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normYJ
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normBoxCox

normBoxCox computes (normalized) Box-Cox transformation

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Syntax

  • Ytra=normBoxCox(Y,ColtoTra,la)example
  • Ytra=normBoxCox(Y,ColtoTra,la,Name,Value)example

Description

example

Ytra =normBoxCox(Y, ColtoTra, la) Comparison between Box-Cox and Yeo-Johnson transformation.

example

Ytra =normBoxCox(Y, ColtoTra, la, Name, Value) Mussels data.

Examples

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  • Comparison between Box-Cox and Yeo-Johnson transformation.

    • close all
    y=(-2:0.1:2)';
    n=length(y);
    la=-1:1:3;
    nla=length(la);
    YtraYJ=zeros(n,nla);
    YtraBC=nan(n,nla);
    posy=y>0;
    for j=1:nla
    YtraYJ(:,j)=normYJ(y,1,la(j),'Jacobian',false);
    YtraBC(posy,j)=normBoxCox(y(posy),1,la(j),'Jacobian',false);
    end
    subplot(1,2,1)
    plot(y,YtraYJ)
    for j=1:nla
    text(y(1), YtraYJ(1,j),['\lambda=' num2str(la(j))])
    end
    xlabel('Original values')
    ylabel('Transformed values')
    title('Yeo-Johnson transformation')
    subplot(1,2,2)
    plot(y,YtraBC)
    xlim([y(1) y(end)])
    for j=1:nla
    text(y(16), YtraBC(22,j),['\lambda=' num2str(la(j))])
    end
    xlabel('Original values')
    ylabel('Transformed values')
    title('Box-Cox transformation')

  • Mussels data.

    • load('mussels.mat');
    Y=mussels{:,:};
    la=[0.5 0 0.5 0 0];
    % Transform all columns of matrix Y according to the values of la
    Y=normBoxCox(Y,[],la);

    Related Examples

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  • Check the inverse tranformation.

    • load('mussels.mat');
    Y=mussels{:,:};
    la=[0.5 0 0.5 0 0];
    % Transform all columns of matrix Y according to the values of la
    Ytra=normBoxCox(Y,[],la,'Jacobian',false);
    Ychk=normBoxCox(Ytra,[],la,'inverse',true);
    disp(max(max(abs(Y-Ychk))))

    Input Arguments

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    Y — Input data. Matrix.

    n x v data matrix; n observations and v variables. Rows of Y represent observations, and columns represent variables.

    Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

    Data Types: single|double

    ColtoTra — Variable to transform. Vector.

    k x 1 integer vector specifying the variables which must be transformed. If it is missing and length(la)=v all variables are transformed

    Data Types: single|double

    la — transformation parameters. Vector.

    k x 1 vector containing set of transformation parameters for the k ColtoTra.

    Data Types: single|double

    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: 'bsb',[3 5 20:30] , 'inverse',true , 'Jacobian',true

    bsb —units to be used in the computation of the Jacobian.vector.

    m x 1 vector or logical vector or length n.

    The default value of bsb is 1:n, that is all units are used to compute the Jacobian. Note that this option takes effect just if option Jacobian is true.

    Example: 'bsb',[3 5 20:30]

    Data Types: double or logical

    inverse —Inverse transformation.logical.

    If inverse is true, the inverse transformation is returned. The default value of inverse is false.

    Example: 'inverse',true

    Data Types: Logical

    Jacobian —Requested Jacobian of transformed values.true (default) | false.

    If true (default) the transformation is normalized to have Jacobian equal to 1. Note that this optional argument is ignored if previous optional argument inverse is true

    Example: 'Jacobian',true

    Data Types: Logical

    Output Arguments

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    Ytra —transformed data matrix. Matrix

    n x v data matrix containing transformed observations When if jacobian=true: ytra = (y^\lambda-1)/ (G^{(\lambda-1)} \lambda);

    else if jacobian=false: ytra = (y^\lambda-1)/ \lambda;

    where G is the geometric mean of the observations.

    When \lambda = 0 if jacobian=true: ytra = G log(y);

    else if jacobian=false: ytra = log(y);

    where G is the geometric mean of the observations.

    References

    Box, G.E.P. and Cox, D.R. (1964), An analysis of transformations (with Discussion), "Journal of the Royal Statistical Society Series B", Vol. 26, pp. 211-252.

    See Also

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