help mata mm_colvar()
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Title

    mm_colvar() -- Variance, by column


Syntax

        real rowvector mm_colvar(X [, w])

        real matrix    mm_meancolvar(X [, w])


        real matrix    mm_variance0(X [, w])

        real matrix    mm_meanvariance0(X [, w])


        real matrix    mm_mse(X, w, mu)

        real rowvector mm_colmse(X, w, mu)


        real matrix    mm_sse(X, w, mu)

        real rowvector mm_colsse(X, w, mu)


    where

            X:  real matrix X (rows are observations, columns variables)

            w:  real colvector w

           mu:  real rowvector mu


Description

    mm_colvar(X, w) returns the variance of each column of X. Essentially,

        mm_colvar(X, w) = diagonal(variance(X, w))'

    See help for mean(). However, mm_colvar() does not compute the
    covariances and is therefore much faster than diagonal(variance()) if X
    contains more than one column. Furthermore, note that mm_colvar() omits
    missing values in X by column, whereas variance() omits missing values
    casewise.

    mm_meancolvar(X, w) returns a matrix containing the mean and the variance
    of each column of X. (Means in row one, variances in row two.)

    mm_variance0(X, w) returns the population variance matrix of X.
    mm_variance0() differs from official Stata's variance() (see help for
    mean()) in that it divides the deviation cross products by N instead of
    N-1, where N is the number of observations. Essentially,

        mm_variance0(X, w) = variance(X, w) * (N-1)/N

    However, mm_variance0() also produces correct results if N==1.

    mm_meanvariance0(X, w) returns mean(X,w)\mm_variance0(X,w).

    mm_mse(X, w, mu) computes the mean squared errors matrix, where errors
    are defined as X:-mu.

    mm_colmse() computes mean squared errors by column.

    mm_sse() and mm_colsse() compute the sum of squared errors.

    w specifies the weights.  Specify w as 1 to obtain unweighted results.


Remarks

    Examples for mm_colvar():

        : x = invnormal(uniform(10000,3))
        
        : mm_colvar(x, 1)
                         1             2             3
            +-------------------------------------------+
          1 |   1.00018384   1.002621747   1.003480729  |
            +-------------------------------------------+

        : mm_meancolvar(x, 1)
                          1              2              3
            +----------------------------------------------+
          1 |  -.0024994158   -.0091972878   -.0035865732  |
          2 |    1.00018384    1.002621747    1.003480729  |
            +----------------------------------------------+

    The formula implemented in mm_mse() and mm_colmse() computes the mean
    squared error as the sum of squared errors divided by N, where N is the
    number of observations (or sum of weights if w!=1).


Conformability

    mm_colvar(X, w):
                X:  n x k
                w:  n x 1 or 1 x 1
           result:  1 x k

    mm_meancolvar(X, w):
                X:  n x k
                w:  n x 1 or 1 x 1
           result:  2 x k

    mm_variance0(X, w):
                X:  n x k
                w:  n x 1 or 1 x 1
           result:  k x k

    mm_meanvariance0(X, w):
                X:  n x k
                w:  n x 1 or 1 x 1
           result:  (k+1) x k

    mm_mse(X, w, mu), mm_sse(X, w, mu):
                X:  n x k
                w:  n x 1 or 1 x 1
               mu:  1 x k
           result:  k x k

    mm_colmse(X, w, mu), mm_colsse(X, w, mu):
                X:  n x k
                w:  n x 1 or 1 x 1
               mu:  1 x k
           result:  1 x k

Diagnostics

    mm_variance0(), mm_meanvariance0(), mm_mse(), and mm_sse() omit from
    calculation rows of X or w that contain missing values (casewise
    deletion). If all rows contain missing values, then the returned result
    contains all missing values.

    Contrarily, mm_colvar(), mm_meancolvar(), mm_colmse(), and mm_colsse()
    omit missing values by column (i.e. not casewise).


Source code

    mm_colvar.mata, mm_variance0.mata, mm_mse.mata

Author

    Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


Also see

    Online:  help for [M-5] mean(), moremata