Examp3.1 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/Examp3.1.R
Examp3.1.RdExamp3.1 is.
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 3.1 Model 1 p-80
#-------------------------------------------------------------
# PROC MIXED DATA=ex31;
# CLASS drug dose herd;
# MODEL PCV2=drug dose(drug)/solution ddfm=satterth;
# RANDOM herd(drug);
# ESTIMATE 'Mean Samorin' intercept 1 drug 0 1 dose(drug) 0 0 1;
# ESTIMATE 'Berenil 2 doses' dose(drug) 1 -1 0;
# ESTIMATE 'Ber vs Sam at dose 1' drug 1 -1 dose(drug) 1 0 -1;
# CONTRAST 'Mean Samorin' intercept 1 drug 0 1 dose(drug) 0 0 1;
# CONTRAST 'Berenil dif 2 doses' dose(drug) 1 -1 0;
# CONTRAST 'Ber vs Sam at dose 1' drug 1 -1 dose(drug) 1 0 -l;
# CONTRAST 'some difference' drug 1 -1 dose(drug) 0.5 0.5 -1,
# drug 0 0 dose(drug) 1 -1 0;
# LSMEANS dose(drug);
# RUN;
library(lmerTest)
str(ex31)
#> 'data.frame': 38 obs. of 6 variables:
#> $ herd : int 1 1 1 1 1 1 1 1 1 2 ...
#> $ animal_id: int 667 1003 1177 227 241 271 44 48 233 1368 ...
#> $ PCV1 : int 17 22 20 22 22 18 22 21 18 18 ...
#> $ PCV2 : int 28 23 28 25 23 18 27 20 30 20 ...
#> $ dose : int 1 1 1 2 2 2 1 1 1 1 ...
#> $ drug : Factor w/ 2 levels "BERENIL","SAMORIN": 1 1 1 1 1 1 2 2 2 1 ...
ex31 <-
ex31 |>
collapse::fmutate(
herd1 = factor(herd),
drug1 = factor(drug),
dose1 = factor(dose),
ber = as.integer(drug == "BERENIL"),
ber1 = as.integer(drug == "BERENIL" & dose == 1L),
pcv_ber1 = PCV1 * as.integer(drug == "BERENIL" & dose == 1L),
pcv_ber2 = PCV1 * as.integer(drug == "BERENIL" & dose == 2L)
)
fm3.1 <-
lmerTest::lmer(
formula = PCV2 ~ drug1 + dose1:drug1 + (1|herd1:drug1)
, data = ex31
, REML = TRUE
, control = lmerControl()
, start = NULL
, verbose = 0L
# , subset
# , weights
# , na.action
# , offset
, contrasts = list(dose1 = "contr.SAS", drug1 = "contr.SAS")
, devFunOnly = FALSE
# , ...
)
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
if (requireNamespace("report", quietly = TRUE)) {
fm3.1 |>
report::report()
}
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> We fitted a linear mixed model (estimated using REML and nloptwrap optimizer)
#> to predict PCV2 with drug1 and dose1 (formula: PCV2 ~ drug1 + dose1:drug1). The
#> model included herd1 as random effects (formula: ~1 | herd1:drug1). The model's
#> total explanatory power is weak (conditional R2 = 0.12) and the part related to
#> the fixed effects alone (marginal R2) is of 0.06. The model's intercept,
#> corresponding to drug1 = BERENIL and dose1 = 1, is at 24.17 (95% CI [22.05,
#> 26.28], t(33) = 23.28, p < .001). Within this model:
#>
#> - The effect of drug1 [BERENIL] is statistically non-significant and positive
#> (beta = 1.10, 95% CI [-1.80, 4.00], t(33) = 0.77, p = 0.445; Std. beta = 0.32,
#> 95% CI [-0.53, 1.17])
#> - The effect of drug1 [BERENIL] × dose11 is statistically non-significant and
#> negative (beta = -2.10, 95% CI [-4.75, 0.55], t(33) = -1.61, p = 0.116; Std.
#> beta = -0.61, 95% CI [-1.39, 0.16])
#>
#> 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)) {
emm3.1 <- emmeans::emmeans(fm3.1, ~ dose1 | drug1, lmer.df = "asymptotic")
print(emm3.1)
print(emmeans::contrast(emm3.1, method = "pairwise"))
}
#> NOTE: A nesting structure was detected in the fitted model:
#> dose1 %in% drug1
#> drug1 = BERENIL:
#> dose1 emmean SE df asymp.LCL asymp.UCL
#> 1 23.2 1.040 Inf 21.1 25.2
#> 2 25.3 0.977 Inf 23.4 27.2
#>
#> drug1 = SAMORIN:
#> dose1 emmean SE df asymp.LCL asymp.UCL
#> 1 24.2 1.040 Inf 22.1 26.2
#>
#> Degrees-of-freedom method: asymptotic
#> Confidence level used: 0.95
#> drug1 = BERENIL:
#> contrast estimate SE df z.ratio p.value
#> dose11 - dose12 -2.1 1.3 Inf -1.612 0.1069
#>
#> drug1 = SAMORIN:
#> contrast estimate SE df z.ratio p.value
#> (nothing) nonEst NA NA NA NA
#>
#> Degrees-of-freedom method: asymptotic
summary(fm3.1)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: PCV2 ~ drug1 + dose1:drug1 + (1 | herd1:drug1)
#> Data: ex31
#>
#> REML criterion at convergence: 192.1
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -2.19435 -0.64365 0.04272 0.47738 1.69413
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> herd1:drug1 (Intercept) 0.6682 0.8175
#> Residual 10.9299 3.3060
#> Number of obs: 38, groups: herd1:drug1, 8
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 24.167 1.038 15.358 23.277 2.14e-13 ***
#> drug1BERENIL 1.102 1.426 13.734 0.773 0.453
#> drug1BERENIL:dose11 -2.102 1.303 31.520 -1.612 0.117
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) dr1BERENIL
#> drg1BERENIL -0.728
#> d1BERENIL:1 0.000 -0.424
#> fit warnings:
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
anova(object = fm3.1, ddf = "Satterthwaite")
#> Missing cells for: drug1SAMORIN:dose12.
#> Interpret type III hypotheses with care.
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> drug1 5.0701 5.0701 1 15.358 0.4639 0.5060
#> drug1:dose1 28.4190 28.4190 1 31.520 2.6001 0.1168
lsmeansLT(model = fm3.1, test.effs = "dose1:drug1")
#> Least Squares Means table:
#>
#> Estimate Std. Error df t value lower upper
#> drug1BERENIL 24.21745 0.76923 5.3 31.483 22.26991 26.16499
#> drug1SAMORIN NA NA NA NA NA NA
#> drug1BERENIL:dose11 23.16667 1.03821 15.4 22.314 20.95825 25.37508
#> drug1SAMORIN:dose11 24.16667 1.03821 15.4 23.277 21.95825 26.37508
#> drug1BERENIL:dose12 25.26823 0.97716 12.1 25.859 23.14188 27.39459
#> drug1SAMORIN:dose12 NA NA NA NA NA NA
#> Pr(>|t|)
#> drug1BERENIL 3.348e-07 ***
#> drug1SAMORIN NA
#> drug1BERENIL:dose11 4.024e-13 ***
#> drug1SAMORIN:dose11 2.140e-13 ***
#> drug1BERENIL:dose12 5.494e-12 ***
#> drug1SAMORIN:dose12 NA
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Confidence level: 95%
#> Degrees of freedom method: Satterthwaite
#-------------------------------------------------------------
## Example 3.1 Model 2 p-84
#-------------------------------------------------------------
# PROC MIXED DATA=ex31;
# CLASS drug dose herd;
# MODEL PCV2=PCV1 drug dose(drug)/solution ddfm=satterth;
# RANDOM herd(drug);
# RUN;
fm3.2 <-
lmerTest::lmer(
formula = PCV2 ~ PCV1 + drug1 + dose1:drug1 + (1|herd1:drug1)
, data = ex31
, REML = TRUE
, control = lmerControl()
, start = NULL
, verbose = 0L
# , subset
# , weights
# , na.action
# , offset
, contrasts = list(dose1 = "contr.SAS", drug1 = "contr.SAS")
, devFunOnly = FALSE
# , ...
)
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
if (requireNamespace("report", quietly = TRUE)) {
fm3.2 |>
report::report()
}
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
#> We fitted a linear mixed model (estimated using REML and nloptwrap optimizer)
#> to predict PCV2 with PCV1, drug1 and dose1 (formula: PCV2 ~ PCV1 + drug1 +
#> dose1:drug1). The model included herd1 as random effects (formula: ~1 |
#> herd1:drug1). The model's total explanatory power is weak (conditional R2 =
#> 0.11) and the part related to the fixed effects alone (marginal R2) is of 0.06.
#> The model's intercept, corresponding to PCV1 = 0, drug1 = BERENIL and dose1 =
#> 1, is at 23.64 (95% CI [11.28, 36.00], t(32) = 3.90, p < .001). Within this
#> model:
#>
#> - The effect of PCV1 is statistically non-significant and positive (beta =
#> 0.03, 95% CI [-0.57, 0.62], t(32) = 0.09, p = 0.930; Std. beta = 0.01, 95% CI
#> [-0.33, 0.36])
#> - The effect of drug1 [BERENIL] is statistically non-significant and positive
#> (beta = 1.13, 95% CI [-1.85, 4.12], t(32) = 0.77, p = 0.446; Std. beta = 0.33,
#> 95% CI [-0.54, 1.20])
#> - The effect of drug1 [BERENIL] × dose11 is statistically non-significant and
#> negative (beta = -2.13, 95% CI [-4.90, 0.63], t(32) = -1.57, p = 0.126; Std.
#> beta = -0.62, 95% CI [-1.43, 0.18])
#>
#> 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)) {
emm3.2 <- emmeans::emmeans(fm3.2, ~ dose1 | drug1, lmer.df = "asymptotic")
print(emm3.2)
print(emmeans::contrast(emm3.2, method = "pairwise"))
}
#> NOTE: A nesting structure was detected in the fitted model:
#> dose1 %in% drug1
#> drug1 = BERENIL:
#> dose1 emmean SE df asymp.LCL asymp.UCL
#> 1 23.2 1.06 Inf 21.1 25.2
#> 2 25.3 1.00 Inf 23.3 27.3
#>
#> drug1 = SAMORIN:
#> dose1 emmean SE df asymp.LCL asymp.UCL
#> 1 24.2 1.05 Inf 22.1 26.2
#>
#> Degrees-of-freedom method: asymptotic
#> Confidence level used: 0.95
#> drug1 = BERENIL:
#> contrast estimate SE df z.ratio p.value
#> dose11 - dose12 -2.13 1.36 Inf -1.571 0.1161
#>
#> drug1 = SAMORIN:
#> contrast estimate SE df z.ratio p.value
#> (nothing) nonEst NA NA NA NA
#>
#> Degrees-of-freedom method: asymptotic
summary(fm3.2)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: PCV2 ~ PCV1 + drug1 + dose1:drug1 + (1 | herd1:drug1)
#> Data: ex31
#>
#> REML criterion at convergence: 192.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -2.14932 -0.63140 0.05373 0.47166 1.69087
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> herd1:drug1 (Intercept) 0.6391 0.7994
#> Residual 11.2803 3.3586
#> Number of obs: 38, groups: herd1:drug1, 8
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 23.64038 6.06889 33.91516 3.895 0.000438 ***
#> PCV1 0.02567 0.29159 33.74677 0.088 0.930362
#> drug1BERENIL 1.13037 1.46551 13.70396 0.771 0.453615
#> drug1BERENIL:dose11 -2.13251 1.35725 30.87596 -1.571 0.126329
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) PCV1 dr1BERENIL
#> PCV1 -0.985
#> drg1BERENIL -0.308 0.187
#> d1BERENIL:1 0.217 -0.220 -0.450
#> fit warnings:
#> fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
anova(object = fm3.2, ddf = "Satterthwaite")
#> Missing cells for: drug1SAMORIN:dose12.
#> Interpret type III hypotheses with care.
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> PCV1 0.0874 0.0874 1 33.747 0.0078 0.9304
#> drug1 5.1489 5.1489 1 14.799 0.4565 0.5097
#> drug1:dose1 27.8474 27.8474 1 30.876 2.4687 0.1263
lsmeansLT(model = fm3.2, test.effs = "herd1:drug1")
#> Least Squares Means table:
#>
#> Estimate Std. Error df t value lower upper
#> drug1BERENIL 24.22268 0.77398 4.9 31.296 22.22655 26.21880
#> drug1SAMORIN NA NA NA NA NA NA
#> drug1BERENIL:dose11 23.15642 1.05515 15.0 21.946 20.90761 25.40523
#> drug1SAMORIN:dose11 24.15856 1.05275 14.9 22.948 21.91379 26.40333
#> drug1BERENIL:dose12 25.28893 1.00290 12.0 25.216 23.10450 27.47336
#> drug1SAMORIN:dose12 NA NA NA NA NA NA
#> Pr(>|t|)
#> drug1BERENIL 7.056e-07 ***
#> drug1SAMORIN NA
#> drug1BERENIL:dose11 8.033e-13 ***
#> drug1SAMORIN:dose11 4.672e-13 ***
#> drug1BERENIL:dose12 8.709e-12 ***
#> drug1SAMORIN:dose12 NA
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Confidence level: 95%
#> Degrees of freedom method: Satterthwaite
#-------------------------------------------------------------
## Example 3.1 Model 3 p-86
#-------------------------------------------------------------
# PROC MIXED DATA=ex31;
# CLASS drug dose herd;
# MODEL PCV2=drug dose(drug) PCV1*dose(drug)/solution ddfm=satterth;
# RANDOM herd(drug);
# RUN;
fm3.3 <-
lmerTest::lmer(
formula = PCV2 ~ drug1 + PCV1*dose1:drug1 + (1|herd1:drug1)
, data = ex31
, REML = TRUE
, control = lmerControl()
, start = NULL
, verbose = 0L
# , subset
# , weights
# , na.action
# , offset
, contrasts = list(dose1 = "contr.SAS", drug1 = "contr.SAS")
, devFunOnly = FALSE
# , ...
)
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
if (requireNamespace("report", quietly = TRUE)) {
fm3.3 |>
report::report()
}
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
#> We fitted a linear mixed model (estimated using REML and nloptwrap optimizer)
#> to predict PCV2 with drug1, PCV1 and dose1 (formula: PCV2 ~ drug1 + PCV1 *
#> dose1:drug1). The model included herd1 as random effects (formula: ~1 |
#> herd1:drug1). The model's total explanatory power is moderate (conditional R2 =
#> 0.14) and the part related to the fixed effects alone (marginal R2) is of 0.09.
#> The model's intercept, corresponding to drug1 = BERENIL, PCV1 = 0 and dose1 =
#> 1, is at 33.12 (95% CI [2.67, 63.57], t(30) = 2.22, p = 0.034). Within this
#> model:
#>
#> - The effect of drug1 [BERENIL] is statistically non-significant and negative
#> (beta = -13.83, 95% CI [-47.83, 20.17], t(30) = -0.83, p = 0.413; Std. beta =
#> 0.34, 95% CI [-0.55, 1.22])
#> - The effect of PCV1 is statistically non-significant and positive (beta =
#> 0.31, 95% CI [-0.46, 1.07], t(30) = 0.82, p = 0.421; Std. beta = 0.18, 95% CI
#> [-0.27, 0.62])
#> - The effect of drug1 [BERENIL] × dose11 is statistically non-significant and
#> positive (beta = 12.13, 95% CI [-17.95, 42.21], t(30) = 0.82, p = 0.417; Std.
#> beta = -0.62, 95% CI [-1.45, 0.20])
#> - The effect of drug1 [BERENIL] × PCV1 × dose11 is statistically
#> non-significant and negative (beta = -0.71, 95% CI [-2.18, 0.77], t(30) =
#> -0.98, p = 0.335; Std. beta = -0.41, 95% CI [-1.26, 0.44])
#> - The effect of drug1SAMORIN × PCV1 × dose11 is statistically non-significant
#> and negative (beta = -0.74, 95% CI [-2.41, 0.93], t(30) = -0.91, p = 0.371;
#> Std. beta = -0.43, 95% CI [-1.40, 0.54])
#>
#> 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)) {
emm3.3 <- emmeans::emmeans(fm3.3, ~ dose1 | drug1, lmer.df = "asymptotic")
print(emm3.3)
print(emmeans::contrast(emm3.3, method = "pairwise"))
}
#> NOTE: A nesting structure was detected in the fitted model:
#> dose1 %in% drug1
#> NOTE: Results may be misleading due to involvement in interactions
#> drug1 = BERENIL:
#> dose1 emmean SE df asymp.LCL asymp.UCL
#> 1 23.3 1.09 Inf 21.2 25.5
#> 2 25.5 1.02 Inf 23.5 27.5
#>
#> drug1 = SAMORIN:
#> dose1 emmean SE df asymp.LCL asymp.UCL
#> 1 24.3 1.08 Inf 22.2 26.4
#>
#> Degrees-of-freedom method: asymptotic
#> Confidence level used: 0.95
#> drug1 = BERENIL:
#> contrast estimate SE df z.ratio p.value
#> dose11 - dose12 -2.13 1.38 Inf -1.548 0.1217
#>
#> drug1 = SAMORIN:
#> contrast estimate SE df z.ratio p.value
#> (nothing) nonEst NA NA NA NA
#>
#> Degrees-of-freedom method: asymptotic
summary(fm3.3)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: PCV2 ~ drug1 + PCV1 * dose1:drug1 + (1 | herd1:drug1)
#> Data: ex31
#>
#> REML criterion at convergence: 188.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -2.03785 -0.67127 0.06847 0.62206 1.47702
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> herd1:drug1 (Intercept) 0.6475 0.8046
#> Residual 11.4692 3.3866
#> Number of obs: 38, groups: herd1:drug1, 8
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 33.1192 14.9092 31.5039 2.221 0.0336 *
#> drug1BERENIL -13.8326 16.6481 31.8493 -0.831 0.4122
#> PCV1 0.3058 0.3752 30.9513 0.815 0.4212
#> drug1BERENIL:dose11 12.1279 14.7286 31.0475 0.823 0.4165
#> drug1BERENIL:PCV1:dose11 -0.7065 0.7218 31.0117 -0.979 0.3352
#> drug1SAMORIN:PCV1:dose11 -0.7425 0.8167 31.8994 -0.909 0.3701
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Correlation of Fixed Effects:
#> (Intr) dr1BERENIL PCV1 d1BERENIL:1 d1BERENIL:P
#> drg1BERENIL -0.896
#> PCV1 0.000 -0.441
#> d1BERENIL:1 0.000 -0.221 0.494
#> d1BERENIL:P 0.000 0.227 -0.515 -0.996
#> d1SAMORIN:P -0.886 0.996 -0.459 -0.227 0.237
#> fit warnings:
#> fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients
anova(object = fm3.3, ddf = "Satterthwaite")
#> Missing cells for: drug1SAMORIN:dose12, drug1SAMORIN:PCV1:dose12.
#> Interpret type III hypotheses with care.
#> Type III Analysis of Variance Table with Satterthwaite's method
#> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
#> drug1 0.0864 0.0864 1 31.982 0.0075 0.9314
#> PCV1 7.6204 7.6204 1 30.951 0.6644 0.4212
#> drug1:dose1 7.7764 7.7764 1 31.048 0.6780 0.4165
#> drug1:PCV1:dose1 16.5665 8.2832 2 31.918 0.7222 0.4934
lsmeansLT(model = fm3.3, test.effs = "dose1:drug1")
#> Least Squares Means table:
#>
#> Estimate Std. Error df t value lower upper
#> drug1BERENIL 24.39310 0.79713 5.1 30.601 22.35878 26.42743
#> drug1SAMORIN NA NA NA NA NA NA
#> drug1BERENIL:dose11 23.32660 1.08564 15.0 21.486 21.01278 25.64041
#> drug1SAMORIN:dose11 24.30457 1.08172 14.7 22.468 21.99515 26.61400
#> drug1BERENIL:dose12 25.45960 1.02085 11.8 24.940 23.23211 27.68710
#> drug1SAMORIN:dose12 NA NA NA NA NA NA
#> Pr(>|t|)
#> drug1BERENIL 5.327e-07 ***
#> drug1SAMORIN NA
#> drug1BERENIL:dose11 1.096e-12 ***
#> drug1SAMORIN:dose11 8.388e-13 ***
#> drug1BERENIL:dose12 1.328e-11 ***
#> drug1SAMORIN:dose12 NA
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Confidence level: 95%
#> Degrees of freedom method: Satterthwaite