Example 4.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-138)

Exam4.1 REML vs ML criterion is used keeping block effects random

References

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

See also

DataSet4.1

Examples

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

##---REML estimates on page 138(article 4.4.3.3)
library(lme4)
Exam4.1REML  <-
  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
#  , ...
  )

VarCompREML4.1  <-
  VarCorr(x     =   Exam4.1REML
          # , sigma = 1
          # , ...
  )
print(VarCompREML4.1, comp=c("Variance"))
#>  Groups   Name        Variance
#>  block    (Intercept) 4.6522  
#>  Residual             8.5559  

##---ML estimates on page 138(article 4.4.3.3)
Exam4.1ML  <-
  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
   #  , ...
  )
VarCompML4.1  <-
  VarCorr(x     =    Exam4.1ML
          # , sigma = 1
          # , ...
  )
print(VarCompML4.1,comp=c("Variance"))
#>  Groups   Name        Variance
#>  block    (Intercept) 4.5030  
#>  Residual             6.0371  

Exam4.1.lm <-
  lm(
      formula     = y~ trt + block
    , data        = DataSet4.1
 #  , subset
 #  , weights
 #  , na.action
    , method      = "qr"
    , model       = TRUE
 #  , x           = FALSE
 #  , y           = FALSE
    , qr          = TRUE
    , singular.ok = TRUE
    , contrasts   = NULL
 #  , offset
 #  , ...
  )
summary(anova(object = Exam4.1.lm))
#>        Df            Sum Sq         Mean Sq          F value     
#>  Min.   :14.00   Min.   :267.1   Min.   : 8.615   Min.   :2.483  
#>  1st Qu.:14.00   1st Qu.:283.3   1st Qu.:15.002   1st Qu.:2.553  
#>  Median :14.00   Median :299.4   Median :21.388   Median :2.623  
#>  Mean   :19.67   Mean   :300.0   Mean   :17.940   Mean   :2.623  
#>  3rd Qu.:22.50   3rd Qu.:316.4   3rd Qu.:22.602   3rd Qu.:2.694  
#>  Max.   :31.00   Max.   :333.4   Max.   :23.816   Max.   :2.764  
#>                                                   NA's   :1      
#>      Pr(>F)        
#>  Min.   :0.009004  
#>  1st Qu.:0.011050  
#>  Median :0.013096  
#>  Mean   :0.013096  
#>  3rd Qu.:0.015142  
#>  Max.   :0.017187  
#>  NA's   :1