VCA (version 1.3.4)

getAmatrix: Determine A-Matrix.

Description

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.