Correspondence Analysis

Statistics > Multivariate Analysis > Correspondence Analysis

 

Helps you to explore relationships in a two-way classification.

This procedure decomposes a contingency table in a manner similar to how principal components analysis decomposes multivariate continuous data. An eigen analysis of the data is performed, and the variability is broken down into underlying dimensions and associated with rows and/or columns.

 

Dialog box items

Variables:
Choose the columns containing the variables to be included in the analysis.

Supplementary Data:
Provides main and supplementary data.

oSupplementary Rows: Enter the number from which VisualStat begins to count supplementary rows. Leave blank if your datasheet does not contains any supplementary row.

oSupplementary Columns: Enter the number from which VisualStat begins to count supplementary columns. Leave blank if your datasheet does not contains any supplementary column.

Report:
The display of outputs of VisualStat.

 

Data

Each row represents one observation. The data represent categories and may be numeric. If a missing value exists in any column, VisualStat ignores the whole row. Missing values are excluded from all calculations.

 

Supplementary Data

When performing a correspondence analysis, you have a main classification set of data on which you perform your analysis. However, you may also have additional or supplementary data in the same form as the main set, because you can see how these supplementary data are "scored" using the results from the main set. These supplementary data may be further information from the same study, information from other studies, or target profiles. VisualStat does not include these data when calculating the components, but you can obtain a profile and display supplementary data in graphs.

You can have row supplementary data or column supplementary data. Row supplementary data constitutes an additional row(s) of the contingency table, while column supplementary data constitutes an additional column(s) of the contingency table. Main variables and observations are located in the top-left position of the DataEditor, while supplementary variables and observations are located in the bottom-right position, like shown in the above figure.

supp_data

 

Plot

Plot:
The Plot tab allows you to specify which plots are produced.

oRow Principal Points: Check to display a plot that shows the row principal coordinates.

oRow Supplementary Points: Check to display a plot that shows the row supplementary coordinates.

oColumn Principal Points: Check to display a plot that shows the column principal coordinates.

oColumn Supplementary Points: Check to display a plot that shows the column supplementary coordinates.

Show/Hide Row Names

oPrincipal Coordinates: Check to plot the row labels near the principal coordinates points.

oSupplementary Coordinates: Check to plot the row labels near the supplementary coordinates points.

Show/Hide Column Names

oPrincipal Coordinates: Check to plot the column labels near the principal coordinates points.

oSupplementary Coordinates: Check to plot the column labels near the supplementary coordinates points.

Axis pairs to plot (X,Y):
Enter the two components to be plotted in the form c(factor1, factor2). By default, a biplot of the first two factors is created.

 

Storage

Stores the coefficients and scores.

Eigenvalues: Check to store eigenvalues.

Eigenvectors: Check to store eigenvectors.

Row Coordinates:  Check to store rows for the principal components coordinates.

Column Coordinates: Check to store columns for the principal components coordinates.

Options

Allows you to control displayed output.

Eigenvalues: Check to print out the eigenvalues.

Eigenvectors: Check to print out the eigenvectors.

Row Profiles: Check to display a table of row profiles and row masses.

Column Profiles: Check to display a table of column profiles and column masses.

Supplementary Row: Check to display a table of supplementary row profiles.

Supplementary Column: Check to display a table of supplementary column profiles.

 

Example

The data are from an international research on time budgets, conducted in different countries under the aegis of UNESCO in 1965 and 1966. The purpose of this research was to study the time budgets of adult populations, subject to the influences of industrialization and urbanization. It is important to note that these data were collected during the Cold War.

The dataset to analyze have 28 categories of people (rows) and 10 primary activities (columns). The number that appears at the intersection of row i and column j represents the average time (in hundredths of hours) devoted to activity j by the subjects of class i.

 

Variables:

The 10 selected activities are:

- PROF Professional work

- TRAN Transport-related professional work

- MENA Housework

- COUR Sopping

- TOIL Amenities, Personal Care

- REPA Meals (consumption)

- TELE Television

- LOIS Leisure other than television

 

Observations:

For 4 countries or groups of countries (USA, Western countries, Yugoslavia and Eastern Europe), were 7 categories of subjects or in all 28 categories. The abbreviations are:

- HA Males

- FA Active women

- FNA Inactive women

- HM Married men

- FM Women married

- HC Single men

- FC Single women

- US or U USA

- WE or W Western countries (Germany, England, Belgium, France)

- ES or E Eastern Europe (Poland, Czechoslovakia)

- YO or Y Yugoslavia

These categories may partly overlap: married women enter active eg in both FM and FA categories. Some analysis were made by adding to the table 15 additional lines, obtained by grouping basic categories:

- HOMM men

- FEMM women

- MARI married

- CELI single

- ...

 

1.Open the DataBook mva.vstz

2.Select the sheet Budget

3.Choose the tab Statistics, the group Multivariate Analysis and the command Correspondence Analysis

4.Select group Data

5.In Variables, select PROF, TRAN, MENA, COUR, TOIL, REPA, TELE and LOIS

6.Select group Supplementary Data (optional)

7.In From the row, enter 29.

8.Click Plot page

9.Check Row Principal Points, Row Supplementary Points, and Column Principal Points.

10.Click Show/Hide Row Names and check Principal Coordinates and Supplementary Coordinates

11.In Axis pairs to plot (X,Y), enter c(1,2) ; c(1,3) ; c(1,4).

12.Click Options page

13.Check Eigenvalues, Row Profiles, Column Profiles and Supplementary Rows.

14.In Number of components, enter 4.

15.Click OK

 

Report window output

 

Correspondence Analysis

 

 

Analysis of Contingency Table

 

------*----------*--------*--------*—————————————————————————————————————————————————————

Axis | Inertia  |  Ratio |  Cumul |      Histogram of Eigenvalues of Matrix

------*----------*--------*--------*—————————————————————————————————————————————————————

   1 | 0.118485 | 0.8270 | 0.8270 |**********|**********|**********|**********|*

   2 | 0.010823 | 0.0755 | 0.9025 |****

   3 | 0.006759 | 0.0472 | 0.9497 |**

   4 | 0.004274 | 0.0298 | 0.9795 |*

   5 | 0.001654 | 0.0115 | 0.9911 |*

   6 | 0.000896 | 0.0063 | 0.9973 |

   7 | 0.000193 | 0.0014 | 0.9987 |

   8 | 0.000134 | 0.0009 | 0.9996 |

   9 | 0.000053 | 0.0004 | 1.0000 |

 

 

Row Components

                                             Component  1            Component  2            Component  3            Component  4  

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

 NUM | Name   |   Qual   Mass  Inert |   Coord   Corr  Contr |   Coord   Corr  Contr |   Coord   Corr  Contr |   Coord   Corr  Contr |

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

   1 | HAUS   |  0.974  0.036  0.035 |   0.330  0.773  0.033 |   0.132  0.123  0.057 |  -0.095  0.064  0.048 |  -0.043  0.013  0.016 |

   2 | FAUS   |  0.700  0.036  0.003 |   0.039  0.118  0.000 |   0.024  0.045  0.002 |  -0.037  0.111  0.007 |  -0.073  0.425  0.045 |

   3 | FNAU   |  0.978  0.036  0.100 |  -0.580  0.840  0.101 |   0.228  0.130  0.171 |  -0.016  0.001  0.001 |  -0.054  0.007  0.024 |

   4 | HMUS   |  0.968  0.036  0.036 |   0.330  0.762  0.033 |   0.126  0.111  0.053 |  -0.111  0.086  0.065 |  -0.036  0.009  0.011 |

   5 | FMUS   |  0.977  0.036  0.043 |  -0.376  0.823  0.043 |   0.143  0.118  0.067 |  -0.040  0.009  0.008 |  -0.067  0.026  0.037 |

   6 | HCUS   |  0.962  0.036  0.033 |   0.313  0.734  0.029 |   0.161  0.195  0.086 |   0.016  0.002  0.001 |  -0.064  0.031  0.034 |

   7 | FCUS   |  0.772  0.036  0.007 |   0.102  0.351  0.003 |   0.084  0.236  0.023 |  -0.015  0.008  0.001 |  -0.073  0.178  0.044 |

   8 | HAWE   |  0.998  0.036  0.028 |   0.311  0.856  0.029 |   0.015  0.002  0.001 |  -0.042  0.016  0.009 |   0.119  0.124  0.117 |

   9 | FAWE   |  0.901  0.036  0.005 |   0.007  0.002  0.000 |  -0.091  0.399  0.028 |  -0.072  0.250  0.028 |   0.072  0.249  0.043 |

  10 | FNAW   |  0.991  0.036  0.096 |  -0.603  0.947  0.110 |   0.086  0.019  0.025 |  -0.030  0.002  0.005 |   0.092  0.022  0.070 |

  11 | HMWE   |  0.997  0.036  0.029 |   0.308  0.822  0.029 |   0.018  0.003  0.001 |  -0.063  0.034  0.021 |   0.126  0.137  0.132 |

  12 | FMWE   |  0.996  0.036  0.055 |  -0.453  0.933  0.062 |   0.007  0.000  0.000 |  -0.073  0.024  0.028 |   0.093  0.039  0.072 |

  13 | HCWE   |  0.997  0.036  0.032 |   0.334  0.877  0.034 |   0.032  0.008  0.003 |   0.036  0.010  0.007 |   0.114  0.102  0.108 |

  14 | FCWE   |  0.768  0.036  0.007 |  -0.015  0.008  0.000 |   0.029  0.029  0.003 |   0.072  0.185  0.028 |   0.124  0.545  0.129 |

  15 | HAYO   |  0.976  0.036  0.025 |   0.304  0.932  0.028 |  -0.050  0.025  0.008 |   0.043  0.018  0.010 |  -0.010  0.001  0.001 |

  16 | FAYO   |  0.987  0.036  0.014 |  -0.010  0.002  0.000 |  -0.212  0.822  0.148 |  -0.081  0.122  0.035 |  -0.047  0.041  0.019 |

  17 | FNAY   |  0.983  0.036  0.127 |  -0.696  0.951  0.146 |  -0.079  0.012  0.020 |   0.100  0.020  0.053 |   0.010  0.000  0.001 |

  18 | HMYO   |  0.975  0.036  0.026 |   0.315  0.953  0.030 |  -0.037  0.013  0.004 |   0.026  0.007  0.004 |  -0.015  0.002  0.002 |

  19 | FMYO   |  0.994  0.036  0.048 |  -0.408  0.872  0.050 |  -0.150  0.119  0.075 |  -0.016  0.001  0.001 |  -0.017  0.001  0.002 |

  20 | HCYO   |  0.990  0.036  0.034 |   0.305  0.686  0.028 |  -0.006  0.000  0.000 |   0.201  0.297  0.212 |  -0.032  0.008  0.009 |

  21 | FCYO   |  0.992  0.036  0.006 |  -0.033  0.048  0.000 |  -0.068  0.207  0.015 |   0.127  0.729  0.086 |  -0.014  0.009  0.002 |

  22 | HAES   |  0.964  0.036  0.024 |   0.300  0.946  0.027 |  -0.033  0.012  0.004 |  -0.020  0.004  0.002 |  -0.016  0.003  0.002 |

  23 | FAES   |  0.982  0.036  0.012 |   0.032  0.021  0.000 |  -0.187  0.722  0.116 |  -0.084  0.146  0.037 |  -0.067  0.094  0.038 |

  24 | FNAE   |  0.997  0.036  0.095 |  -0.612  0.978  0.113 |   0.038  0.004  0.005 |   0.076  0.015  0.031 |  -0.009  0.000  0.001 |

  25 | HMES   |  0.966  0.036  0.023 |   0.288  0.905  0.025 |  -0.019  0.004  0.001 |  -0.072  0.057  0.028 |  -0.001  0.000  0.000 |

  26 | FMES   |  0.982  0.036  0.016 |  -0.169  0.436  0.009 |  -0.155  0.364  0.079 |  -0.094  0.135  0.047 |  -0.056  0.047  0.026 |

  27 | HCES   |  0.979  0.036  0.039 |   0.354  0.804  0.038 |   0.004  0.000  0.000 |   0.164  0.173  0.143 |  -0.017  0.002  0.002 |

  28 | FCES   |  0.899  0.036  0.004 |  -0.017  0.020  0.000 |  -0.041  0.112  0.006 |   0.101  0.669  0.054 |  -0.039  0.098  0.012 |

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

 

 

Supplementary Row

                                             Component  1            Component  2            Component  3            Component  4  

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

 NUM | Name   |   Qual   Mass  Inert |   Coord   Corr  Contr |   Coord   Corr  Contr |   Coord   Corr  Contr |   Coord   Corr  Contr |

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

   1 | HOMM   |  0.997  0.036  0.025 |   0.317  0.988  0.030 |   0.028  0.008  0.003 |   0.007  0.000  0.000 |   0.010  0.001  0.001 |

   2 | FEMM   |  0.997  0.036  0.014 |  -0.237  0.987  0.017 |  -0.022  0.009  0.002 |  -0.005  0.000  0.000 |  -0.007  0.001  0.000 |

   3 | MARI   |  0.935  0.036  0.001 |  -0.021  0.116  0.000 |  -0.008  0.018  0.000 |  -0.056  0.798  0.017 |   0.004  0.003  0.000 |

   4 | CELI   |  0.989  0.036  0.009 |   0.167  0.765  0.008 |   0.023  0.015  0.002 |   0.087  0.209  0.040 |  -0.001  0.000  0.000 |

   5 | USA    |  0.987  0.036  0.006 |   0.022  0.022  0.000 |   0.128  0.733  0.054 |  -0.043  0.083  0.010 |  -0.058  0.149  0.028 |

   6 | WEST   |  0.990  0.036  0.003 |  -0.016  0.022  0.000 |   0.013  0.014  0.001 |  -0.024  0.047  0.003 |   0.105  0.907  0.093 |

   7 | YOUG   |  0.977  0.036  0.003 |  -0.031  0.081  0.000 |  -0.086  0.605  0.024 |   0.057  0.268  0.017 |  -0.017  0.024  0.002 |

   8 | EST    |  0.941  0.036  0.001 |   0.025  0.126  0.000 |  -0.056  0.627  0.010 |   0.010  0.020  0.001 |  -0.029  0.169  0.007 |

   9 | HA     |  0.994  0.036  0.025 |   0.311  0.981  0.029 |   0.016  0.003  0.001 |  -0.029  0.009  0.005 |   0.011  0.001  0.001 |

  10 | FA     |  0.961  0.036  0.005 |   0.016  0.013  0.000 |  -0.116  0.667  0.044 |  -0.069  0.238  0.025 |  -0.030  0.044  0.007 |

  11 | FNA    |  0.999  0.036  0.098 |  -0.623  0.984  0.117 |   0.069  0.012  0.015 |   0.032  0.003  0.005 |   0.010  0.000  0.001 |

  12 | HM     |  0.994  0.036  0.025 |   0.310  0.956  0.029 |   0.023  0.005  0.002 |  -0.054  0.029  0.016 |   0.019  0.004  0.003 |

  13 | FM     |  0.998  0.036  0.032 |  -0.351  0.961  0.037 |  -0.039  0.012  0.005 |  -0.056  0.024  0.016 |  -0.013  0.001  0.001 |

  14 | HC     |  0.999  0.036  0.030 |   0.327  0.889  0.032 |   0.048  0.019  0.008 |   0.104  0.091  0.058 |   0.000  0.000  0.000 |

  15 | FC     |  0.699  0.036  0.002 |   0.010  0.013  0.000 |   0.001  0.000  0.000 |   0.071  0.685  0.027 |  -0.001  0.000  0.000 |

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

 

 

Column Components

                                             Component  1            Component  2            Component  3            Component  4  

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

 NUM | Name   |   Qual   Mass  Inert |   Coord   Corr  Contr |   Coord   Corr  Contr |   Coord   Corr  Contr |   Coord   Corr  Contr |

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

   1 | PROF   |  0.998  0.188  0.320 |   0.483  0.953  0.369 |  -0.098  0.039  0.166 |  -0.038  0.006  0.041 |  -0.003  0.000  0.000 |

   2 | TRAN   |  0.947  0.036  0.075 |   0.510  0.868  0.079 |  -0.084  0.023  0.023 |  -0.006  0.000  0.000 |  -0.129  0.055  0.139 |

   3 | MENA   |  0.998  0.115  0.400 |  -0.687  0.951  0.459 |  -0.152  0.047  0.248 |  -0.018  0.001  0.006 |  -0.010  0.000  0.003 |

   4 | ENFA   |  0.897  0.014  0.078 |  -0.809  0.813  0.077 |   0.064  0.005  0.005 |  -0.225  0.063  0.104 |  -0.113  0.016  0.041 |

   5 | COUR   |  0.920  0.045  0.027 |  -0.174  0.349  0.012 |   0.115  0.153  0.055 |   0.039  0.018  0.010 |  -0.186  0.400  0.367 |

   6 | TOIL   |  0.496  0.040  0.004 |  -0.006  0.003  0.000 |   0.048  0.164  0.008 |  -0.005  0.002  0.000 |  -0.068  0.328  0.043 |

   7 | REPA   |  0.974  0.049  0.016 |  -0.092  0.185  0.003 |   0.053  0.062  0.013 |  -0.058  0.074  0.025 |   0.172  0.653  0.342 |

   8 | SOMM   |  0.853  0.327  0.003 |  -0.019  0.248  0.001 |   0.007  0.032  0.001 |   0.005  0.018  0.001 |   0.028  0.555  0.059 |

   9 | TELE   |  0.980  0.041  0.044 |   0.022  0.003  0.000 |   0.309  0.629  0.365 |  -0.229  0.347  0.322 |  -0.008  0.000  0.001 |

  10 | LOIS   |  0.965  0.144  0.033 |  -0.004  0.001  0.000 |   0.093  0.262  0.115 |   0.152  0.698  0.491 |   0.012  0.005  0.005 |

———-——*————————*—————-——-—---------———*—————--------————--————*—————--------————--————*—————--------————--————*—————--------————--————*

 

 

 

 

 

Chart window output

 

Plot 1

 

 

Plot 2

 

 

Plot 3

 

 

Interpreting the results

In a very summarized way, we say that the first component separates those who have an occupation of those who do not exercise - is the separation of tasks related to social structures (opposition work - caring for children and shopping).

The second component separates the countries of the Western countries of the East, characterized by a greater time spent in leisure activities in the former than in the latter. As a corollary, there is a greater time devoted to work (professional or household) in the Eastern than in Western countries.

The third component separates the single non-married, separation due to the types of recreation. The first is devoted to leisure outside their habitat, the latter devoted to family recreation (occupations due to children, television).

The fourth component important very low, reflecting a separation within the West between the United States and European countries. This separation is due to an increased emphasis on meals and sleep in European countries at the expense (compared to U.S.) time spent on errand and personal care. This is a clear separation among women in both groups cited.

 

 

 

See Also:


Report | Numeric Formats