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Dataplot Vol 2 Vol 1

BINARY MATCH DISSIMILARITY

Name:
    BINARY MATCH DISSIMILARITY (LET)
    BINARY MATCH SIMILARITY (LET)
    BINARY ROGERS MATCH DISSIMILARITY (LET)
    BINARY ROGERS MATCH SIMILARITY (LET)
    BINARY SOKAL MATCH DISSIMILARITY (LET)
    BINARY SOKAL MATCH SIMILARITY (LET)
    BINARY JACCARD DISSIMILARITY (LET)
    BINARY JACCARD SIMILARITY (LET)
    BINARY ASYMMETRIC SOKAL MATCH DISSIMILARITY (LET)
    BINARY ASYMMETRIC SOKAL MATCH SIMILARITY (LET)
    BINARY ASYMMETRIC DICE MATCH DISSIMILARITY (LET)
    BINARY ASYMMETRIC DICE MATCH SIMILARITY (LET)
Type:
    Let Subcommand
Purpose:
    Given two binary (i.e., 0 or 1 values) response variables, compute various matching statistics that define either a similarity or dissimilarity score.
Description:
    Given two variables with n parired observations where each variable has exactly two possible outcomes, we can generate the following 2x2 table:

        Variable 2  
      Variable 1 Not Present Present Row Total

      Not Present A B A + B
      Present C D C + D

      Column Total A + C B + D A + B + C + D

    In the data, we use a value of "0" to denote "not present" and a value of "1" to denote "present".

    The parameters A, B, C, and D denote the counts for each category. The various matching statistics combine A, B, C, and D in various ways. A distinction is made between "symmetric" and "asymmetric" matching statistics. Symmetric statistics are typically preferred when the "0" and the "1" outcome are considered equally meaningful. Asymmetric statistics are preferred when the "1" outcome is more meaningful. The case where matching the presence of rare events is what is considered important is an example where the asymmetric scores would be recommended.

    Specifically

      Symmetric Binary Variables
        Similarity:
        Matching Coefficient:   \( \frac{A + D} {A + B + C + D} \)
        Rogers and Tanimoto:   \( \frac{A + D} {(A + D) + 2(B + C)} \)
        Sokal and Sneath:   \( \frac{2(A + D)} {2(A + D) + (B + C)} \)

        Dissimilarity:
        Matching Coefficient:   \( \frac{B + C} {A + B + C + D} \)
        Rogers and Tanimoto:   \( \frac{2(B + C)} {(A + D) + 2(B + C)} \)
        Sokal and Sneath:   \( \frac{B + C} {2((A + D) + (B + C)} \)

      Asymmetric Binary Variables (most important value coded as 1)

        Similarity:
        Jaccard Coefficient:   \( \frac{A}{A+B+C} \)
        Dice Coefficient:   \( \frac{2A}{2A + B + C} \)
        Sokal Coefficient:   \( \frac{A}{A + 2(B + C)} \)

        Dissimilarity:
        Jaccard Coefficient:   \( \frac{B + C}{A + B + C} \)
        Dice Coefficient:   \( \frac{B + C}{2A + B + C} \)
        Sokal Coefficient:   \( \frac{2(B + C)}{A + 2(B + C)} \)

    These statistics are often used to create dissimilarity or similarity matrices that will be used as input to various multivariate procedures such as clustering.

    The above statstics where taken from Kauffman and Rousseeuw (see Reference below). They recommend using the matching coefficient for the symmetric case and the Jaccard coefficient for the asymmetric case. However, the above list is not exhaustive and other authors recommend other choices. Also, other sources may have somewhat different formulas for these statistics.

Syntax 1:
    LET <par> = BINARY MATCH DISSIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed matching dissimilarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    LET <par> = BINARY MATCH SIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed matching similarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 3:
    LET <par> = BINARY ROGERS MATCH DISSIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Rogers and Tanimato matching dissimilarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 4:
    LET <par> = BINARY ROGERS MATCH SIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Rogers and Tanimato matching similarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 5:
    LET <par> = BINARY SOKAL MATCH DISSIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Sokal and Sneath matching dissimilarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 6:
    LET <par> = BINARY SOKAL MATCH SIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Sokal and Sneath matching similarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 7:
    LET <par> = BINARY JACCARD DISSIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Jaccard dissimilarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 8:
    LET <par> = BINARY JACCARD SIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Jaccard similarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 9:
    LET <par> = BINARY ASYMMETRIC SOKAL MATCH DISSIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Sokal asymmetric matching dissimilarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 10:
    LET <par> = BINARY ASYMMETRIC SOKAL MATCH SIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Sokal asymmetric matching similarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 11:
    LET <par> = BINARY ASYMMETRIC DICE MATCH DISSIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Dice asymmetric matching dissimilarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 12:
    LET <par> = BINARY ASYMMETRIC DICE MATCH SIMILARITY <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed Dice asymmetric matching similarity coefficient is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = BINARY MATCHING DISSIMILARITY Y1 Y2
    LET A = BINARY MATCHING DISSIMILARITY Y1 Y2 ...
                            SUBSET Y1 0 1 SUBSET Y2 0 1
    LET A = BINARY MATCHING SIMILARITY Y1 Y2
    LET A = BINARY ROGERS MATCH DISSIMILARITY Y1 Y2
    LET A = BINARY ROGERS MATCH SIMILARITY Y1 Y2
    LET A = BINARY SOKAL MATCH DISSIMILARITY Y1 Y2
    LET A = BINARY SOKAL MATCH SIMILARITY Y1 Y2
    LET A = BINARY JACCARD DISSIMILARITY Y1 Y2
    LET A = BINARY JACCARD SIMILARITY Y1 Y2
    LET A = BINARY ASYMMETRIC SOKAL MATCH DISSIMILARITY Y1 Y2
    LET A = BINARY ASYMMETRIC SOKAL MATCH SIMILARITY Y1 Y2
    LET A = BINARY ASYMMETRIC DICE MATCH DISSIMILARITY Y1 Y2
    LET A = BINARY ASYMMETRIC DICE MATCH SIMILARITY Y1 Y2
Note:
    The two response variables must have the same number of elements. For raw data, the response variables should only contain the values 0 and 1. See the next Note for a discussion of how to enter the A, B, C, and D values directly.
Note:
    There are two ways you can define the response variables:
    1. Raw data - in this case, the variables contain 0's and 1's.

      If the data is not coded as 0's and 1's, Dataplot will check for the number of distinct values. If there are two distinct values, the minimum value is converted to 0's and the maximum value is converted to 1's. If there is a single distinct value, it is converted to 0's if it is less than 0.5 and to 1's if it is greater than or equal to 0.5. If there are more than two distinct values, an error is returned.

    2. Summary data - if there are two observations, the data is assummed to be the 2x2 summary table. That is,

        Y1(1) = A
        Y1(2) = C
        Y2(1) = B
        Y2(2) = D
Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    None
Related Commands: Reference:
    Kaufman and Rousseeuw (1990), "Finding Groups in Data: An Introduction To Cluster Analysis", Wiley.
Applications:
    Clustering, Multivariate Analysis
Implementation Date:
    2017/08
Program:
     
    .  Example from page 24 of Kaufman and Rousseeuw text.
    .  The rows are 8 people and the columns are 10 binary variables
    .
    set write decimals 3
    dimension 100 columns
    .
    read matrix x
    1   0  1  1  0  0  1  0  0  0
    0   1  0  0  1  0  0  0  0  0
    0   0  1  0  0  0  1  0  0  1
    0   1  0  0  0  0  0  1  1  0
    1   1  0  0  1  1  0  1  1  0
    1   1  0  0  1  0  1  1  0  0
    0   0  0  1  0  1  0  0  0  0
    0   0  0  1  0  1  0  0  0  0
    end of data
    .
    let d = generate matrix binary match dissimilarity ...
            x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
    print d1 d2 d3 d4 d5
    print d6 d7 d8 d9 d10
    .
    let ad = generate matrix binary jaccard dissimilarity ...
             x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
    print ad1 ad2 ad3 ad4 ad5
    print ad6 ad7 ad8 ad9 ad10
        
    The following output is generated
    ---------------------------------------------------------------------------
                 D1             D2             D3             D4             D5
    ---------------------------------------------------------------------------
              0.000          0.375          0.375          0.500          0.250
              0.375          0.000          0.750          0.875          0.125
              0.375          0.750          0.000          0.375          0.625
              0.500          0.875          0.375          0.000          0.750
              0.250          0.125          0.625          0.750          0.000
              0.500          0.625          0.625          0.250          0.500
              0.250          0.625          0.125          0.500          0.500
              0.250          0.125          0.625          0.750          0.250
              0.375          0.250          0.500          0.625          0.375
              0.500          0.625          0.125          0.500          0.500
     
     
    ---------------------------------------------------------------------------
                 D6             D7             D8             D9            D10
    ---------------------------------------------------------------------------
              0.500          0.250          0.250          0.375          0.500
              0.625          0.625          0.125          0.250          0.625
              0.625          0.125          0.625          0.500          0.125
              0.250          0.500          0.750          0.625          0.500
              0.500          0.500          0.250          0.375          0.500
              0.000          0.750          0.500          0.375          0.500
              0.750          0.000          0.500          0.625          0.250
              0.500          0.500          0.000          0.125          0.500
              0.375          0.625          0.125          0.000          0.375
              0.500          0.250          0.500          0.375          0.000
     
     
     
    ---------------------------------------------------------------------------
                AD1            AD2            AD3            AD4            AD5
    ---------------------------------------------------------------------------
              0.000          0.500          0.429          0.571          0.333
              0.500          0.000          0.750          0.875          0.200
              0.429          0.750          0.000          0.429          0.625
              0.571          0.875          0.429          0.000          0.750
              0.333          0.200          0.625          0.750          0.000
              0.571          0.714          0.625          0.333          0.571
              0.333          0.714          0.167          0.571          0.571
              0.333          0.200          0.625          0.750          0.333
              0.429          0.333          0.500          0.625          0.429
              0.500          0.625          0.143          0.500          0.500
     
     
    ---------------------------------------------------------------------------
                AD6            AD7            AD8            AD9           AD10
    ---------------------------------------------------------------------------
              0.571          0.333          0.333          0.429          0.500
              0.714          0.714          0.200          0.333          0.625
              0.625          0.167          0.625          0.500          0.143
              0.333          0.571          0.750          0.625          0.500
              0.571          0.571          0.333          0.429          0.500
              0.000          0.750          0.571          0.429          0.500
              0.750          0.000          0.571          0.625          0.286
              0.571          0.571          0.000          0.167          0.500
              0.429          0.625          0.167          0.000          0.375
              0.500          0.286          0.500          0.375          0.000
     
        

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Date created: 09/20/2017
Last updated: 09/20/2017

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