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.

model2restrictionMatrix(largeModel, smallModel)

restrictionMatrix2model(largeModel, LL)

Arguments

largeModel, smallModel	Model objects of the same "type". Possible types are linear mixed effects models and linear models (including generalized linear models)
LL	A restriction matrix.

Value

model2restrictionMatrix: A restriction matrix. restrictionMatrix2model: A model object.

Note

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

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., http://www.jstatsoft.org/v59/i09/

See also

PBmodcomp, PBrefdist, KRmodcomp

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 <- model2restrictionMatrix(sug, sug.h); L.h
#> 1 x 8 sparse Matrix of class "dgCMatrix"
#>                                            
#> [1,] -2.220446e-16 1.01349e-16 . . . . . -1
L.s <- model2restrictionMatrix(sug, sug.s); L.s
#> 4 x 8 sparse Matrix of class "dgCMatrix"
#>                                                                                
#> [1,]  .            .             .            -0.91766294  0.2294157  0.2294157
#> [2,]  .            .             .             0.06362848  0.8907987 -0.3181424
#> [3,]  .            1.665335e-16  .             0.10482848  0.1048285  0.8386279
#> [4,] -3.885781e-16 .            -2.220446e-16 -0.37796447 -0.3779645 -0.3779645
#>                              
#> [1,]  0.2294157  1.801957e-16
#> [2,] -0.3181424 -1.014701e-16
#> [3,] -0.5241424  .           
#> [4,] -0.7559289  .           

## Construct submodels from restriction matrices
mod.h <- restrictionMatrix2model(sug, L.h); mod.h
#> 
#> Call:
#> lm(formula = sugpct ~ .X1 + .X2 + .X3 + .X4 + .X5 + .X6 + .X7 - 
#>     1, data = new.data)
#> 
#> Coefficients:
#>      .X1       .X2       .X3       .X4       .X5       .X6       .X7  
#>  -0.0500   -0.0800    0.1167    0.1667   -0.1000   -0.3500  -16.8933  
#> 
mod.s <- restrictionMatrix2model(sug, L.s); mod.s
#> 
#> Call:
#> lm(formula = sugpct ~ .X1 + .X2 + .X3 + .X4 - 1, data = new.data)
#> 
#> Coefficients:
#>      .X1       .X2       .X3       .X4  
#>  -8.0892   -8.0910  -12.4612   -0.1133  
#> 

## The models have the same fitted values
plot(fitted(mod.h), fitted(sug.h))
plot(fitted(mod.s), fitted(sug.s))
## and the same log likelihood
logLik(mod.h)
#> 'log Lik.' 36.03257 (df=8)
logLik(sug.h)
#> 'log Lik.' 36.03257 (df=8)
logLik(mod.s)
#> 'log Lik.' 7.397588 (df=5)
logLik(sug.s)
#> 'log Lik.' 7.397588 (df=5)