is_estimable: Determines if contrasts are estimable.
Description
Determines if contrasts are estimable, that is, if the contrasts can
be written as a linear function of the data.
Usage
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 $B$.