Example 2.5.3.1: confidence intervals with Satterthwaite degrees of freedom
Source:R/examples.R
Examp2.5.3.1.RdFour linear combinations of the fixed effects of ex125: their variances 0.478, 1.0975, 0.698 and
1.272 combine the variance components, and their Satterthwaite degrees of freedom (5, 6.2, 10 and 8.2) the
degrees of freedom of the mean squares of Table 2.5.3.1.
References
Duchateau, L., Janssen, P. and Rowlands, G. J. (1998). Linear Mixed Models. An Introduction with Applications in Veterinary Research. International Livestock Research Institute, Nairobi.
See also
Other VetResearchLMM examples:
Examp1.3.2,
Examp2.2.1.7,
Examp2.3.2,
Examp2.4.2.2,
Examp2.4.3.1,
Examp2.5.1.1,
Examp2.5.2.1,
Examp2.5.4.1,
Examp2.6.1,
Examp3.1,
Examp3.2,
Examp3.3
Author
Muhammad Yaseen (myaseen208@gmail.com)
Examples
# SAS program of the book (Appendix B):
# proc mixed data=ex125;
# class drug dose region;
# model pcv = drug dose drug*dose / ddfm=satterth;
# random region drug*region;
# estimate 'drug dif' drug -1 1 drug*dose -0.5 -0.5 0.5 0.5;
# estimate 'Samorin mean' intercept 1 drug 0 1 dose 0.5 0.5 drug*dose 0 0 0.5 0.5;
# estimate 'Samorin HvsL' dose 1 -1 drug*dose 0 0 1 -1;
# estimate 'Samorin high' intercept 1 drug 0 1 dose 1 0 drug*dose 0 0 1 0;
# run;
fm <-
vlm_fit(
fixed = Pcv ~ Drug + dose + Drug:dose
, data = ex125
, random = ~ Region + Region:Drug
, repeated = NULL
, method = "REML"
, ddfm = "satterth"
, type = 3
, class = NULL
, bound = TRUE
, control = list()
)
vlm_estimate(
fit = fm
, L = list(
"drug dif" = list(Drug = c(-1, 1), "Drug:dose" = c(-0.5, -0.5, 0.5, 0.5))
, "Samorin mean" = list(Intercept = 1, Drug = c(0, 1),
dose = c(0.5, 0.5), "Drug:dose" = c(0, 0, 0.5, 0.5))
, "Samorin HvsL" = list(dose = c(1, -1), "Drug:dose" = c(0, 0, 1, -1))
, "Samorin high" = list(Intercept = 1, Drug = c(0, 1),
dose = c(1, 0), "Drug:dose" = c(0, 0, 1, 0))
)
, random = NULL
, level = 0.95
)
#> Estimates (denominator df: satterth)
#>
#> Estimates
#> label estimate se df t p lower upper space
#> drug dif -5.558 0.6917 5.000 -8.036 0.000483 -7.336 -3.780 broad
#> Samorin mean 19.31 1.048 6.205 18.43 < 1e-04 16.77 21.85 broad
#> Samorin HvsL 4.350 0.8359 10.00 5.204 0.000399 2.487 6.213 broad
#> Samorin high 21.48 1.128 8.208 19.05 < 1e-04 18.89 24.07 broad
#>
#> Sources: Duchateau, Janssen and Rowlands (1998); McLean, Sanders and Stroup
#> (1991); Satterthwaite (1946); Giesbrecht and Burns (1985); Fai and Cornelius
#> (1996). Full references: vlm_cite(x).
# the mean squares and their expectations (Table 2.5.3.1)
em <-
vlm_ems(
fixed = Pcv ~ Region + Drug + Region:Drug + dose + Drug:dose
, data = ex125
, random = ~ Region + Region:Drug
, type = 3
, class = NULL
)
em
#> Type 3 analysis of variance of Pcv
#>
#> Analysis of variance
#> source df ss ms ems
#> Region 5 117.4 23.47 Var(Residual) + 4 Var(Region) + 2 Var(Region:Drug)
#> Drug 1 185.4 185.4 Var(Residual) + 2 Var(Region:Drug) + Q(Drug)
#> Region:Drug 5 14.35 2.870 Var(Residual) + 2 Var(Region:Drug)
#> dose 1 45.65 45.65 Var(Residual) + Q(dose)
#> Drug:dose 1 15.20 15.20 Var(Residual) + Q(Drug:dose)
#> Residual 10 20.96 2.096 Var(Residual)
#> F den_df p
#> 8.178 5 0.018857
#> 64.58 5 0.000483
#> 1.369 10 0.313691
#> 21.78 10 0.000886
#> 7.251 10 0.022594
#> . .
#>
#> Error terms of the tests
#> source error
#> Region 1 MS(Region:Drug)
#> Drug 1 MS(Region:Drug)
#> Region:Drug 1 MS(Residual)
#> dose 1 MS(Residual)
#> Drug:dose 1 MS(Residual)
#>
#> Type 3 estimates of the variance components
#> component estimate
#> Region 5.151
#> Region:Drug 0.3870
#> Residual 2.096
#>
#> Sources: Duchateau, Janssen and Rowlands (1998); Searle, Casella and McCulloch
#> (1992); Satterthwaite (1946). Full references: vlm_cite(x).