CORRMV <Survo_data>,L
computes means, standard deviations, and correlations from active
variables and observations by accepting also cases containing
missing values. The standard CORR module leaves out all incomplete
cases.
The default method (METHOD=1) is a simplified EM algorithm by S.Mustonen.
In this method the data set is first standardized (means=0 stddevs=1)
and the missing values are replaced by 0's.
Thereafter estimates for missing values are improved iteratively
by linear regressions where each variable is explained by all other
variables. In each iteration, old estimates of missing values are
replaced by the regression estimates.
In one iteration, all regression parameters are obtained simply by
updating the moment matrix of variables and by inverting it by the
Cholesky method.
Convergence of the process can be monitored by the mean squared
difference of consecutive estimates of missing values.
After ITER iterations (default ITER=20) the procedure is interrupted.
To obtain unbiased estimates for variances, in sums of squares each term
of a missing value is extended by the residual variance of the corres-
ponding regression model.
If the line for results (L) is given, the means, standard deviations,
and correlations are printed in the edit field from line L onwards.
If RESULTS=0 is given, only a summary of results is printed.
In any case the results are saved in matrix files MSN.M and CORR.M
as in CORR.
By default, missing values are not replaced by any estimates. However,
if a specification IMPUTE (or REPLACE) is given, missing values are
filled in.
By IMPUTE=REG they are replaced by their regression estimates.
Please note that regression estimates of missing values are too
well-adapted and the variability in the data is reduced. Thus, if means,
standard deviations, and correlations were recomputed from the patched
data, the variances would become smaller than those given by CORRMV
from incomplete data. Also correlations would be more biased.
By IMPUTE=REG+rand(123456789) missing values are replaced by
reg.est+u*s
where s is the square root of the residual variance of the regression
model in question and u is a standard normal variate obtained by
using the pseudo-random number generator rand with seed 123456789.
In this case means, std.devs and correlations recomputed from the
patched data are less biased.
When METHOD=PAIRWISE is used, correlations are computed for non-
missing pairs of observations. This may lead to more biased results
than METHOD=1. Also the correlation matrix (CORR.M) may have negative
eigenvalues (i.e. it is not positive definite or semidefinite).
In METHOD=PAIRWISE the frequencies of observations for each pair
of observations is saved as PAIRFREQ.M .
1 = More information on additional multivariate operations
M = More information on multivariate analysis
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