missing values and svd

Is it possible to manage a svd analysis within a matrix containing NA
values.

The answer is full of NAs, so little use.

If not how do I could overcome this problem.

What problem?  I.e. why do you want to do this?

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Dear All,

Is it possible to manage a svd analysis within a matrix containing NA
values. If not how do I could overcome this problem.

Surely, mathematically speaking the SVD (which is a mathematical
operation, not a statistical analysis) of a matrix with missing
values is undefined.

There are two obvious options for how to proceed, though, if you
find yourself in that situation because of missing data.

1) Strike out the rows and columns with missing values, and just
use the reduced matrix.

2) "Fill in" the missing values in the data by some imputation
procedure and then proceed as if you had complete data. This
could be done by entering the expected values of the missing
data given the known ("complete") data, but it makes more sense
to proceed as follows.

For imputation, you will probably want to evaluate the uncertainty
associated with the imputed values, for which one approach could
be multiple imputation: Impute by sampling from an estimated
distribution of missing values given the complete data, evaluate
the SVD for that sample, then repeat the whole process until you
have enough data from the simulation to infer the distribution
of variability in the SVD.

In any case, imputation requires care in the selection of the
model used for the missing data.

Best wishes,
Ted.


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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 03-Dec-02                                       Time: 15:27:04
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