Function getAmatrix finds A-matrices used to express ANOVA sum of squares as quadratic forms in $y$.
Usage
getAmatrix(X1, X2)
Arguments
X1
(matrix) lower order model matrix (comprising all factors entering model before 'X2'-factor)
X2
(matrix) higher order model matrix (entering model after 'X1' factors)
Value
(matrix) for obtaining quadratic forms in $y$ expression ANOVA sum of squares
Details
Compute A-Matrix for expressing ANOVA Type-1 sequential sum of squares $m_{SS}$ as quadratic form in $y$ (column vector of observations),
$y^{T}Ay = m_{SS}$.
In random models, when the intercept is the only fixed effect, the design matrix of fixed effects is equal to a column vector
where each element is equal to one (1). In this setting, it holds $1^{T}A1 = 0$, i.e. all elements of A summing to zero.
This function is not intended to be used directly.