Examp2.5.1.1 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.

Examp2.5.1.1 is used for inspecting probability distribution and to define a plausible process through linear models and generalized linear models.

References

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

Author

Muhammad Yaseen (myaseen208@gmail.com)

Examples

#-------------------------------------------------------------
## Example 2.5.1.1 p-67
#-------------------------------------------------------------
 # PROC MIXED DATA=ex125;
 # CLASS drug dose region;
 # MODEL pcv=drug dose drug*dose / solution covb;
 # RANDOM region drug*region;
 # RUN;
 
library(lme4)
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 ...

fm2.9 <- 
  lme4::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
    #  , ...
       )                       
 if (requireNamespace("report", quietly = TRUE)) {
   fm2.9 |>
     report::report()
 }
#> We fitted a linear mixed model (estimated using REML and nloptwrap optimizer)
#> to predict Pcv with dose and Drug (formula: Pcv ~ dose * Drug). The model
#> included Drug as random effects (formula: list(~1 | Drug:Region, ~1 | Region)).
#> The model's total explanatory power is substantial (conditional R2 = 0.89) and
#> the part related to the fixed effects alone (marginal R2) is of 0.58. The
#> model's intercept, corresponding to dose = h and Drug = BERENIL, is at 17.13
#> (95% CI [14.75, 19.51], t(17) = 15.19, p < .001). Within this model:
#> 
#>   - The effect of dose [h] is statistically significant and positive (beta =
#> 4.35, 95% CI [2.59, 6.11], t(17) = 5.20, p < .001; Std. beta = 1.04, 95% CI
#> [0.62, 1.47])
#>   - The effect of Drug [BERENIL] is statistically significant and positive (beta
#> = 7.15, 95% CI [5.23, 9.07], t(17) = 7.86, p < .001; Std. beta = 1.72, 95% CI
#> [1.26, 2.18])
#>   - The effect of dose [h] × Drug [BERENIL] is statistically significant and
#> negative (beta = -3.18, 95% CI [-5.68, -0.69], t(17) = -2.69, p = 0.015; Std.
#> beta = -0.76, 95% CI [-1.36, -0.17])
#> 
#> 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.
 if (requireNamespace("emmeans", quietly = TRUE)) {
   emm2.9 <- emmeans::emmeans(fm2.9, ~ dose | Drug, lmer.df = "asymptotic")
   print(emm2.9)
   print(emmeans::contrast(emm2.9, method = "pairwise"))
 }
#> Drug = BERENIL:
#>  dose emmean   SE  df asymp.LCL asymp.UCL
#>  h      25.4 1.13 Inf      23.2      27.7
#>  l      24.3 1.13 Inf      22.1      26.5
#> 
#> Drug = samorin:
#>  dose emmean   SE  df asymp.LCL asymp.UCL
#>  h      21.5 1.13 Inf      19.3      23.7
#>  l      17.1 1.13 Inf      14.9      19.3
#> 
#> Degrees-of-freedom method: asymptotic 
#> Confidence level used: 0.95 
#> Drug = BERENIL:
#>  contrast estimate    SE  df z.ratio p.value
#>  h - l        1.17 0.836 Inf   1.396  0.1628
#> 
#> Drug = samorin:
#>  contrast estimate    SE  df z.ratio p.value
#>  h - l        4.35 0.836 Inf   5.204 <0.0001
#> 
#> Degrees-of-freedom method: asymptotic 
 summary(fm2.9)
#> Linear mixed model fit by REML ['lmerMod']
#> 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 t value
#> (Intercept)        17.1333     1.1280  15.189
#> doseh               4.3500     0.8359   5.204
#> DrugBERENIL         7.1500     0.9098   7.859
#> doseh:DrugBERENIL  -3.1833     1.1822  -2.693
#> 
#> Correlation of Fixed Effects:
#>             (Intr) doseh  DBEREN
#> doseh       -0.371              
#> DrugBERENIL -0.403  0.459       
#> ds:DBERENIL  0.262 -0.707 -0.650
 anova(fm2.9)
#> Analysis of Variance Table
#>           npar Sum Sq Mean Sq F value
#> dose         1  45.65   45.65 21.7754
#> Drug         1 135.39  135.39 64.5796
#> dose:Drug    1  15.20   15.20  7.2507
 summary(fm2.9)$vcov
#> 4 x 4 Matrix of class "dpoMatrix"
#>                   (Intercept)      doseh DrugBERENIL doseh:DrugBERENIL
#> (Intercept)         1.2723747 -0.3494028  -0.4139028         0.3494028
#> doseh              -0.3494028  0.6988057   0.3494028        -0.6988057
#> DrugBERENIL        -0.4139028  0.3494028   0.8278056        -0.6988057
#> doseh:DrugBERENIL   0.3494028 -0.6988057  -0.6988057         1.3976114

Examp2.5.1.1 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.

References

See also

Author

Examples