Example 3.5 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-85)

Exam3.5 fixed location, factorial treatment structure, Gaussian response

References

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

See also

DataSet3.2

Examples

data(DataSet3.2)
DataSet3.2$A <- factor(x = DataSet3.2$A)
DataSet3.2$B <- factor(x = DataSet3.2$B)
DataSet3.2$loc <- factor(x = DataSet3.2$loc, level = c(8, 1, 2, 3, 4, 5, 6, 7))
Exam3.5.lm <-
  lm(
         formula     =  Y~ A + B +loc
       , data        =  DataSet3.2
    #  , subset
    #  , weights
    #  , na.action
       , method      =  "qr"
       , model       =  TRUE
    #  , x           =  FALSE
    #  , y           =  FALSE
       , qr          =  TRUE
       , singular.ok =  TRUE
       , contrasts   =  NULL
    #  , offset
    #  , ...
  )

##---a0 marginal mean
list3.5.a0 <- list(B = c("0" = 1,"1" = 0) )
library(phia)
Test3.5.a0 <-
  summary(testFactors(
      model  =  Exam3.5.lm
    , levels =  list3.5.a0)
    )

##---b0 marginal mean
list3.5.b0 <- list(B = c("0" = 1,"1" = 0) )
Test3.5.b0 <-
summary(testFactors(
    model  =  Exam3.5.lm
  , levels =  list3.5.b0)
  )

##---Simple effect of A on B0
Test3.5.AB0 <-
  summary(testInteractions(
      model  =  Exam3.5.lm
    , custom =  list3.5.b0
    , across =  "B")
    )

##---Simple effect of B on A0
Test3.5.BA0 <-
  summary(testInteractions(
      model  =  Exam3.5.lm
    , custom =  list3.5.a0
    , across =  "A")
    )

##---Simple Effect of A over B
(SimpleEffect3.5.AB <-
  summary(testInteractions(
      model  =  Exam3.5.lm
    , fixed  =   "A"
    , across =  "B")
    )
    )
#>      Value              Df         Sum of Sq           F        
#>  Min.   :-2.688   Min.   : 1.0   Min.   :57.78   Min.   :20.85  
#>  1st Qu.:-2.688   1st Qu.: 1.0   1st Qu.:57.78   1st Qu.:20.85  
#>  Median :-2.688   Median : 1.0   Median :57.78   Median :20.85  
#>  Mean   :-2.688   Mean   : 8.0   Mean   :58.84   Mean   :20.85  
#>  3rd Qu.:-2.688   3rd Qu.:11.5   3rd Qu.:59.38   3rd Qu.:20.85  
#>  Max.   :-2.688   Max.   :22.0   Max.   :60.97   Max.   :20.85  
#>  NA's   :1                                       NA's   :1      
#>      Pr(>F)         
#>  Min.   :0.0003027  
#>  1st Qu.:0.0003027  
#>  Median :0.0003027  
#>  Mean   :0.0003027  
#>  3rd Qu.:0.0003027  
#>  Max.   :0.0003027  
#>  NA's   :1          

##---Simple Effect of B over A
(SimpleEffect3.5.BA <-
  summary(testInteractions(
      model  =  Exam3.5.lm
    , fixed  =   "B"
    , across =  "A")
    )
)
#>      Value            Df         Sum of Sq           F         
#>  Min.   :0.55   Min.   : 1.0   Min.   : 2.42   Min.   :0.8732  
#>  1st Qu.:0.55   1st Qu.: 1.0   1st Qu.: 2.42   1st Qu.:0.8732  
#>  Median :0.55   Median : 1.0   Median : 2.42   Median :0.8732  
#>  Mean   :0.55   Mean   : 8.0   Mean   :21.94   Mean   :0.8732  
#>  3rd Qu.:0.55   3rd Qu.:11.5   3rd Qu.:31.69   3rd Qu.:0.8732  
#>  Max.   :0.55   Max.   :22.0   Max.   :60.97   Max.   :0.8732  
#>  NA's   :1                                     NA's   :1       
#>      Pr(>F)      
#>  Min.   :0.7204  
#>  1st Qu.:0.7204  
#>  Median :0.7204  
#>  Mean   :0.7204  
#>  3rd Qu.:0.7204  
#>  Max.   :0.7204  
#>  NA's   :1       
#-------------------------------------------------------------
## Individula least squares treatment means
#-------------------------------------------------------------
(Lsm3.5 <-
  lsmeans::lsmeans(
      object  = Exam3.5.lm
    , specs   = ~A*B
    # , ...
  )
)
#>  A B   lsmean        SE df lower.CL upper.CL
#>  0 0 24.81875 0.5097156 22 23.76166 25.87584
#>  1 0 24.26875 0.5097156 22 23.21166 25.32584
#>  0 1 27.50625 0.5097156 22 26.44916 28.56334
#>  1 1 26.95625 0.5097156 22 25.89916 28.01334
#> 
#> Results are averaged over the levels of: loc 
#> Confidence level used: 0.95