Examp2.5.2.1 from Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).Linear Mixed Models. An Introduction with applications in Veterinary Research. International Livestock Research Institute.

Source: R/Examp2.5.2.1.R

Examp2.5.2.1 is used for inspecting probability distribution and to define a plausible process through linear models and generalized linear models.

References

  1. Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).Linear Mixed Models. An Introduction with applications in Veterinary Research. International Livestock Research Institute.

See also

ex124

Examples

#-------------------------------------------------------------
## Example 2.5.2.1 p-68
#-------------------------------------------------------------
 # PROC MIXED DATA=ex125;
 # CLASS drug dose region;
 # MODEL pcv=drug dose drug*dose / solution covb;
 # RANDOM region drug*region;
 # LSMEANS drug*dose;
 # RUN;

library(lmerTest)
str(ex125)
#> 'data.frame':	24 obs. of  4 variables:
#>  $ Region: int  1 1 1 1 2 2 2 2 3 3 ...
#>  $ Drug  : Factor w/ 2 levels "BERENIL","samorin": 1 1 2 2 1 1 2 2 1 1 ...
#>  $ dose  : Factor w/ 2 levels "h","l": 1 2 1 2 1 2 1 2 1 2 ...
#>  $ Pcv   : num  22.6 21.8 19.1 16.4 29 28.8 25.3 18.2 24 23.7 ...

fm2.10 <-
  lmerTest::lmer(
         formula    = Pcv ~ dose*Drug + (1|Region/Drug)
       , data       = ex125
       , REML       = TRUE
       , control    = lmerControl()
       , start      = NULL
       , verbose    = 0L
    #  , subset
    #  , weights
    #  , na.action
    #  , offset
       , contrasts  = list(dose = "contr.SAS", Drug = "contr.SAS")
       , devFunOnly = FALSE
    #  , ...
       )
summary(fm2.10)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: Pcv ~ dose * Drug + (1 | Region/Drug)
#>    Data: ex125
#> 
#> REML criterion at convergence: 92.4
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -1.71077 -0.51628  0.08414  0.70276  1.16129 
#> 
#> Random effects:
#>  Groups      Name        Variance Std.Dev.
#>  Drug:Region (Intercept) 0.387    0.6221  
#>  Region      (Intercept) 5.151    2.2695  
#>  Residual                2.096    1.4479  
#> Number of obs: 24, groups:  Drug:Region, 12; Region, 6
#> 
#> Fixed effects:
#>                   Estimate Std. Error      df t value Pr(>|t|)    
#> (Intercept)        17.1333     1.1280  8.2080  15.189 2.69e-07 ***
#> doseh               4.3500     0.8359 10.0000   5.204 0.000399 ***
#> DrugBERENIL         7.1500     0.9098 11.8185   7.859 4.96e-06 ***
#> doseh:DrugBERENIL  -3.1833     1.1822 10.0000  -2.693 0.022594 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Correlation of Fixed Effects:
#>             (Intr) doseh  DBEREN
#> doseh       -0.371              
#> DrugBERENIL -0.403  0.459       
#> ds:DBERENIL  0.262 -0.707 -0.650
anova(fm2.10)
#> Type III Analysis of Variance Table with Satterthwaite's method
#>           Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
#> dose       45.65   45.65     1    10 21.7755 0.0008856 ***
#> Drug      135.39  135.39     1     5 64.5796 0.0004826 ***
#> dose:Drug  15.20   15.20     1    10  7.2507 0.0225945 *  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
summary(fm2.10)$vcov
#> 4 x 4 Matrix of class "dpoMatrix"
#>                   (Intercept)      doseh DrugBERENIL doseh:DrugBERENIL
#> (Intercept)         1.2723750 -0.3494028  -0.4139028         0.3494028
#> doseh              -0.3494028  0.6988055   0.3494028        -0.6988055
#> DrugBERENIL        -0.4139028  0.3494028   0.8278056        -0.6988055
#> doseh:DrugBERENIL   0.3494028 -0.6988055  -0.6988055         1.3976111
lsmeansLT(model = fm2.10)
#> Least Squares Means table:
#> 
#>                   Estimate Std. Error  df t value   lower   upper  Pr(>|t|)    
#> doseh              23.4667     1.0322 5.9  22.735 20.9316 26.0018 5.592e-07 ***
#> dosel              20.7083     1.0322 5.9  20.062 18.1732 23.2434 1.161e-06 ***
#> DrugBERENIL        24.8667     1.0477 6.2  23.735 22.3234 27.4099 2.515e-07 ***
#> Drugsamorin        19.3083     1.0477 6.2  18.429 16.7651 21.8516 1.185e-06 ***
#> doseh:DrugBERENIL  25.4500     1.1280 8.2  22.562 22.8603 28.0397 1.120e-08 ***
#> dosel:DrugBERENIL  24.2833     1.1280 8.2  21.528 21.6936 26.8731 1.637e-08 ***
#> doseh:Drugsamorin  21.4833     1.1280 8.2  19.046 18.8936 24.0731 4.396e-08 ***
#> dosel:Drugsamorin  17.1333     1.1280 8.2  15.189 14.5436 19.7231 2.688e-07 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#>   Confidence level: 95%
#>   Degrees of freedom method: Satterthwaite