How to generate a standard biplot from correspondence analysis

[carlos viviano]

Greetings. I want to generate a biplot for correspondence analysis, as described by Greenacre in Chapter 13, "Biplots in Correspondence Analysis," of his book "The Practice of Correspondence Analysis" (2008). The Stata manual only explains how to create biplots with the counts in a contingency table, but this is far from a biplot for correspondence analysis.

[Nick Cox]

Could you tell us more about the distinction you're making?

ca allows weights -- which is the way that I've used it to include not just row and column categories but also measures of abundance of various kinds.

Biplots I usually find complicated and confusing, which may be chicken and egg with needing some experience in knowing how to read them.

I'd rather shuffle row and column categories to a better order.

[carlos viviano]

In the image, the columns have been converted to vector arrows so that the rows can be referenced relative to their position on each vector arrow. The example is from Greenacre, pages 97-104. http://ndl.ethernet.edu.et/bitstream...nacre_2007.pdf

[Nick Cox]

The book in question is (note the different title as compared with #1):

Greenacre, M. Correspondence Analysis in Practice.

1993. London: Academic Press.
2007. Boca Raton, FL: Chapman & Hall/CRC,
2017. Boca Raton, FL: CRC Press.

Any edition will do for the data example. It would have helped us if you listed the data, but I will do that now.

I am still puzzled, because the data are in effect a contingency table, and it's easy enough to get an equivalent of the display you copy in #2

* Example generated by -dataex-. For more info, type help dataex
clear
input float area byte category float(freq total)
 1 1  3  85
 1 2 19  85
 1 3 39  85
 1 4 14  85
 1 5 10  85
 2 1  1  29
 2 2  2  29
 2 3 13  29
 2 4  1  29
 2 5 12  29
 3 1  6 130
 3 2 25 130
 3 3 49 130
 3 4 21 130
 3 5 29 130
 4 1  3 120
 4 2 15 120
 4 3 41 120
 4 4 35 120
 4 5 26 120
 5 1 10 114
 5 2 22 114
 5 3 47 114
 5 4  9 114
 5 5 26 114
 6 1  3  88
 6 2 11  88
 6 3 25  88
 6 4 15  88
 6 5 34  88
 7 1  1  37
 7 2  6  37
 7 3 14  37
 7 4  5  37
 7 5 11  37
 8 1  0  86
 8 2 12  86
 8 3 34  86
 8 4 17  86
 8 5 23  86
 9 1  2  29
 9 2  5  29
 9 3 11  29
 9 4  4  29
 9 5  7  29
10 1  2  75
10 2 11  75
10 3 37  75
10 4  5  75
10 5 20  75
end
label values area order
label def order 1 "Geology", modify
label def order 2 "Biochemistry", modify
label def order 3 "Chemistry", modify
label def order 4 "Zoology", modify
label def order 5 "Physics", modify
label def order 6 "Engineering", modify
label def order 7 "Microbiology", modify
label def order 8 "Botany", modify
label def order 9 "Statistics", modify
label def order 10 "Mathematics", modify
label values category category
label def category 1 "A", modify
label def category 2 "B", modify
label def category 3 "C", modify
label def category 4 "D", modify
label def category 5 "E", modify

 
. ca area category [fw=freq]

Correspondence analysis                       Number of obs      =        793
                                              Pearson chi2(36)   =      69.31
                                              Prob > chi2        =     0.0007
                                              Total inertia      =     0.0874
    10 active rows                            Number of dim.     =          2
    5 active columns                          Expl. inertia (%)  =      83.64

                |   Singular   Principal                              Cumul.
      Dimension |      value     inertia           chi2    Percent   percent
    ------------+-----------------------------------------------------------
          Dim 1 |   .2056337    .0422852          33.53      48.38     48.38
          Dim 2 |   .1755732     .030826          24.44      35.27     83.64
          Dim 3 |   .1089875    .0118783           9.42      13.59     97.23
          Dim 4 |   .0491726    .0024179           1.92       2.77    100.00
    ------------+-----------------------------------------------------------
          Total |               .0874074          69.31        100

Statistics for row and column categories in symmetric normalization

                 |          Overall          |        Dimension_1        
      Categories |    Mass  Quality   %inert |   Coord   Sqcorr  Contrib 
    -------------+---------------------------+---------------------------
    area         |                           |                           
         Geology |   0.107    0.908    0.130 |   0.084    0.014    0.004 
    Biochemistry |   0.037    0.911    0.112 |   0.523    0.211    0.049 
       Chemistry |   0.164    0.646    0.020 |   0.039    0.029    0.001 
         Zoology |   0.151    0.950    0.233 |  -0.775    0.917    0.442 
         Physics |   0.144    0.837    0.181 |   0.651    0.792    0.296 
     Engineering |   0.111    0.861    0.144 |  -0.215    0.084    0.025 
    Microbiology |   0.047    0.703    0.009 |   0.047    0.027    0.000 
          Botany |   0.108    0.630    0.066 |  -0.379    0.559    0.076 
      Statistics |   0.037    0.465    0.011 |   0.235    0.421    0.010 
     Mathematics |   0.095    0.570    0.094 |   0.460    0.500    0.097 
    -------------+---------------------------+---------------------------
    category     |                           |                           
               A |   0.039    0.512    0.176 |   0.938    0.458    0.167 
               B |   0.161    0.822    0.103 |   0.224    0.185    0.039 
               C |   0.391    0.505    0.098 |   0.200    0.376    0.076 
               D |   0.159    0.981    0.373 |  -0.963    0.930    0.717 
               E |   0.250    0.985    0.249 |   0.008    0.000    0.000 
    ---------------------------------------------------------------------

                 |        Dimension_2        
      Categories |   Coord   Sqcorr  Contrib 
    -------------+---------------------------
    area         |                           
         Geology |   0.735    0.894    0.330 
    Biochemistry |  -1.033    0.701    0.222 
       Chemistry |   0.193    0.617    0.035 
         Zoology |   0.161    0.034    0.022 
         Physics |   0.167    0.045    0.023 
     Engineering |  -0.709    0.777    0.318 
    Microbiology |  -0.254    0.677    0.017 
          Botany |  -0.147    0.072    0.013 
      Statistics |   0.083    0.045    0.001 
     Mathematics |  -0.185    0.069    0.018 
    -------------+---------------------------
    category     |                           
               A |   0.348    0.054    0.027 
               B |   0.449    0.636    0.186 
               C |   0.127    0.129    0.036 
               D |   0.246    0.052    0.055 
               E |  -0.700    0.985    0.697 
    -----------------------------------------

. cabiplot

(The signs of scores are reversed on one dimension, but as usual with the kind of eigen calculation involved, signs of scores are arbitrary.)

The data show numbers of researchers in various areas (disciplines) in different funding categories. A B C D E are an ordered scale, A means most funded and E being not funded at all.

The ordering of areas from Geology to Mathematics has no rationale obvious to me, so one way forward is to score A to E as 1 to 5 and re-order categories on say the resulting means: Low means imply well funded and high means imply poorly funded.

I used myaxis and tabplot from the Stata Journal.

. expand freq
(1 zero count ignored; observation not deleted)
(744 observations created)

. myaxis area2=area, sort(mean category)

. tabplot category area2 , percent(area2) showval xla(, labsize(vsmall)) subtitle(% in area)

I don't see enormous differences between subject areas. But either way, what does the biplot show you that the bar chart doesn't?

[Nick Cox]

The first example in https://www.statalist.org/forums/for...updated-on-ssc
also took a dataset from Greenacre's book.

tabplot was written up at https://journals.sagepub.com/doi/pdf...867X1601600214

[carlos viviano]

Thank you very much. I wasn't familiar with TabPlot. I'll start using it.

[Hemanshu Kumar]

A small warning for Stata novices who may run into this thread: Stata is case-sensitive, so while tabplot as referenced in #5 will work (after installation), typing TabPlot as referenced in #6 will not.