F-test and degrees of freedom based on Satterthwaite approximation

An approximate F-test based on the Satterthwaite approach.

SATmodcomp(
  largeModel,
  smallModel,
  details = 0,
  eps = sqrt(.Machine$double.eps)
)

# S3 method for lmerMod
SATmodcomp(
  largeModel,
  smallModel,
  details = 0,
  eps = sqrt(.Machine$double.eps)
)

Arguments

largeModel: An lmerMod model.
smallModel: An lmerMod model, a restriction matrix or a model formula. See example section.
details: If larger than 0 some timing details are printed.
eps: A small number.

Details

Notice: It cannot be guaranteed that the results agree with other implementations of the Satterthwaite approach!

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/

Author

Søren Højsgaard, sorenh@math.aau.dk

Examples


(fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy))
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#>    Data: sleepstudy
#> REML criterion at convergence: 1743.628
#> Random effects:
#>  Groups   Name        Std.Dev. Corr
#>  Subject  (Intercept) 24.741       
#>           Days         5.922   0.07
#>  Residual             25.592       
#> Number of obs: 180, groups:  Subject, 18
#> Fixed Effects:
#> (Intercept)         Days  
#>      251.41        10.47  
L1 <- cbind(0,1)
SATmodcomp(fm1, L1)
#> large : Reaction ~ Days + (Days | Subject)
#> <environment: 0x7fd3a2df0dd8>
#> small (restriction matrix) : 
#>     
#>  0 1
#>      statistic    ndf ddf   p.value    
#> [1,]    45.853  1.000  17 3.264e-06 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(fm2 <- lmer(Reaction ~ Days + I(Days^2) + (Days|Subject), sleepstudy))
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + I(Days^2) + (Days | Subject)
#>    Data: sleepstudy
#> REML criterion at convergence: 1742.816
#> Random effects:
#>  Groups   Name        Std.Dev. Corr
#>  Subject  (Intercept) 24.761       
#>           Days         5.925   0.06
#>  Residual             25.534       
#> Number of obs: 180, groups:  Subject, 18
#> Fixed Effects:
#> (Intercept)         Days    I(Days^2)  
#>     255.449        7.434        0.337  

## Test for no effect of Days. There are three ways of using the function:

## 1) Define 2-df contrast - since L has 2 (linearly independent) rows
## the F-test is on 2 (numerator) df:
L2 <- rbind(c(0, 1, 0), c(0, 0, 1))
SATmodcomp(fm2, L2)
#> large : Reaction ~ Days + I(Days^2) + (Days | Subject)
#> <environment: 0x7fd3a2df0dd8>
#> small (restriction matrix) : 
#>       
#>  0 1 0
#>  0 0 1
#>      statistic    ndf    ddf   p.value    
#> [1,]    23.754  2.000 51.563 4.876e-08 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

## 2) Use two model objects 
fm3 <- update(fm2, ~. - Days - I(Days^2))
SATmodcomp(fm2, fm3)
#> large : Reaction ~ Days + I(Days^2) + (Days | Subject)
#> <environment: 0x7fd3a2df0dd8>
#> small (restriction matrix) : 
#>                        
#>  0  0.1104315 0.9938837
#>  0 -0.9938837 0.1104315
#>      statistic    ndf    ddf   p.value    
#> [1,]    23.754  2.000 51.563 4.876e-08 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

## 3) Specify restriction as formula
SATmodcomp(fm2, ~. - Days - I(Days^2))
#> large : Reaction ~ Days + I(Days^2) + (Days | Subject)
#> <environment: 0x7fd3a2df0dd8>
#> small (restriction matrix) : 
#>                        
#>  0  0.1104315 0.9938837
#>  0 -0.9938837 0.1104315
#>      statistic    ndf    ddf   p.value    
#> [1,]    23.754  2.000 51.563 4.876e-08 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1