Examp1.3.2 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.

Examp1.3.2 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

Author

1. Muhammad Yaseen (myaseen208@gmail.com)

Examples

#-------------------------------------------------------------
## Example 1.3.2 p-16
#-------------------------------------------------------------
 # PROC GLM DATA=ex124;
 # CLASS herd dose drug;
 # MODEL PCVdif=drug herd(drug) dose dose*drug;
 # RANDOM herd(drug);
 # RUN;

library(lme4)
#> Loading required package: Matrix
str(ex124)
#> 'data.frame':	40 obs. of  4 variables:
#>  $ herd  : int  1 1 1 1 1 1 1 1 1 1 ...
#>  $ drug  : Factor w/ 2 levels "Berenil","Samorin": 1 1 1 1 1 1 1 1 1 1 ...
#>  $ dose  : Factor w/ 2 levels "h","l": 2 2 2 2 2 1 1 1 1 1 ...
#>  $ PCVdif: num  2.5 1.6 3.5 2.6 2.8 6.9 6.8 7.2 5.9 6.5 ...
summary(ex124)
#>       herd           drug    dose       PCVdif     
#>  Min.   :1.00   Berenil:20   h:20   Min.   :1.600  
#>  1st Qu.:1.75   Samorin:20   l:20   1st Qu.:3.225  
#>  Median :2.50                       Median :5.250  
#>  Mean   :2.50                       Mean   :5.263  
#>  3rd Qu.:3.25                       3rd Qu.:7.225  
#>  Max.   :4.00                       Max.   :8.700  

ex124 <-
  ex124 |>
  collapse::fmutate(
    herd1 = factor(herd),
    drug1 = factor(drug),
    dose1 = factor(dose)
  )

fm1.1 <-
  aov(
      formula     = PCVdif ~ drug1 + Error(herd1:drug1) + dose1 + dose1:drug1
    , data        = ex124
    , projections = FALSE
    , qr          = TRUE
    , contrasts   = NULL
  #  , ...
    )
#> Warning: Error() model is singular
if (requireNamespace("report", quietly = TRUE)) {
  fm1.1 |>
    report::report()
}
#> The repeated-measures ANOVA (formula: PCVdif ~ drug1 + Error(herd1:drug1) +
#> dose1 + dose1:drug1) suggests that:
#> 
#>   - The main effect of dose1 is statistically significant and medium (F(1, 34) =
#> 732.39, p < .001; Eta2 (partial) = 0.13, 95% CI [0.00, 1.00])
#>   - The interaction between drug1 and dose1 is statistically not significant and
#> large (F(1, 34) = 0.66, p = 0.421; Eta2 (partial) = 0.96, 95% CI [0.93, 1.00])
#>   - The main effect of drug1 is statistically NA and small (F(, 34) = , ; Eta2
#> (partial) = 0.02, 95% CI [0.00, 1.00])
#> 
#> Effect sizes were labelled following Field's (2013) recommendations.
summary(fm1.1)
#> 
#> Error: herd1:drug1
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> drug1      1  1.722   1.722   0.305  0.636
#> Residuals  2 11.300   5.650               
#> 
#> Error: Within
#>             Df Sum Sq Mean Sq F value Pr(>F)    
#> dose1        1 172.64  172.64 732.394 <2e-16 ***
#> drug1:dose1  1   0.16    0.16   0.663  0.421    
#> Residuals   34   8.01    0.24                   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1