model-coerce function

Conversion between a model object and a restriction matrix

Testing a small model under a large model corresponds imposing restrictions on the model matrix of the larger model and these restrictions come in the form of a restriction matrix. These functions converts a model to a restriction matrix and vice versa.

model2restriction_matrix(largeModel, smallModel, sparse = FALSE)

restriction_matrix2model(largeModel, L, REML = TRUE, ...)

make_model_matrix(X, L)

make_restriction_matrix(X, X2)

Arguments

• largeModel, smallModel: Model objects of the same "type". Possible types are linear mixed effects models and linear models (including generalized linear models)
• sparse: Should the restriction matrix be sparse or dense?
• L: A restriction matrix; a full rank matrix with as many columns as X has.
• REML: Controls if new model object should be fitted with REML or ML.
• ...: Additional arguments; not used.
• X, X2: Model matrices. Must have same number of rows.

Returns

model2restriction_matrix: A restriction matrix. restriction_matrix2model: A model object.

Details

make_restriction_matrix Make a restriction matrix. If span(X2) is in span(X) then the corresponding restriction matrix L is returned.

Note

That these functions are visible is a recent addition; minor changes may occur.

Examples

library(pbkrtest)
data("beets", package = "pbkrtest")
sug <- lm(sugpct ~ block + sow + harvest, data=beets)
sug.h <- update(sug, .~. - harvest)
sug.s <- update(sug, .~. - sow)

## Construct restriction matrices from models
L.h <- model2restriction_matrix(sug, sug.h); L.h
L.s <- model2restriction_matrix(sug, sug.s); L.s

## Construct submodels from restriction matrices
mod.h <- restriction_matrix2model(sug, L.h); mod.h
mod.s <- restriction_matrix2model(sug, L.s); mod.s

## Sanity check: The models have the same fitted values and log likelihood
plot(fitted(mod.h), fitted(sug.h))
plot(fitted(mod.s), fitted(sug.s))
logLik(mod.h)
logLik(sug.h)
logLik(mod.s)
logLik(sug.s)

References

Ulrich Halekoh, Søren Højsgaard (2014)., A Kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models - The R Package pbkrtest., Journal of Statistical Software, 58(10), 1-30., https://www.jstatsoft.org/v59/i09/

See Also

PBmodcomp, PBrefdist, KRmodcomp

Author(s)

Ulrich Halekoh uhalekoh@health.sdu.dk , Søren Højsgaard sorenh@math.aau.dk