swp function

Sweep operator

Sweeps a covariance matrix with respect to a subset of indices.

swp(V, b)

Arguments

• V: a symmetric positive definite matrix, the covariance matrix.
• b: a subset of indices of the columns of V.

Details

The sweep operator has been introduced by Beaton (1964) as a tool for inverting symmetric matrices (see Dempster, 1969).

Returns

a square matrix U of the same order as V. If a is the complement of b, then U[a,b] is the matrix of regression coefficients of a given b and U[a,a]

is the corresponding covariance matrix of the residuals.

If b is empty the function returns V.

If b is the vector 1:nrow(V) (or its permutation) then the function returns the opposite of the inverse of V.

References

Beaton, A.E. (1964). The use of special matrix operators in statistical calculus. Ed.D. thesis, Harvard University. Reprinted as Educational Testing Service Research Bulletin 64-51. Princeton.

Dempster, A.P. (1969). Elements of continuous multivariate analysis. Reading: Addison-Wesley.

Author(s)

Giovanni M. Marchetti

See Also

fitDag

Examples

## A very simple example
V <- matrix(c(10, 1, 1, 2), 2, 2)
swp(V, 2)