Examp3.2 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/Examp3.2.R

Examp3.2 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 3.3 p-88
#-------------------------------------------------------------
# PROC MIXED DATA=ex32;
# CLASS sex sire_id breed;
# MODEL ww = sex agew breed/SOLUTION DDFM=SATTERTH;
# RANDOM sire_id(breed)/SOLUTION;
# LSMEANS breed/ADJUST = TUKEY;
# RUN;

 library(lmerTest)
 str(ex32)
#> 'data.frame':	65 obs. of  5 variables:
#>  $ breed  : int  1 1 1 1 1 1 1 1 1 1 ...
#>  $ sire_id: int  1971 1971 1971 1971 1972 1972 1972 1972 1972 1972 ...
#>  $ sex    : Factor w/ 2 levels "F","M": 1 1 1 2 1 2 1 1 2 1 ...
#>  $ agew   : int  145 140 140 122 152 151 146 139 132 131 ...
#>  $ Ww     : num  11.2 15.4 10.9 11.4 16 13.2 14.9 7.9 15.7 13.1 ...
 ex32$sire_id1 <- factor(ex32$sire_id)
 ex32$breed1   <- factor(ex32$breed)

 fm3.4 <-
  lmerTest::lmer(
         formula    = Ww ~ sex + agew + breed1 + (1|sire_id1:breed1)
       , data       = ex32
       , REML       = TRUE
       , control    = lmerControl()
       , start      = NULL
       , verbose    = 0L
    #  , subset
    #  , weights
    #  , na.action
    #  , offset
       , contrasts  = list(sex = "contr.SAS", breed1 = "contr.SAS")
       , devFunOnly = FALSE
    #  , ...
       )
 summary(fm3.4)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: Ww ~ sex + agew + breed1 + (1 | sire_id1:breed1)
#>    Data: ex32
#> 
#> REML criterion at convergence: 284.3
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -2.5654 -0.6608  0.2366  0.6499  2.2953 
#> 
#> Random effects:
#>  Groups          Name        Variance  Std.Dev. 
#>  sire_id1:breed1 (Intercept) 1.052e-16 1.026e-08
#>  Residual                    5.447e+00 2.334e+00
#> Number of obs: 65, groups:  sire_id1:breed1, 15
#> 
#> Fixed effects:
#>             Estimate Std. Error       df t value Pr(>|t|)    
#> (Intercept) -0.36196    3.12869 57.00000  -0.116 0.908304    
#> sexF        -1.43763    0.61338 57.00000  -2.344 0.022600 *  
#> agew         0.08386    0.02393 57.00000   3.505 0.000898 ***
#> breed11      3.07302    1.13643 57.00000   2.704 0.009013 ** 
#> breed12      2.34510    1.22697 57.00000   1.911 0.060999 .  
#> breed13      0.54799    1.34825 57.00000   0.406 0.685939    
#> breed14      2.68929    1.18700 57.00000   2.266 0.027291 *  
#> breed15     -0.32865    1.24771 57.00000  -0.263 0.793188    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Correlation of Fixed Effects:
#>         (Intr) sexF   agew   bred11 bred12 bred13 bred14
#> sexF     0.121                                          
#> agew    -0.944 -0.257                                   
#> breed11 -0.146  0.065 -0.121                            
#> breed12 -0.023  0.161 -0.240  0.684                     
#> breed13  0.162  0.152 -0.406  0.643  0.651              
#> breed14 -0.077  0.187 -0.196  0.702  0.685  0.654       
#> breed15 -0.514  0.067  0.279  0.612  0.541  0.433  0.579
 anova(object = fm3.4, ddf = "Satterthwaite")
#> Type III Analysis of Variance Table with Satterthwaite's method
#>         Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
#> sex     29.924  29.924     1    57  5.4932 0.0226004 *  
#> agew    66.904  66.904     1    57 12.2819 0.0008979 ***
#> breed1 109.411  21.882     5    57  4.0170 0.0034289 ** 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 lsmeansLT(model = fm3.4)
#> Least Squares Means table:
#> 
#>         Estimate Std. Error df t value    lower    upper  Pr(>|t|)    
#> sexF    10.71994    0.42885 57  24.997  9.86118 11.57869 < 2.2e-16 ***
#> sexM    12.15756    0.43216 57  28.132 11.29218 13.02295 < 2.2e-16 ***
#> breed11 13.12398    0.60557 57  21.672 11.91136 14.33661 < 2.2e-16 ***
#> breed12 12.39605    0.72013 57  17.214 10.95402 13.83809 < 2.2e-16 ***
#> breed13 10.59894    0.87738 57  12.080  8.84202 12.35587 < 2.2e-16 ***
#> breed14 12.74025    0.65697 57  19.392 11.42469 14.05581 < 2.2e-16 ***
#> breed15  9.72230    0.86252 57  11.272  7.99513 11.44948 3.896e-16 ***
#> breed16 10.05096    0.96866 57  10.376  8.11126 11.99066 9.546e-15 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#>   Confidence level: 95%
#>   Degrees of freedom method: Satterthwaite