In hojsgaard/pbkrtest: Parametric Bootstrap, Kenward-Roger and Satterthwaite Based Methods for Test in Mixed Models

require( pbkrtest )
prettyVersion <- packageDescription("pbkrtest")$Version
prettyDate <- format(Sys.Date())

knitr::opts_chunk$set(echo = TRUE)
options("warn"=-1)  ## FIXME Fragile; issue with rankMatrix(, method="qr.R")

Package version: r prettyVersion

Consider two linear models; the smaller is a submodel of the large:

N <- 4
dat <- data.frame(int=rep(1, N), x=1:N, y=rnorm(N))

lg <- lm(y ~ x + I(x^2), data=dat)
sm <- lm(y ~ x, data=dat)
lg
sm

The corresponding model matrices are

Xlg <- model.matrix(lg)
Xsm <- model.matrix(sm)
Xlg
Xsm

Given the two model matrices, the restriction matrix which describes the restrictions that should be made to the model matrix of the large model to produce the model matrix of the small model:

L <- make_restriction_matrix(Xlg, Xsm)
L 

Given the model matrix of the large model and the restriction matrix, the model matrix of the small model can be constructed as:

Xsm_2 <- make_model_matrix(Xlg, L)
Xsm_2

The same operation can be made directly on model objects:

L <- model2restriction_matrix(lg, sm)
L

Likewise, given the large model and the restriction matrix, the small model can be constructed:

sm_2 <- restriction_matrix2model(lg, L)
sm_2
sm_2 |> model.matrix()

Lastly, model matrices can be compared

## The first column space contains the second
compare_column_space(Xlg, Xsm)
## The second column space contains the first
compare_column_space(Xsm, Xlg)
## The two column spaces are identical
compare_column_space(Xlg, Xlg) 

hojsgaard/pbkrtest documentation built on Feb. 4, 2023, 7:32 a.m.