Example 5.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-172)

Exam5.3 Inference using empirical standard error with different Bias connection

References

1. Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.

See also

DataSet4.1

Examples

data(DataSet4.1)
DataSet4.1$trt   <- factor(x = DataSet4.1$trt)
DataSet4.1$block <- factor( x = DataSet4.1$block)

##---REML estimates on page 172
library(lme4)
# library(lmerTest)
Exam5.3REML      <-
  lmer(
         formula    = y ~ trt + (1|block)
       , data       = DataSet4.1
       , REML       = TRUE
    #  , control    = lmerControl()
       , start      = NULL
    #  , verbose    = 0L
    #  , subset
    #  , weights
    #  , na.action
    #  , offset
       , contrasts  = NULL
       , devFunOnly = FALSE
    #  , ...
  )
##---Standard Error Type "Model Based" with no Bias Connection
AnovaExam5.3REML  <- anova( object = Exam5.3REML )
AnovaExam5.3REML
#> Analysis of Variance Table
#>     Df Sum Sq Mean Sq F value
#> trt 14 183.41    13.1  1.5312

##---Standard Error Type "Model Based" with "Kenward-Roger approximation" Bias Connection
# library(pbkrtest)
anova( object = Exam5.3REML, ddf  = "Kenward-Roger")
#> Analysis of Variance Table
#>     Df Sum Sq Mean Sq F value
#> trt 14 183.41    13.1  1.5312

##---ML estimates on page 172
Exam5.3ML      <-
  lmer(
        formula      = y ~ trt + ( 1|block )
       , data        = DataSet4.1
       , REML        = FALSE
   #   , control     = lmerControl()
       , start       = NULL
   #   , verbose     = 0L
   #   , subset
   #   , weights
   #   , na.action
   #   , offset
       , contrasts   = NULL
       , devFunOnly  = FALSE
   #   , ...
  )

##---Standard Error Type "Model Based" with no Bias Connection
AnovaExam5.3ML  <- anova( object = Exam5.3ML )
AnovaExam5.3ML
#> Analysis of Variance Table
#>     Df Sum Sq Mean Sq F value
#> trt 14 175.26  12.518  2.0736

##---Standard Error Type "Model Based" with "Kenward-Roger approximation" Bias Connection
anova( object = Exam5.3ML, ddf = "Kenward-Roger")
#> Analysis of Variance Table
#>     Df Sum Sq Mean Sq F value
#> trt 14 175.26  12.518  2.0736