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moonplot

moonplot draws the Correspondence Analysis (CA) moonplot.

Syntax

Description

example

moonplot(out) moonplot with all the default options.

example

moonplot(out, Name, Value) moonplot with option changedimsign.

Examples

expand all

  • moonplot with all the default options.
  • Prepare the data.

    load('csdPerceptions')
    N=csdPerceptions;
    out=CorAna(N,'plots',0);
    moonplot(out);
    Summary
                 Singular_value    Inertia    Accounted_for    Cumulative
                 ______________    _______    _____________    __________
    
        dim_1         0.54          0.29          0.78            0.78   
        dim_2         0.25          0.06          0.17            0.95   
        dim_3         0.11          0.01          0.03            0.98   
        dim_4         0.09          0.01          0.02            1.00   
        dim_5         0.02          0.00          0.00            1.00   
        dim_6         0.01          0.00          0.00            1.00   
        dim_7         0.01          0.00          0.00            1.00   
    
    ROW POINTS
    Results for dimension: 1
                    Scores    CntrbPnt2In    CntrbDim2In
                    ______    ___________    ___________
    
        Coke        -0.24        0.05           0.52    
        V            0.45        0.14           0.93    
        RedBull      0.47        0.14           0.92    
        LiftPlus     0.46        0.08           0.90    
        DietCoke    -0.09        0.00           0.02    
        Fanta       -1.27        0.54           0.88    
        Lift        -0.50        0.03           0.34    
        Pepsi       -0.27        0.01           0.36    
    
    Results for dimension: 2
                    Scores    CntrbPnt2In    CntrbDim2In
                    ______    ___________    ___________
    
        Coke        -0.20        0.17           0.36    
        V            0.11        0.04           0.06    
        RedBull      0.13        0.05           0.07    
        LiftPlus     0.15        0.04           0.09    
        DietCoke    -0.54        0.16           0.76    
        Fanta        0.47        0.33           0.12    
        Lift        -0.50        0.15           0.34    
        Pepsi       -0.26        0.06           0.33    
    
    COLUMN POINTS
    Results for dimension: 1
                       Scores    CntrbPnt2In    CntrbDim2In
                       ______    ___________    ___________
    
        Kids           -1.32        0.43           0.92    
        Teens           0.04        0.00           0.02    
        EnjoyLife      -0.08        0.00           0.06    
        PicksYouUp      0.49        0.10           0.88    
        Refreshes      -0.29        0.02           0.21    
        CheersYouUp    -0.24        0.01           0.83    
        Energy          0.60        0.14           0.81    
        Up_to_date      0.29        0.03           0.88    
        Fun            -0.92        0.20           0.92    
        WhenTired       0.45        0.07           0.93    
        Relax          -0.25        0.01           0.20    
    
    Results for dimension: 2
                       Scores    CntrbPnt2In    CntrbDim2In
                       ______    ___________    ___________
    
        Kids            0.37        0.15           0.07    
        Teens          -0.24        0.16           0.65    
        EnjoyLife      -0.29        0.13           0.79    
        PicksYouUp      0.18        0.06           0.11    
        Refreshes      -0.42        0.16           0.44    
        CheersYouUp    -0.06        0.00           0.05    
        Energy          0.27        0.14           0.17    
        Up_to_date      0.08        0.01           0.07    
        Fun             0.23        0.06           0.06    
        WhenTired       0.12        0.02           0.07    
        Relax          -0.45        0.11           0.67    
    
    -----------------------------------------------------------
    Overview ROW POINTS
                    Mass    Score_1    Score_2    Inertia    CntrbPnt2In_1    CntrbPnt2In_2    CntrbDim2In_1    CntrbDim2In_2
                    ____    _______    _______    _______    _____________    _____________    _____________    _____________
    
        Coke        0.27     -0.24      -0.20      0.03          0.05             0.17             0.52             0.36     
        V           0.21      0.45       0.11      0.05          0.14             0.04             0.93             0.06     
        RedBull     0.18      0.47       0.13      0.04          0.14             0.05             0.92             0.07     
        LiftPlus    0.11      0.46       0.15      0.03          0.08             0.04             0.90             0.09     
        DietCoke    0.04     -0.09      -0.54      0.01          0.00             0.16             0.02             0.76     
        Fanta       0.10     -1.27       0.47      0.18          0.54             0.33             0.88             0.12     
        Lift        0.04     -0.50      -0.50      0.03          0.03             0.15             0.34             0.34     
        Pepsi       0.06     -0.27      -0.26      0.01          0.01             0.06             0.36             0.33     
    
    Overview COLUMN POINTS
                       Mass    Score_1    Score_2    Inertia    CntrbPnt2In_1    CntrbPnt2In_2    CntrbDim2In_1    CntrbDim2In_2
                       ____    _______    _______    _______    _____________    _____________    _____________    _____________
    
        Kids           0.07     -1.32       0.37      0.14          0.43             0.15             0.92             0.07     
        Teens          0.18      0.04      -0.24      0.02          0.00             0.16             0.02             0.65     
        EnjoyLife      0.10     -0.08      -0.29      0.01          0.00             0.13             0.06             0.79     
        PicksYouUp     0.12      0.49       0.18      0.03          0.10             0.06             0.88             0.11     
        Refreshes      0.06     -0.29      -0.42      0.02          0.02             0.16             0.21             0.44     
        CheersYouUp    0.06     -0.24      -0.06      0.00          0.01             0.00             0.83             0.05     
        Energy         0.12      0.60       0.27      0.05          0.14             0.14             0.81             0.17     
        Up_to_date     0.09      0.29       0.08      0.01          0.03             0.01             0.88             0.07     
        Fun            0.07     -0.92       0.23      0.06          0.20             0.06             0.92             0.06     
        WhenTired      0.09      0.45       0.12      0.02          0.07             0.02             0.93             0.07     
        Relax          0.03     -0.25      -0.45      0.01          0.01             0.11             0.20             0.67     
    
    -----------------------------------------------------------
    Legend
    CntrbPnt2In = relative contribution of points to explain total Inertia of the latent dimension
                  The sum of the numbers in a column is equal to 1
    CntrbDim2In = relative contribution of latent dimension to explain total Inertia of a point
                  CntrbDim2In_1+CntrbDim2In_2+...+CntrbDim2In_K=1
    
    Click here for the graphical output of this example (link to Ro.S.A. website).

  • moonplot with option changedimsign.
  • Prepare the data.

    load mobilephone
    out=CorAna(mobilephone,'plots',0);
    % Use of option changedimsign
    moonplot(out,'changedimsign',[true false])
    Summary
                 Singular_value    Inertia    Accounted_for    Cumulative
                 ______________    _______    _____________    __________
    
        dim_1         0.48          0.23          0.66            0.66   
        dim_2         0.25          0.06          0.19            0.84   
        dim_3         0.20          0.04          0.12            0.96   
        dim_4         0.09          0.01          0.02            0.98   
        dim_5         0.06          0.00          0.01            1.00   
        dim_6         0.03          0.00          0.00            1.00   
        dim_7         0.02          0.00          0.00            1.00   
    
    ROW POINTS
    Results for dimension: 1
                           Scores    CntrbPnt2In    CntrbDim2In
                           ______    ___________    ___________
    
        AAPTCellularOne     0.44        0.07           0.58    
        NewTel              0.70        0.19           0.83    
        OneTel              0.76        0.29           0.68    
        Optus              -0.37        0.10           0.80    
        Orange              0.08        0.00           0.07    
        Telstra            -0.48        0.20           0.63    
        VirginMobile        0.23        0.02           0.24    
        Vodafone           -0.42        0.12           0.76    
    
    Results for dimension: 2
                           Scores    CntrbPnt2In    CntrbDim2In
                           ______    ___________    ___________
    
        AAPTCellularOne     0.21        0.06           0.13    
        NewTel              0.09        0.01           0.01    
        OneTel             -0.46        0.38           0.25    
        Optus               0.01        0.00           0.00    
        Orange              0.21        0.07           0.49    
        Telstra            -0.27        0.22           0.20    
        VirginMobile        0.38        0.22           0.66    
        Vodafone            0.12        0.03           0.06    
    
    COLUMN POINTS
    Results for dimension: 1
                                        Scores    CntrbPnt2In    CntrbDim2In
                                        ______    ___________    ___________
    
        Bureaucratic                    -0.21        0.01           0.22    
        LowService                       0.13        0.00           0.48    
        Friendly                        -0.13        0.00           0.13    
        LowPrices                        0.07        0.00           0.02    
        Fashionable                     -0.13        0.00           0.06    
        UnFashionable                    0.26        0.02           0.55    
        Reliable                        -0.54        0.06           0.92    
        HereTodayGoneTomorrow            1.18        0.26           0.76    
        GoodCoverage                    -0.73        0.10           0.82    
        NetworkOftenDown                 0.23        0.02           0.78    
        TheBestPhones                   -0.33        0.02           0.82    
        ConvenientlyLocatedStores       -0.63        0.09           0.92    
        HighPrices                      -0.41        0.03           0.43    
        Unreliable                       0.59        0.08           0.81    
        MeetMyCommunicationNeeds        -0.38        0.03           0.89    
        LeadersMobilePhoneTechnology    -0.43        0.04           0.97    
        ILikeThem                       -0.24        0.01           0.57    
        IHateThem                        0.28        0.03           0.95    
        DonotKnowMuchAboutThem           0.82        0.18           0.58    
    
    Results for dimension: 2
                                        Scores    CntrbPnt2In    CntrbDim2In
                                        ______    ___________    ___________
    
        Bureaucratic                    -0.26        0.06           0.33    
        LowService                      -0.11        0.01           0.31    
        Friendly                         0.29        0.07           0.63    
        LowPrices                        0.33        0.09           0.52    
        Fashionable                      0.39        0.12           0.56    
        UnFashionable                   -0.10        0.01           0.09    
        Reliable                        -0.12        0.01           0.04    
        HereTodayGoneTomorrow           -0.58        0.22           0.18    
        GoodCoverage                    -0.27        0.05           0.11    
        NetworkOftenDown                 0.03        0.00           0.02    
        TheBestPhones                    0.08        0.00           0.05    
        ConvenientlyLocatedStores       -0.05        0.00           0.01    
        HighPrices                      -0.26        0.04           0.18    
        Unreliable                      -0.25        0.05           0.14    
        MeetMyCommunicationNeeds         0.00        0.00           0.00    
        LeadersMobilePhoneTechnology    -0.03        0.00           0.00    
        ILikeThem                        0.15        0.02           0.22    
        IHateThem                       -0.04        0.00           0.02    
        DonotKnowMuchAboutThem           0.50        0.25           0.22    
    
    -----------------------------------------------------------
    Overview ROW POINTS
                           Mass    Score_1    Score_2    Inertia    CntrbPnt2In_1    CntrbPnt2In_2    CntrbDim2In_1    CntrbDim2In_2
                           ____    _______    _______    _______    _____________    _____________    _____________    _____________
    
        AAPTCellularOne    0.09      0.44       0.21      0.03          0.07             0.06             0.58             0.13     
        NewTel             0.09      0.70       0.09      0.05          0.19             0.01             0.83             0.01     
        OneTel             0.12      0.76      -0.46      0.10          0.29             0.38             0.68             0.25     
        Optus              0.17     -0.37       0.01      0.03          0.10             0.00             0.80             0.00     
        Orange             0.10      0.08       0.21      0.01          0.00             0.07             0.07             0.49     
        Telstra            0.19     -0.48      -0.27      0.07          0.20             0.22             0.63             0.20     
        VirginMobile       0.10      0.23       0.38      0.02          0.02             0.22             0.24             0.66     
        Vodafone           0.15     -0.42       0.12      0.04          0.12             0.03             0.76             0.06     
    
    Overview COLUMN POINTS
                                        Mass    Score_1    Score_2    Inertia    CntrbPnt2In_1    CntrbPnt2In_2    CntrbDim2In_1    CntrbDim2In_2
                                        ____    _______    _______    _______    _____________    _____________    _____________    _____________
    
        Bureaucratic                    0.05     -0.21      -0.26      0.01          0.01             0.06             0.22             0.33     
        LowService                      0.06      0.13      -0.11      0.00          0.00             0.01             0.48             0.31     
        Friendly                        0.05     -0.13       0.29      0.01          0.00             0.07             0.13             0.63     
        LowPrices                       0.05      0.07       0.33      0.01          0.00             0.09             0.02             0.52     
        Fashionable                     0.05     -0.13       0.39      0.01          0.00             0.12             0.06             0.56     
        UnFashionable                   0.06      0.26      -0.10      0.01          0.02             0.01             0.55             0.09     
        Reliable                        0.05     -0.54      -0.12      0.02          0.06             0.01             0.92             0.04     
        HereTodayGoneTomorrow           0.04      1.18      -0.58      0.08          0.26             0.22             0.76             0.18     
        GoodCoverage                    0.04     -0.73      -0.27      0.03          0.10             0.05             0.82             0.11     
        NetworkOftenDown                0.07      0.23       0.03      0.00          0.02             0.00             0.78             0.02     
        TheBestPhones                   0.05     -0.33       0.08      0.01          0.02             0.00             0.82             0.05     
        ConvenientlyLocatedStores       0.05     -0.63      -0.05      0.02          0.09             0.00             0.92             0.01     
        HighPrices                      0.04     -0.41      -0.26      0.02          0.03             0.04             0.43             0.18     
        Unreliable                      0.05      0.59      -0.25      0.02          0.08             0.05             0.81             0.14     
        MeetMyCommunicationNeeds        0.05     -0.38       0.00      0.01          0.03             0.00             0.89             0.00     
        LeadersMobilePhoneTechnology    0.05     -0.43      -0.03      0.01          0.04             0.00             0.97             0.00     
        ILikeThem                       0.05     -0.24       0.15      0.01          0.01             0.02             0.57             0.22     
        IHateThem                       0.08      0.28      -0.04      0.01          0.03             0.00             0.95             0.02     
        DonotKnowMuchAboutThem          0.06      0.82       0.50      0.07          0.18             0.25             0.58             0.22     
    
    -----------------------------------------------------------
    Legend
    CntrbPnt2In = relative contribution of points to explain total Inertia of the latent dimension
                  The sum of the numbers in a column is equal to 1
    CntrbDim2In = relative contribution of latent dimension to explain total Inertia of a point
                  CntrbDim2In_1+CntrbDim2In_2+...+CntrbDim2In_K=1
    
    Click here for the graphical output of this example (link to Ro.S.A. website).

    Input Arguments

    expand all

    out — Structure containing the output of function CorAna. Structure.

    Structure containing the following fields.

    Value Description
    Lr

    cell of length containing the labels of active rows (i.e. the rows which participated to the fit).

    Lc

    cell of length J containing the labels of active columns (i.e. the columns which participated to the fit).

    n

    Grand total. out.n is equal to sum(sum(out.N)).

    This is the number of observations.

    Dr

    Square matrix of size I containing on the diagonal the row masses. This is matrix D_r.

    D_r=diag(r)

    Dc

    Square matrix of size J containing on the diagonal the column masses. This is matrix D_c.

    D_c=diag(c)

    InertiaExplained

    matrix with 4 columnn.

    - First column contains the singular values (the sum of the squared singular values is the total inertia).

    - Second column contains the eigenvalues (the sum of the eigenvalues is the total inertia).

    - Third column contains the variance explained by each latent dimension.

    - Fourth column contains the cumulative variance explained by each dimension.

    LrSup

    cell containing the labels of the supplementary rows (i.e. the rows whicg did not participate to the fit).

    LcSup

    cell containing the labels of supplementary columns (i.e. the columns which did not participate to the fit).

    SupRowsN

    matrix of size length(LrSup)-by-c referred to supplementary rows. If there are no supplementary rows this field is not present.

    SupColsN

    matlab of size r-by-length(LcSup) referred to supplementary columns.

    If there are no supplementary columns this field is not present.

    RowsPriSup

    Principal coordinates of supplementary rows.

    If there are no supplementary rows this field is not present.

    RowsStaSup

    Standard coordinates of supplementary rows.

    If there are no supplementary rows this field is not present.

    RowsSymSup

    Symmetrical coordinates of supplementary rows.

    If there are no supplementary rows this field is not present.

    ColsPriSup

    Principal coordinates of supplementary columns.

    If there are no supplementary columns this field is not present.

    ColsStaSup

    Standard coordinates of of supplementary columns.

    If there are no supplementary columns this field is not present.

    ColsSymSup

    Symmetrical coordinates of supplementary columns.

    If there are no supplementary columns this field is not present.

    Data Types: struct

    Name-Value Pair Arguments

    Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

    Example: 'plots',plots=struct; plots.colorcols='k' , 'addx',0.01 , 'addy',0.01 , 'changedimsign', [true false] , 'xlimx',[-1 1] , 'ylimy',[0 1] , 'd1',2 , 'd2',3 ,'h',h1 where h1=subplot(2,1,1)

    plots —Customize plot appearance.scalar | structure.

    If plots is not a structure, a plot which shows the Principal coordinates of rows and columns is shown on the screen. If plots is a structure it may contain the following fields:

    Value Description
    alpha

    type of plot, scalar in the interval [0 1] or a string identifying the type of coordinates to use in the plot.

    If plots.alpha='rowprincipal' the row points are in principal coordinates and the column coordinates are standard coordinates. Distances between row points are (approximated) chi-squared distances (row-metric-preserving). The position of the row points are at the weighted average of the column points.

    Note that 'rowprincipal' can also be specified setting plots.alpha=1.

    If plots.alpha='colprincipal', the column coordinates are referred to as principal coordinates and the row coordinates as standard coordinates.

    Distances between column points are (approximated) chi-squared distances (column-metric-preserving). The position of the column points are at the weighted average of the row points.

    Note that 'colprincipal' can also be specified setting plots.alpha=0.

    If plots.alpha='symbiplot', the row and column coordinates are scaled similarly. The sum of weighted squared coordinates for each dimension is equal to the corresponding singular values. These coordinates are often called symmetrical coordinates. This representation is particularly useful if one is primarily interested in the relationships between categories of row and column variables rather than in the distances among rows or among columns. 'symbiplot' can also be specified setting plots.alpha=0.5;

    If plots.alpha='bothprincipal', both the rows and columns are depicted in principal coordinates. Such a plot is often referred to as a symmetrical plot or French symemtrical model. Note that such a symmetrical plot does not provide a feasible solution in the sense that it does not approximate matrix D_r^{-0.5}(P-rc')D_c^{-0.5}.

    If plots.alpha='bothstandard', both the rows and columns are depicted in standard coordinates.

    If plots.alpha='rowgab', rows are in principal coordinates and columns are in standard coordinates multiplied by the mass. This biplot has been suggested by Gabriel and Odoroff (1990).

    If plots.alpha='colgab', columns are in principal coordinates and rows are in standard coordinates multiplied by the mass. This biplot has been suggested by Gabriel and Odoroff (1990).

    If plots.alpha='rowgreen', rows are in principal coordinates and columns are in standard coordinates multiplied by square root of the mass.

    This biplot has been suggested by Greenacre and incorporates the contribution of points. In this display, points that contribute very little to the solution, are close to the center of the biplot and are relatively unimportant to the interpretation. This biplot is often referred as contribution biplot because it visually shows the most contributing points (Greenacre 2006b).

    If plots.alpha='colgreen', columns in principal coordinates and rows in standard coordinates multiplied by the square root of the mass.

    This biplot has been suggested by Greenacre and incorporates the contribution of points. In this display, points that contribute very little to the solution, are close to the center of the biplot and are relatively unimportant to the interpretation. This biplot is often referred as contribution biplot because it shows visually the most contributing points (Greenacre 2006b).

    If plots.alpha=scalar in the interval [0 1], row coordinates are given by D_r^{-1/2} U \Gamma^\alpha and column coordinates are given by D_c^{-1/2} V \Gamma^{1-\alpha}. Note that for any choice of \alpha the matrix product D_r^{-1/2} U \Gamma^\alpha (D_c^{-1/2} V \Gamma^{1-\alpha})^T optimally approximates matrix D_r^{-0.5}(P-rc')D_c^{-0.5}, in the sense that the sum of squared differences between D_r^{1/2} D_r^{-1/2} U \Gamma^\alpha (D_c^{-1/2} V \Gamma^{1-\alpha})^T D_c^{1/2} and D_r^{-0.5}(P-rc')D_c^{-0.5} is as small as possible.

    FontSize

    scalar which specifies the font size of row labels. The default value is 10.

    FontSizeSup

    scalar which specifies the font size of row labels of supplementary points. The default value is 10.

    MarkerSize

    scalar which specifies the marker size of symbols associated with rows. The default value is 10.

    SymbolRows

    character which specifies the symbol to use for row points. If this field is not present the default symbols is 'o'.

    SymbolRowsSup

    character which specifies the symbol to use for supplementary row points. If this field is not present the default symbols is 'o'.

    ColorRows

    character which specifies the symbol to use for row points or RGB triplet. If this field is not present the default color is 'b'.

    ColorCols

    character which specifies the symbol to use for column points or RGB triplet. If this field is not present the default color is 'r'.

    ColorRowsSup

    character which specifies the symbol to use for row points or RGB triplet. If this field is not present the default color is 'b'.

    ColorColsSup

    character which specifies the symbol to use for supplementary column points or RGB triplet. If this field is not present the default color is 'r'.

    MarkerFaceColorRows

    character which specifies the marker fill color to use for active row points or RGB triplet. If this field is not present the default color is 'auto'.

    MarkerFaceColorRowsSup

    character which specifies the marker fill color to use for supplementary row points or RGB triplet. If this field is not present the default color is 'auto'.

    Example: 'plots',plots=struct; plots.colorcols='k'

    Data Types: double

    addx —horizontal displacement for labels.scalar.

    Amount of horizontal displacement which has been put on the labels in the plot. The defalut value of addx is 0.04.

    Example: 'addx',0.01

    Data Types: double

    addy —vertical displacement for labels.scalar.

    Amount of vertical displacement which has been put on the labels in the plot. The defalut value of addy is 0.

    Example: 'addy',0.01

    Data Types: double

    changedimsign —change chosen dimension sign.boolean vector of length 2.

    Sometimes for better interpretability it is necessary to change the sign of the coordinates for the chosen dimension. If changedimsign(1) is true the sign of the coordinates for first chosen dimension is changed. If changedimsign(2) is true the sign of the coordinates for first chosen dimension is changed. As default the dimensions are the first and the second however, they can be changed using option plots.dim. The defaul value of changedimsign is [false false] that is the sign is not changed.

    Example: 'changedimsign', [true false]

    Data Types: boolean

    xlimx —Min and Max of the x axis.vector.

    Vector with two elements controlling minimum and maximum of the x axis.

    Example: 'xlimx',[-1 1]

    Data Types: double

    ylimy —Min and Max of the y axis.vector.

    Vector with two elements controlling minimum and maximum of the y axis.

    Example: 'ylimy',[0 1]

    Data Types: double

    d1 —Dimension to show on the horizontal axis.positive integer.

    Positive integer in the range 1, 2, .., K which indicates the dimension to show on the x axis. The default value of d1 is 1.

    Example: 'd1',2

    Data Types: single | double

    d2 —Dimension to show on the vertical axis.positive integer.

    Positive integer in the range 1, 2, .., K which indicates the dimension to show on the y axis. The default value of d2 is 2.

    Example: 'd2',3

    Data Types: single | double

    h —the axis handle of a figure where to send the moonplot.this can be used to host the moonplot in a subplot of a complex figure formed by different panels (for example a panel with moonplot from plots.

    alpha=0.2 and another with moonplot from plots.alpha=0.5).

    Example: 'h',h1 where h1=subplot(2,1,1)

    Data Types: Axes object (supplied as a scalar)

    Output Arguments

    References

    Benzecri, J.-P. (1992), "Correspondence Analysis Handbook", New-York, Dekker.

    Benzecri, J.-P. (1980), "L'analyse des donnees tome 2: l'analyse des correspondances", Paris, Bordas.

    Greenacre, M.J. (1993), "Correspondence Analysis in Practice", London, Academic Press.

    Bock, T. (2011), Improving the display of correspondence analysis using moon plots, "International Journal of Market Research", Vol. 53, pp. 307-326.

    Gabriel, K.R. and Odoroff, C. (1990), Biplots in biomedical research, "Statistics in Medicine", Vol. 9, pp. 469-485.

    Greenacre, M.J. (1993), Biplots in correspondence Analysis, "Journal of Applied Statistics", Vol. 20, pp. 251-269.

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