Example 8.4 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-259)

Exam8.4 Multifactor treatment and Multilevel design structures

References

1. Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.

See also

DataSet8.4

Author

1. Muhammad Yaseen (myaseen208@gmail.com)

2. Adeela Munawar (adeela.uaf@gmail.com)

Examples

data(DataSet8.4)
DataSet8.4$block <- factor(x = DataSet8.4$block)
DataSet8.4$a <- factor(x = DataSet8.4$a)
DataSet8.4$b <- factor(x = DataSet8.4$b)

library(lmerTest)
Exam8.4lmer   <-
           lmer(
                y ~ a + b %in% a +
                    (1|block) + (1|block:a) + (1|block:b)
              , data = DataSet8.4
              )
#> boundary (singular) fit: see help('isSingular')
anova(Exam8.4lmer, ddf = "Kenward-Roger")
#> Type III Analysis of Variance Table with Kenward-Roger's method
#>     Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)   
#> a    35.89  17.946     2 14.648  1.7568 0.20707   
#> a:b 477.15  79.525     6 13.573  7.4008 0.00114 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

library(emmeans)
emmeans(object = Exam8.4lmer, specs = ~a|b)
#> NOTE: A nesting structure was detected in the fitted model:
#>     b %in% a
#> a = 1, b = 1:
#>  emmean   SE   df lower.CL upper.CL
#>     9.2 2.39 26.3     4.29     14.1
#> 
#> a = 2, b = 1:
#>  emmean   SE   df lower.CL upper.CL
#>    14.3 2.39 26.3     9.42     19.2
#> 
#> a = 3, b = 1:
#>  emmean   SE   df lower.CL upper.CL
#>    12.8 2.39 26.3     7.92     17.7
#> 
#> a = 1, b = 2:
#>  emmean   SE   df lower.CL upper.CL
#>    28.7 2.39 26.3    23.79     33.6
#> 
#> a = 2, b = 2:
#>  emmean   SE   df lower.CL upper.CL
#>    24.5 2.39 26.3    19.55     29.4
#> 
#> a = 3, b = 2:
#>  emmean   SE   df lower.CL upper.CL
#>    21.1 2.39 26.3    16.14     26.0
#> 
#> a = 1, b = 3:
#>  emmean   SE   df lower.CL upper.CL
#>    27.6 2.39 26.3    22.65     32.5
#> 
#> a = 2, b = 3:
#>  emmean   SE   df lower.CL upper.CL
#>    25.3 2.39 26.3    20.40     30.2
#> 
#> a = 3, b = 3:
#>  emmean   SE   df lower.CL upper.CL
#>    18.9 2.39 26.3    13.95     23.8
#> 
#> Degrees-of-freedom method: kenward-roger 
#> Confidence level used: 0.95