Determines if contrasts are estimable.

Determines if contrasts are estimable, that is, if the contrasts can be written as a linear function of the data.

is_estimable(K, null.basis)

Arguments

K

A matrix.

null.basis

A basis for a null space (can be found with null_basis()).

Value

A logical vector.

Details

Consider the setting \(E(Y)=Xb\). A linear function of \(b\), say \(l'b\) is estimable if and only if there exists an \(r\) such that \(r'X=l'\) or equivalently \(l=X'r\). Hence \(l\) must be in the column space of \(X'\), i.e. in the orthogonal complement of the null space of \(X\). Hence, with a basis \(B\) for the null space, is_estimable() checks if each row \(l\) of the matrix \(K\) is perpendicular to each column basis vector in \(B\).

References

http://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf

See also

null_basis

Author

Søren Højsgaard, sorenh@math.aau.dk

Examples

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