Multiple Correspondence Analysis --------------------------------
^mca^ varlist [^if^ exp] [^in^ range] ^[^weight^],^[^d(^#^) q(^#^) n^otr > ans]
^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 numerica > l 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(^#^)^ fir > st 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@