Examp2.6.1 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.

Examp2.6.1 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 2.6.1 p-76
#-------------------------------------------------------------
 # PROC MIXED DATA=ex125;
 # CLASS drug dose region;
 # MODEL pcv=drug dose drug*dose / ddfm=satterth;
 # RANDOM region drug*region;
 # CONTRAST 'drug dif' drug -1 1 drug*dose -0.5 -0.5 0.5 0.5;
 # CONTRAST 'all' drug 1 -1 dose 0  0 drug*dose 0.5  0.5 -0.5 -0.5,
 #                drug 0  0 dose 1 -1 drug*dose 0.5 -0.5  0.5 -0.5,
 #                drug 0  0 dose 0  0 drug*dose 0.5 -0.5 -0.5  0.5;
 # 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 ...
 ex125$Region1 <- factor(ex125$Region)
 fm2.14 <-
  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(fm2.14)
#> 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(object = fm2.14, ddf = "Satterthwaite")
#> 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

 library(multcomp)
 Contrasts3 <-
           matrix(c(
                    0, 0, -1, -0.5
                   )
                , ncol = 4
                , byrow = TRUE
                , dimnames = list(
                   c("C1")
                 , rownames(summary(fm2.14)$coef)
                )
               )

 Contrasts3
#>    (Intercept) doseh DrugBERENIL doseh:DrugBERENIL
#> C1           0     0          -1              -0.5
 summary(glht(fm2.14, linfct=Contrasts3))
#> 
#> 	 Simultaneous Tests for General Linear Hypotheses
#> 
#> Fit: lmerTest::lmer(formula = Pcv ~ dose * Drug + (1 | Region/Drug), 
#>     data = ex125, REML = TRUE, control = lmerControl(), start = NULL, 
#>     verbose = 0L, contrasts = list(dose = "contr.SAS", Drug = "contr.SAS"), 
#>     devFunOnly = FALSE)
#> 
#> Linear Hypotheses:
#>         Estimate Std. Error z value Pr(>|z|)    
#> C1 == 0  -5.5583     0.6917  -8.036 8.88e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> (Adjusted p values reported -- single-step method)
#> 

if(packageVersion("lmerTest") >= "3.0")
   contest(fm2.14, Contrasts3, joint = FALSE)
#>     Estimate Std. Error df   t value     lower     upper    Pr(>|t|)
#> C1 -5.558333  0.6916667  5 -8.036144 -7.336319 -3.780348 0.000482595