help mata mean()
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Title
[M-5] mean() -- Means, variances, and correlations
Syntax
real rowvector mean(X [, w])
real matrix variance(X [, w])
real matrix quadvariance(X [, w])
real matrix meanvariance(X [, w])
real matrix quadmeanvariance(X [, w])
real matrix correlation(X [, w])
real matrix quadcorrelation(X [, w])
where
X: real matrix X (rows are observations, columns are variables)
w: real colvector w and is optional.
Description
mean(X, w) returns the weighted-or-unweighted column means of data matrix
X. mean() uses quad precision in forming sums and so is very accurate.
variance(X, w) returns the weighted-or-unweighted variance matrix of X.
In the calculation, means are removed and those means are calculated in
quad precision, but quad precision is not otherwise used.
quadvariance(X, w) returns the weighted-or-unweighted variance matrix of
X. Calculation is highly accurate; quad precision is used in forming all
sums.
meanvariance(X, w) returns mean(X,w)\variance(X,w).
quadmeanvariance(X, w) returns mean(X,w)\quadvariance(X,w).
correlation(X, w) returns the weighted-or-unweighted correlation matrix
of X. correlation() obtains the variance matrix from variance().
quadcorrelation(X, w) returns the weighted-or-unweighted correlation
matrix of X. quadcorrelation() obtains the variance matrix from
quadvariance().
In all cases, w specifies the weight. Omit w, or specify w as 1 to
obtain unweighted means.
In all cases, rows of X or w that contain missing values are omitted from
the calculation, which amounts to casewise deletion.
Remarks
1. There is no quadmean() function because mean(), in fact, is
quadmean(). The fact that mean() defaults to the quad-precision
calculation reflects our judgment that the extra computational cost
in computing means in quad precision is typically justified.
2. The fact that variance() and correlation() do not default to using
quad precision for their calculations reflects our judgment that the
extra computational cost is typically not justified. The emphasis on
this last sentence is on the word typically.
It is easier to justify means in part because the extra computational
cost is less: there are only k means but k(k+1)/2 variances and
covariances.
3. If you need just the mean or just the variance matrix, call mean() or
variance() (or quadvariance()). If you need both, there is a
CPU-time savings to be had by calling meanvariance() instead of the
two functions separately (or quadmeanvariance() instead of calling
mean() and quadvariance()).
The savings is not great -- one mean() calculation is saved -- but
the greater rows(X), the greater the savings.
Upon getting back the combined result, it can be efficiently broken
into its components via
: var = meanvariance(X)
: means = var[1,.]
: var = var[|2,1 \ .,.|]
Conformability
mean(X, w):
X: n x k
w: n x 1 or 1 x 1 (optional, w=1 assumed)
result: 1 x k
variance(X, w), quadvariance(X, w), correlation(X, w), quadcorrelation(X,
w):
X: n x k
w: n x 1 or 1 x 1 (optional, w=1 assumed)
result: k x k
meanvariance(X, w), quadmeanvariance(X, w):
X: n x k
w: n x 1 or 1 x 1 (optional, w=1 assumed)
result: (k+1) x k
Diagnostics
All functions omit from the calculation rows that contain missing values
unless all rows contain missing values. Then the returned result
contains all missing values.
Source code
mean.mata, variance.mata, quadvariance.mata, meanvariance.mata,
quadmeanvariance.mata, correlation.mata, quadcorrelation.mata
Also see
Manual: [M-5] mean()
Help: [M-4] statistical
