MCA OF THE TASTE EXAMPLE USING SPAD (VERSION 7.4)

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MCA

OF THE

T

ASTE

E

XAMPLE

U

SING

SPAD (

VERSION

7.4)

B

RIGITTE

L

E

ROUX

1 AND

P

HILIPPE

BONNET

2

U

NIVERSITÉ

P

ARIS

D

ESCARTES

1 INTRODUCTION... 2

2 GETTING STARTED... 2

2.1 Opening the archived project “TasteMCA_en” ... 2

2.2 Creating a new project and importing the data base ... 5

3 MCA of the Taste Example... 9

3.1 Setting the parameters... 9

3.2 Results of MCA ... 11

• Elementary Statistical Results... 11

• Eigenvalues and modified rates ... 12

• Principal coordinates and contributions ... 14

• Graphs of the cloud of categories and of the cloud of individuals... 14

Interpretation of axes using contributions ... 17

Graphs for Interpreting Axes... 18

• Clouds of categories... 18

• Cloud of individuals... 23

4 APPENDIX ... 26

4.1 Generalities of the graph editor... 26

The toolbar of the graph editor... 26

The fundamental rules for formating a graph... 26

4.2 Storing principal coordinates ... 27

1_{E-mail :}_{[email protected]}_—_{www.mi.parisdescartes.fr/~lerb/} 2

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1 INTRODUCTION

This guide aims to help you to perform with SPAD software the analyses presented in the monograph “MULTIPLE CORRESPONDENCE ANALYSIS”

by Brigitte Le ROUX and Henry ROUANET

Series: Quantitative Applications in the Social Sciences, n°163

SAGE, CA: Thousand Oaks (2010)

Numbers of pages, Figures or Tables refer to this book, that we call hereafter “MCA-SAGE”.

2 GETTING STARTED

You must have at your disposal the 7.4 version of SPAD3 or the last release of the 7.0 version, that is 7.0.84.

2.1 Opening the archived project “TasteMCA_en”

Download the archived project: TasteMCA_en.spad4.

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Then specify the path of the SPAD project.

Click on Open

Click on OK

Click on the search button

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Click on Yes to open the project.

Here is the main diagram of our study.

For all methods the parameters have been set and the running has been done.

If you want to perform this kind of analysis on another dataset, look at the parameters of methods by double-clicking on the method icon and do the dame for your dataset.

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If you want to see the results of a method, right-click on the icon of the method. See below the example for 1 - MCA .

Several types of results are available.

• Results editor: results as condensed text;

• Excel ouput: all results are returned in the Excel environment (Excel must be installed on your computer).

The other outputs are graphs: for MCA, clouds of points in principal planes.

2.2 Creating a new project and importing the data base

Open SPAD, choose Create a new project and give a name to your project, for instance My_tasteExample.

Click on OK.

Choose the type of file to be imported (here an Excel file) and double-click.

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Then the icon Excel datasheet appears in the Diagram window.

Set the parameters of the method by double-clicking on the method Import Excel datasheet, the following window appears.

Open the Excel file “Taste_Example.xls” and choose the Excel datasheet

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The role of each variable has been automatically defined. However, in this example, ID must not be a categorical variable but an identifier. To turn it into an Identifier, right-click on the line ID then choose Role>Identifier as follows.

Then you obtain the following results (ID is now an Identifier).

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• Remark.

If you don’t change the role of ID, the following message appears in the Executions Window.

If you click on the log icon, you obtain a message indicating that the number of categories exceeds the maximum. Change the role of the variable (here categorical → identifier).

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3 MCA of the Taste Example

In the window Methods, click on MCA – Multiple Correspondence Analysis then drag and drop the method icon on the diagram of data import.

3.1 Setting the parameters

Double-click on the icon of the MCA method. The window of parameters for MCA has 4 tabs to choose from Variables, Cases, Weighting, Parameters.

1. Click on Variables in order to select the active questions (variables) and the supplementary questions (variables).

a) select the active questions (rolling menu: Variable selection: choose Active categorical variables): and transfer the four variables (Tv, Film, Art, Eat) by using the button with one arrow ;

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2. Click on Cases to choose active/supplementary individuals (cases); then click on Logical filter and choose Isup=1 and validate.

3. Click on Weighting and clik on the radio button Uniform.

4. Click on Parameters

In GDA methodology, there is no assignment of rare modalities: one then performs specific MCA

By default, the coordinates of the individuals are not included in the output.

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• Running MCA: Right-click on the icon of the method and choose Execute

3.2 Results of MCA

• Elementary Statistical Results

Right-click on the MCA icon and choose Results>Results editor.

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Hereafter are the absolute frequencies of the active categories (see MCA-SAGE, Table 3.3, page 45).

Verify the frequencies and the choice of active and supplementary questions and active individuals in the text file.

The absolute frequencies of categories can also be found in the Excel5 sheet Cormu-1.

• Eigenvalues and modified rates

In Cormu-4 there are the variances of axes (eigenvalues) (see MCA-SAGE, Table 3.4, page 46). To calculate the modified rates, make the following calculations:

1) Modified values (column E) for the eigenvalues inferior to the average eigenvalue (that is 1/Q, where Q is the number of active variables, in this case: 1/4= 0.25),

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2) Modified rates (modified values divided by the sum of all modified values specified in column E).

Modified eigenvalues and modified variance rates also appeared in the text file (see below). Sum of modified

eigenvalues greater than 1/Q=1/4=0.25. E29=SUM(E4:E15) (cell $E$29) G4=SUM($F4$ :F4) F4=E4/$E$29 E4=( (4/3)*(B4-1/4) )^2

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To interpret the axes we essentially use the sheets Cormu-4 and Cormu-6 and then construct graphs of modalities for the interpretation of axes.

• Principal coordinates and contributions

Coordinates of active categories are in Cormu-5, their contributions are in Cormu-6 (see MCA-SAGE, Table 3.5, page 48) and their qualities of representation in Cormu-7. The coordinates of supplementary categories are in Cormu-8.

• Graphs of the cloud of categories and of the cloud of individuals

Producing graphs with SPAD is very easy and user-friendly.

All the graphs of chapters 1 and 3 of the MCA-SAGE book are pre-recorded.

To enter the graph editor, right-click on the icon of the MCA method and proceed as follows.

Then do Graph>Open>Record as shown below.

You obtain the following list of pre-registred graphs, that refer to the Figures of the MCA-SAGE book.

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Interpretation of axes using contributions

The interpretation of axes is based upon the contributions of categories (given in sheet cormu-6) (see MCA-SAGE, p. 52).

For each axis, mark the categories with an above average contribution, that is, 100/29=3.4%. In the following table, the most contributing categories are highlighted (see MCA-SAGE, Table 3.5, page 48).

Contributions of active categories

CORMU-6

Label Relative Weight

(%)

Squared distance to

origin

Axis 1 Axis 2 Axis 3

TV Tv-News 4.527 4.52273 8.78 0.00 0.10 Tv-Comedy 3.128 6.99342 4.85 8.21 0.63 Tv-Police 1.687 13.81710 0.15 0.79 0.85 Tv-Nature 3.272 6.64151 4.91 0.09 0.55 Tv-Sport 2.798 7.93382 0.01 0.14 18.58 Tv-Films 2.407 9.38462 1.98 3.30 2.72 Tv-Drama 2.757 8.06716 1.70 0.02 8.17 Tv-Soap 4.424 4.65116 8.37 15.10 6.80 TOTAL 25.000 30.75 27.65 38.40 Film Action 8.004 2.12339 0.10 0.37 10.53 Comedy 4.835 4.17021 6.79 1.29 1.40 CostumeDrama 2.881 7.67857 12.69 0.01 13.63 Documentary 2.058 11.15000 5.37 0.22 1.72 Horror 1.276 18.59680 3.80 3.62 0.04 Musical 1.790 12.96550 0.08 8.43 0.07 Romance 2.078 11.02970 5.55 9.10 9.44 SciFi 2.078 11.02970 0.23 2.68 2.66 TOTAL 25.000 34.60 25.72 39.50 Art PerformanceArt 2.160 10.57140 0.04 0.03 0.03 Landscape 13.004 0.92247 1.73 5.64 3.92 RenaissanceArt 1.132 21.09090 3.04 1.80 1.12 StillLife 1.461 16.11270 1.20 0.89 0.06 Portrait 2.407 9.38462 6.26 2.07 0.15 ModernArt 2.263 10.04550 5.03 5.95 0.57 Impressionism 2.572 8.72000 2.01 7.13 5.38 TOTAL 25.000 19.31 23.52 11.22 Eat Fish&Chips 2.202 10.35510 0.37 3.89 0.66 Pub 5.782 3.32384 1.15 6.46 0.14 IndianRest 8.272 2.02239 5.34 4.01 0.36 ItalianRest 4.691 4.32895 0.01 3.87 2.94 FrenchRest 2.037 11.27270 8.21 1.38 3.50 SteakHouse 2.016 11.39800 0.26 3.49 3.27 TOTAL 25.000 15.34 23.11 10.88

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Graphs for Interpreting Axes

• Clouds of categories

Enter the graph editor and choose the preferences

1. Define Preferences>Style for the page

Check the following options.

Then click on OK to save your preferences.

In GDA, figures are geometric maps: the distance scale must be the same in all directions

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2. Define thePreferences_{for the active categories}_{(Style for the groups).}

Select one color and one symbol for active categories (for example a red filled circle), and choose for: “size of symbols” the option “proportional to weights” and for lables the option“long”, as indicated below.

Minimum size is 1 Maximum size is 8 Choose the minimum and the maximum size for the symbols : Drawing>Adjust the proportionality

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Construction of graph for interpreting an axis

Select Graph>New, which gives you the following window:

1. Select the active questions by marking active categorical variables, then OK.

2. If preferred, redraw the graph symmetrically to the horizontal axis by using .or/and symetrically to the vertical axis by using

3. In order not to show more than the 14 of the 29 (49%) categories that contribute the most to axis 1:

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Then Selection>Statistical filtering of the selection .

Choose the options Contribution to one axis, here axis 1, and give the percentage of points to be drawn (49%) as shown below.

b. Show the labels by clicking on the button ; c. Unselect the points by using the icon .

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After working on the location of the labels, one obtains a graph like the following:

Now you can improve the graph using the powerful possibilities of the graph editor (see the help by clicking on ? in the graph window).

To interpret axis 2, perform the same steps as for axis 1. For axis 2, use the contributions to axis 2 as the statistical criterion for selecting the modalities, and do the same for axis 3.

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• Cloud of individuals

• To obtain the cloud of individuals with points proportional to superposition:

1. Set the parameters of proportionality: Drawing/Adjust the proportionality and choose Maximal size of the symbols in pixels (for example 8).

2. Select all the points (Selection/Off all points), and go to the menu Format/Colors, symbols,… and check the item Proportional size: Superposition.

3. and click on (total unselection)

4. Adjust the proportionality of symbols Drawing>Adjust the propotionality; choose the minimum (2) and the maximum (8).

One obtains, in the plane of axes 1-2, the following graph6:

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If you wish to redraw the graph symmetrically to the horizontal axis or/and to the vertical axis, use then

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Concentration ellipses for Gender. Do the following operations

1. Format> Of cases by…

2. Select the variable Gender which will function as structuring factor, by clicking on variable selection

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… and so on

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4 APPENDIX

4.1 Generalities of the graph editor

The toolbar of the graph editor

The initial pre-selection for a new graph is important: It is necessary to pre-select the variables and the individuals you think you will be interested in analyzing in the graph.

The fundamental rules for formating a graph

Selection

then

Format (action)

then

Unselection

Start with selecting a point or a group of points, then format them, and finally do a total unselection.

The Selection menu permits to select points, either by groups of points, or point by point.

The selection can be done either by using the Selection menu or by the buttons on the toolbar.

Select axes

Point by point selection

Total deselection Selection by framing Display labels Remove labels Display as ghosts Back to normal Information on points Refresh Symmetries Symbol size proportional to criterion

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It is thus advisable to Refresh the graph by hiting the space bar. You can do that also either click on the icon on the toolbar or use the menu: Drawing>Refresh.

4.2 Storing principal coordinates

To recover the coordinates [factor loadings] of individuals (or the classes of partitions) in a SPAD Database, drag and drop the method Deployment – Archiving>Archiving>Factor loadings and partitions on the MCA icon.

Then set the parameters, that is, put the 3 axes in the bottom window.