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Example 8.2 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-252)

Source: R/Exam8.2.R
Exam8.2.Rd

Exam8.2 Incomplete strip-plot

References

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

See also

DataSet8.2

Author

  1. Muhammad Yaseen (myaseen208@gmail.com)

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

Examples


data(DataSet8.2)
DataSet8.2$block <- factor(x = DataSet8.2$block)
DataSet8.2$a <- factor(x = DataSet8.2$a)
DataSet8.2$b <- factor(x = DataSet8.2$b)

library(lmerTest)

Exam8.2lmer <-
          lmer(
                 formula = y ~ a*b + (1|block) + (1|block:a) + (1|block:b)
               , data    = DataSet8.2
               )
anova(Exam8.2lmer,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   29.712 14.8561     2 8.8426  6.6173 0.017504 * 
#> b   10.435  5.2176     2 8.4720  2.3240 0.156808   
#> a:b 94.718 23.6795     4 5.8536 10.5474 0.007533 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

library(emmeans)
emmeans(object  = Exam8.2lmer, specs = ~a|b)
#> b = 1:
#>  a emmean   SE   df lower.CL upper.CL
#>  1   21.2 2.18 24.4     16.7     25.7
#>  2   22.2 2.18 24.4     17.7     26.7
#>  3   21.1 2.18 24.4     16.6     25.6
#> 
#> b = 2:
#>  a emmean   SE   df lower.CL upper.CL
#>  1   30.4 2.18 24.4     25.9     34.9
#>  2   28.4 2.18 24.4     23.9     32.9
#>  3   18.5 2.18 24.4     14.0     23.0
#> 
#> b = 3:
#>  a emmean   SE   df lower.CL upper.CL
#>  1   28.2 2.18 24.4     23.7     32.7
#>  2   26.9 2.18 24.4     22.4     31.4
#>  3   18.5 2.18 24.4     14.0     23.0
#> 
#> Degrees-of-freedom method: kenward-roger 
#> Confidence level used: 0.95 
emmip(
       object  = emmeans(object  = Exam8.2lmer, specs = ~a|b)
     , formula = a~b
     , ylab    = "y Lsmeans"
     , main    = "Lsmeans for a*b"
      )


##---Simple effect comparisons of a*b Least Squares Means by a ( page # 254)
emmeans(Exam8.2lmer, pairwise ~ b|a)
#> $emmeans
#> a = 1:
#>  b emmean   SE   df lower.CL upper.CL
#>  1   21.2 2.18 24.4     16.7     25.7
#>  2   30.4 2.18 24.4     25.9     34.9
#>  3   28.2 2.18 24.4     23.7     32.7
#> 
#> a = 2:
#>  b emmean   SE   df lower.CL upper.CL
#>  1   22.2 2.18 24.4     17.7     26.7
#>  2   28.4 2.18 24.4     23.9     32.9
#>  3   26.9 2.18 24.4     22.4     31.4
#> 
#> a = 3:
#>  b emmean   SE   df lower.CL upper.CL
#>  1   21.1 2.18 24.4     16.6     25.6
#>  2   18.5 2.18 24.4     14.0     23.0
#>  3   18.5 2.18 24.4     14.0     23.0
#> 
#> Degrees-of-freedom method: kenward-roger 
#> Confidence level used: 0.95 
#> 
#> $contrasts
#> a = 1:
#>  contrast estimate   SE   df t.ratio p.value
#>  b1 - b2   -9.1852 2.34 12.9  -3.934  0.0046
#>  b1 - b3   -6.9538 2.34 12.9  -2.978  0.0271
#>  b2 - b3    2.2314 2.34 12.9   0.956  0.6164
#> 
#> a = 2:
#>  contrast estimate   SE   df t.ratio p.value
#>  b1 - b2   -6.1962 2.34 12.9  -2.653  0.0491
#>  b1 - b3   -4.6945 2.34 12.9  -2.010  0.1492
#>  b2 - b3    1.5017 2.34 12.9   0.643  0.7994
#> 
#> a = 3:
#>  contrast estimate   SE   df t.ratio p.value
#>  b1 - b2    2.6576 2.34 12.9   1.138  0.5089
#>  b1 - b3    2.6063 2.34 12.9   1.116  0.5215
#>  b2 - b3   -0.0513 2.34 12.9  -0.022  0.9997
#> 
#> Degrees-of-freedom method: kenward-roger 
#> P value adjustment: tukey method for comparing a family of 3 estimates 
#>