Examp2.6.1 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.
Source:R/Examp2.6.1.R
Examp2.6.1.RdExamp2.6.1 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 2.6.1 p-76
#-------------------------------------------------------------
# PROC MIXED DATA=ex125;
# CLASS drug dose region;
# MODEL pcv=drug dose drug*dose / ddfm=satterth;
# RANDOM region drug*region;
# CONTRAST 'drug dif' drug -1 1 drug*dose -0.5 -0.5 0.5 0.5;
# CONTRAST 'all' drug 1 -1 dose 0 0 drug*dose 0.5 0.5 -0.5 -0.5,
# drug 0 0 dose 1 -1 drug*dose 0.5 -0.5 0.5 -0.5,
# drug 0 0 dose 0 0 drug*dose 0.5 -0.5 -0.5 0.5;
# RUN;
library(lmerTest)
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 ...
ex125 <-
ex125 |>
collapse::fmutate(Region1 = factor(Region))
fm2.14 <-
lmerTest::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)) {
fm2.14 |>
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)) {
emm2.14 <- emmeans::emmeans(fm2.14, ~ dose | Drug, lmer.df = "asymptotic")
print(emm2.14)
print(emmeans::contrast(emm2.14, 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(fm2.14)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> 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 df t value Pr(>|t|)
#> (Intercept) 17.1333 1.1280 8.2080 15.189 2.69e-07 ***
#> doseh 4.3500 0.8359 10.0000 5.204 0.000399 ***
#> DrugBERENIL 7.1500 0.9098 11.8185 7.859 4.96e-06 ***
#> doseh:DrugBERENIL -3.1833 1.1822 10.0000 -2.693 0.022595 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) doseh DBEREN
#> doseh -0.371
#> DrugBERENIL -0.403 0.459
#> ds:DBERENIL 0.262 -0.707 -0.650
anova(object = fm2.14, ddf = "Satterthwaite")
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> dose 45.65 45.65 1 10 21.7754 0.0008856 ***
#> Drug 135.39 135.39 1 5 64.5796 0.0004826 ***
#> dose:Drug 15.20 15.20 1 10 7.2507 0.0225945 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
library(multcomp)
Contrasts3 <-
matrix(c(
0, 0, -1, -0.5
)
, ncol = 4
, byrow = TRUE
, dimnames = list(
c("C1")
, rownames(summary(fm2.14)$coef)
)
)
Contrasts3
#> (Intercept) doseh DrugBERENIL doseh:DrugBERENIL
#> C1 0 0 -1 -0.5
summary(glht(fm2.14, linfct=Contrasts3))
#>
#> Simultaneous Tests for General Linear Hypotheses
#>
#> Fit: lmerTest::lmer(formula = Pcv ~ dose * Drug + (1 | Region/Drug),
#> data = ex125, REML = TRUE, control = lmerControl(), start = NULL,
#> verbose = 0L, contrasts = list(dose = "contr.SAS", Drug = "contr.SAS"),
#> devFunOnly = FALSE)
#>
#> Linear Hypotheses:
#> Estimate Std. Error z value Pr(>|z|)
#> C1 == 0 -5.5583 0.6917 -8.036 8.88e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> (Adjusted p values reported -- single-step method)
#>
if(packageVersion("lmerTest") >= "3.0")
contest(fm2.14, Contrasts3, joint = FALSE)
#> Estimate Std. Error df t value lower upper Pr(>|t|)
#> C1 -5.558333 0.6916667 5 -8.036145 -7.336319 -3.780348 0.0004825951