (Eds.), Correspondence Analysis in the
Social Sciences - Recent Developments and Applications, Academic Press,
London.
[6] Greenacre M. and J. Blasius (Eds.) (1994), Correspondence Analysis in the
Social Sciences - Recent Developments and Applications, Academic Press,
London.
[7] Volle Michel (1985), L'analyse des donnees, 3e ed., Economica.
Also see
--------
@coranal@, @factor@, @pca@, @canon@, @tabulate@, @matrix@