Examp2.4.3.1 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.

Examp2.4.3.1 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

Author

1. Muhammad Yaseen (myaseen208@gmail.com)

Examples

#-------------------------------------------------------------
## Example 2.4.3.1 p-66
#-------------------------------------------------------------
 # PROC MIXED DATA=ex127;
 # CLASS sire;
 # MODEL ww=;
 # RANDOM sire/solution;
 # RUN;
 
library(lme4)
str(ex127)
#> 'data.frame':	43 obs. of  2 variables:
#>  $ sire: int  1 1 1 2 2 2 2 2 2 2 ...
#>  $ Ww  : num  11.1 10.8 11.3 15.9 13 12.6 14.6 13.6 12.5 15.7 ...
fm2.8 <- 
  lme4::lmer(
         formula    = Ww~(1|sire)
       , data       = ex127
       , REML       = TRUE
       , control    = lmerControl()
       , start      = NULL
       , verbose    = 0L
    #  , subset
    #  , weights
    #  , na.action
    #  , offset
       , contrasts  = NULL
       , devFunOnly = FALSE
    #  , ...
       )  
if (requireNamespace("report", quietly = TRUE)) {
  fm2.8 |>
    report::report()
}
#>  We fitted a constant (intercept-only) linear mixed model (estimated using REML
#> and nloptwrap optimizer) to predict Ww (formula: Ww ~ 1). The model included
#> sire as random effect (formula: ~1 | sire). The model's intercept is at 13.97
#> (95% CI [12.47, 15.47], t(40) = 18.79, p < .001).
#> 
#> Standardized parameters were obtained by fitting the model on a standardized
#> version of the dataset. 95% Confidence Intervals (CIs) and p-values were
#> computed using a Wald t-distribution approximation.
summary(fm2.8)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Ww ~ (1 | sire)
#>    Data: ex127
#> 
#> REML criterion at convergence: 188.9
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -1.5024 -0.7106 -0.2259  0.8414  1.9459 
#> 
#> Random effects:
#>  Groups   Name        Variance Std.Dev.
#>  sire     (Intercept) 3.686    1.920   
#>  Residual             3.542    1.882   
#> Number of obs: 43, groups:  sire, 8
#> 
#> Fixed effects:
#>             Estimate Std. Error t value
#> (Intercept)  13.9686     0.7435   18.79
lme4::fixef(fm2.8)
#> (Intercept) 
#>    13.96863 
lme4::ranef(fm2.8)
#> $sire
#>   (Intercept)
#> 1  -2.1979037
#> 2  -0.0318874
#> 3  -1.7434719
#> 4   3.1587811
#> 5   0.8691909
#> 6  -0.8627975
#> 7   1.3556763
#> 8  -0.5475878
#> 
#> with conditional variances for “sire”