pacman::p_load(
here, ggplot2, ggpubr, packcircles, metafor, devtools,
patchwork, tidyverse, ape,
R.rsp, emmeans
)
devtools::install_github("daniel1noble/orchaRd", force = TRUE)
devtools::install_github("daniel1noble/metaAidR", force = TRUE)
library(orchaRd)
library(metaAidR)
options(digits = 3, scipen = 5)run.model<-function(mydata,formula){
mydata<-as.data.frame(mydata)
Z <- make_VCV_matrix(mydata, V="Z_var", cluster = "Study_no", obs="es_ID")
rma.mv(yi=ES_biol, V=Z,
method="REML",
mods= formula,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID,
~1|research_group),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = mydata)
}
plot_continuous<-function(data, model, moderator, xlab){
pred <- predict.rma(model)
data %>% mutate(fit=pred$pred,
ci.lb=pred$ci.lb,
ci.ub=pred$ci.ub,
pr.lb=pred$cr.lb,
pr.ub=pred$cr.ub) %>%
ggplot(aes(x = moderator, y = ES_biol)) +
geom_ribbon(aes(ymin = pr.lb, ymax = pr.ub, color = NULL), alpha = .1) +
geom_ribbon(aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
geom_point(aes(size=(1/sqrt(mydata$Z_var))), shape= 21, alpha=0.7, fill="#6F94B7", col="#305980") +
geom_line(aes(y = fit), linewidth = 1.5)+
labs(x = xlab, y = "Effect size", size = "Precision (1/SE)") +
theme_bw() +
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank()) +
scale_size_continuous(range=c(1,12))+
geom_hline(yintercept = 0, linetype = 2, colour = "black", alpha=0.5)+
theme(text = element_text(size = 18, colour = "black", hjust = 0.5),
legend.text=element_text(size=14),
legend.position=c(0,0),
legend.justification = c(0,0),
legend.background = element_blank(),
legend.direction="horizontal",
legend.title = element_text(size=15),
panel.border=element_rect(colour="black", fill=NA, size=1.2))
}Raw data (both the “biological” and “physical” effect sizes) can be downloaded from this link. The files is a compressed archive with all datasets and the phylogenetic tree birdtree.tre.
mydata <- read.csv(here("data", "ES_biol_2023.csv"), sep = ";")
# load phylogenetic tree
mytree <- multi2di(read.tree(here("data", "bird_tree.tre")))
mytree$edge.length[which(mytree$edge.length == 0)] = 1e-10
#subset tree to the species list
subtree <- drop.tip(mytree, setdiff(mytree$tip.label, mydata$tip_label))
cor <- vcv(subtree, cor = T)
#calculate weights
mydata$Z_var <- 1/(mydata$n-3)
mydata$weight <- 1/mydata$Z_varM0.0 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~ 1,
random = list(~1|tip_label,
~1|research_group,
~1|Study_no,
~1|es_ID),
R = list(tip_label = cor),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = mydata)
summary(M0.0)
Multivariate Meta-Analysis Model (k = 421; method: REML)
logLik Deviance AIC BIC AICc
-22.9203 45.8407 55.8407 76.0420 55.9856
Variance Components:
estim sqrt nlvls fixed factor R
sigma^2.1 0.0043 0.0654 25 no tip_label yes
sigma^2.2 0.0050 0.0706 25 no research_group no
sigma^2.3 0.0179 0.1339 59 no Study_no no
sigma^2.4 0.0194 0.1395 402 no es_ID no
Test for Heterogeneity:
Q(df = 420) = 1258.4298, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.0819 0.0464 -1.7656 0.0775 -0.1728 0.0090 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M0.1 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~ 1,
random = list(~1|tip_label,
~1|research_group,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = mydata)
summary(M0.1)
Multivariate Meta-Analysis Model (k = 421; method: REML)
logLik Deviance AIC BIC AICc
-21.4089 42.8179 52.8179 73.0191 52.9628
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0108 0.1040 25 no tip_label
sigma^2.2 0.0021 0.0456 25 no research_group
sigma^2.3 0.0140 0.1181 59 no Study_no
sigma^2.4 0.0194 0.1392 402 no es_ID
Test for Heterogeneity:
Q(df = 420) = 1258.4298, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.0602 0.0354 -1.6997 0.0892 -0.1296 0.0092 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1i2_ml(M0.1) I2_Total I2_tip_label I2_research_group I2_Study_no
76.51 17.89 3.44 23.10
I2_es_ID
32.08 M1.0<- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~ colour_type-1+sex+age+measured_part+study_type+raw_or_model+method ,
random = list(~1|tip_label,
~1|research_group,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = mydata)
summary(M1.0)
Multivariate Meta-Analysis Model (k = 421; method: REML)
logLik Deviance AIC BIC AICc
-5.5864 11.1728 43.1728 107.3922 44.5605
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0113 0.1062 25 no tip_label
sigma^2.2 0.0008 0.0278 25 no research_group
sigma^2.3 0.0157 0.1254 59 no Study_no
sigma^2.4 0.0176 0.1327 402 no es_ID
Test for Residual Heterogeneity:
QE(df = 409) = 1078.8773, p-val < .0001
Test of Moderators (coefficients 1:12):
QM(df = 12) = 37.0666, p-val = 0.0002
Model Results:
estimate se zval pval ci.lb
colour_typecarotenoid-based -0.3099 0.0947 -3.2726 0.0011 -0.4956
colour_typemelanin-based -0.1118 0.0960 -1.1647 0.2441 -0.2998
colour_typestructural -0.1693 0.1039 -1.6292 0.1033 -0.3729
sexM -0.0897 0.0499 -1.7977 0.0722 -0.1876
sexM/F -0.0144 0.0589 -0.2451 0.8064 -0.1298
ageJUV 0.1004 0.0592 1.6953 0.0900 -0.0157
ageMIXED 0.1131 0.1003 1.1277 0.2595 -0.0835
measured_partfeathers -0.0365 0.0533 -0.6844 0.4937 -0.1411
study_typeO 0.0849 0.0596 1.4253 0.1541 -0.0319
raw_or_modelraw 0.0739 0.0474 1.5585 0.1191 -0.0190
methodphoto 0.1453 0.0694 2.0954 0.0361 0.0094
methodspectro 0.1258 0.0603 2.0868 0.0369 0.0077
ci.ub
colour_typecarotenoid-based -0.1243 **
colour_typemelanin-based 0.0763
colour_typestructural 0.0344
sexM 0.0081 .
sexM/F 0.1010
ageJUV 0.2164 .
ageMIXED 0.3096
measured_partfeathers 0.0680
study_typeO 0.2017
raw_or_modelraw 0.1668
methodphoto 0.2813 *
methodspectro 0.2440 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1orchard_plot(M1.0, mod = "colour_type", group = "Study_no", by="method", xlab = "Correlation coefficient", transfm = "none", alpha = 0.4, angle = 0, cb = FALSE, legend.pos = "top.left", condition.lab = "Method") + theme(legend.direction = "vertical")
#extraction of marginal estimates for colour type from the M1.0:
res_colour_type <- orchaRd::mod_results(M1.0, mod = "colour_type", group = "Study_no")
res_colour_type name estimate lowerCL upperCL lowerPR upperPR
1 Carotenoid-based -0.14833 -0.2293 -0.0673 -0.574 0.277
2 Melanin-based 0.04984 -0.0507 0.1504 -0.380 0.479
3 Structural -0.00766 -0.1251 0.1098 -0.441 0.426
orchard_plot(M1.0, mod = "sex", group = "Study_no", xlab = "Correlation coefficient (r)", angle = 0,legend.pos = "top.left", cb = FALSE) + theme(legend.direction = "vertical")
res_sex <- orchaRd::mod_results(M1.0, mod = "sex", group = "Study_no")
res_sex name estimate lowerCL upperCL lowerPR upperPR
1 F -0.0497 -0.161 0.0618 -0.482 0.382
2 M -0.1394 -0.234 -0.0445 -0.568 0.289
3 M/F -0.0641 -0.151 0.0226 -0.490 0.362
orchard_plot(M1.0, mod = "age", group = "Study_no", xlab = "Correlation coefficient (r)", angle = 0,legend.pos = "top.left", cb = FALSE) + theme(legend.direction = "vertical")
res_age <- orchaRd::mod_results(M1.0, mod = "age", group = "Study_no")
res_age name estimate lowerCL upperCL lowerPR upperPR
1 AD -0.11037 -0.188 -0.033 -0.535 0.314
2 JUV -0.01001 -0.128 0.108 -0.444 0.424
3 MIXED 0.00272 -0.197 0.203 -0.460 0.466
orchard_plot(M1.0, mod = "measured_part", group = "Study_no", xlab = "Correlation coefficient (r)", angle = 0,legend.pos = "top.left", cb = FALSE) + theme(legend.direction = "vertical")
res_measured_part <- orchaRd::mod_results(M1.0, mod = "measured_part", group = "Study_no")
res_measured_part name estimate lowerCL upperCL lowerPR upperPR
1 Bare part -0.0688 -0.167 0.0293 -0.498 0.36
2 Feathers -0.1053 -0.189 -0.0218 -0.531 0.32
orchard_plot(M1.0, mod = "raw_or_model", group = "Study_no", xlab = "Correlation coefficient (r)", angle = 0,legend.pos = "top.left", cb = FALSE) + theme(legend.direction = "vertical")
res_raw_or_model <- orchaRd::mod_results(M1.0, mod = "raw_or_model", group = "Study_no")
res_raw_or_model name estimate lowerCL upperCL lowerPR upperPR
1 Model -0.1248 -0.213 -0.0371 -0.551 0.302
2 Raw -0.0509 -0.137 0.0348 -0.477 0.375
orchard_plot(M1.0, mod = "study_type", group = "Study_no", xlab = "Correlation coefficient (r)", angle = 0,legend.pos = "top.left", cb = TRUE) + theme(legend.direction = "vertical")
res_study_type <- orchaRd::mod_results(M1.0, mod = "study_type", group = "Study_no")
res_study_type name estimate lowerCL upperCL lowerPR upperPR
1 E -0.146 -0.258 -0.0336 -0.578 0.286
2 O -0.061 -0.140 0.0181 -0.486 0.364
orchard_plot(M1.0, mod = "method", group = "Study_no", xlab = "Correlation coefficient (r)", angle = 0,legend.pos = "top.left", cb = TRUE) + theme(legend.direction = "vertical")
res_method <- orchaRd::mod_results(M1.0, mod = "method", group = "Study_no")
res_method name estimate lowerCL upperCL lowerPR upperPR
1 Other -0.2131 -0.334 -0.09190 -0.648 0.222
2 Photo -0.0677 -0.169 0.03384 -0.497 0.362
3 Spectro -0.0872 -0.169 -0.00513 -0.513 0.338
hue <- subset(mydata, HSB == "hue")
# summary(hue)
mydata$Z_var <- 1/(mydata$n-3)
mydata$weight <- 1/mydata$Z_var
M2.1 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+colour_type:pollution_type+
sex+age+measured_part+study_type +raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = hue)Warning: Redundant predictors dropped from the model.summary(M2.1)# interaction not significant
Multivariate Meta-Analysis Model (k = 95; method: REML)
logLik Deviance AIC BIC AICc
18.1084 -36.2167 -2.2167 38.4889 7.4976
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0172 0.1310 13 no tip_label
sigma^2.2 0.0206 0.1437 25 no Study_no
sigma^2.3 0.0088 0.0937 95 no es_ID
Test for Residual Heterogeneity:
QE(df = 81) = 229.2318, p-val < .0001
Test of Moderators (coefficients 2:14):
QM(df = 13) = 13.9010, p-val = 0.3809
Model Results:
estimate se zval
intrcpt -0.2172 0.2265 -0.9588
colour_typemelanin-based 0.0986 0.2038 0.4837
colour_typestructural 0.0058 0.1826 0.0320
pollution_typepersistent_organic_pollutants 0.0890 0.0954 0.9325
pollution_typeurbanisation 0.0639 0.1132 0.5649
sexM -0.1095 0.0878 -1.2475
sexM/F 0.0660 0.1216 0.5428
ageJUV 0.0661 0.1411 0.4687
ageMIXED 0.1046 0.1907 0.5485
measured_partfeathers -0.1072 0.1255 -0.8546
study_typeO 0.0065 0.2008 0.0326
raw_or_modelraw -0.1607 0.1042 -1.5414
methodspectro 0.1754 0.1420 1.2356
colour_typestructural:pollution_typeurbanisation 0.2831 0.3262 0.8678
pval ci.lb ci.ub
intrcpt 0.3376 -0.6611 0.2268
colour_typemelanin-based 0.6286 -0.3009 0.4980
colour_typestructural 0.9745 -0.3520 0.3637
pollution_typepersistent_organic_pollutants 0.3511 -0.0980 0.2760
pollution_typeurbanisation 0.5721 -0.1579 0.2858
sexM 0.2122 -0.2816 0.0626
sexM/F 0.5873 -0.1724 0.3044
ageJUV 0.6393 -0.2104 0.3427
ageMIXED 0.5833 -0.2692 0.4785
measured_partfeathers 0.3928 -0.3531 0.1387
study_typeO 0.9740 -0.3871 0.4002
raw_or_modelraw 0.1232 -0.3650 0.0436
methodspectro 0.2166 -0.1028 0.4537
colour_typestructural:pollution_typeurbanisation 0.3855 -0.3563 0.9225
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M2.1 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+sex+age+measured_part
+ study_type +raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = hue)
summary(M2.1)
Multivariate Meta-Analysis Model (k = 95; method: REML)
logLik Deviance AIC BIC AICc
17.9865 -35.9730 -3.9730 34.5345 4.3962
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0171 0.1306 13 no tip_label
sigma^2.2 0.0200 0.1414 25 no Study_no
sigma^2.3 0.0088 0.0937 95 no es_ID
Test for Residual Heterogeneity:
QE(df = 82) = 234.1609, p-val < .0001
Test of Moderators (coefficients 2:13):
QM(df = 12) = 13.2791, p-val = 0.3491
Model Results:
estimate se zval pval
intrcpt -0.2637 0.2185 -1.2066 0.2276
colour_typemelanin-based 0.1110 0.2027 0.5473 0.5842
colour_typestructural 0.0869 0.1560 0.5571 0.5775
pollution_typepersistent_organic_pollutants 0.0974 0.0948 1.0275 0.3042
pollution_typeurbanisation 0.0873 0.1092 0.7996 0.4239
sexM -0.1119 0.0877 -1.2764 0.2018
sexM/F 0.0746 0.1206 0.6181 0.5365
ageJUV 0.1031 0.1336 0.7723 0.4400
ageMIXED 0.1306 0.1861 0.7018 0.4828
measured_partfeathers -0.1152 0.1247 -0.9239 0.3555
study_typeO 0.0350 0.1966 0.1779 0.8588
raw_or_modelraw -0.1289 0.0964 -1.3369 0.1813
methodspectro 0.1703 0.1409 1.2081 0.2270
ci.lb ci.ub
intrcpt -0.6920 0.1646
colour_typemelanin-based -0.2864 0.5083
colour_typestructural -0.2189 0.3928
pollution_typepersistent_organic_pollutants -0.0884 0.2831
pollution_typeurbanisation -0.1267 0.3014
sexM -0.2837 0.0599
sexM/F -0.1619 0.3110
ageJUV -0.1586 0.3649
ageMIXED -0.2342 0.4954
measured_partfeathers -0.3597 0.1292
study_typeO -0.3504 0.4203
raw_or_modelraw -0.3179 0.0601
methodspectro -0.1060 0.4465
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1saturation <- subset(mydata, HSB == "saturation")
# summary(saturation)
M2.2 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+colour_type:pollution_type
+sex+age+measured_part+ study_type +raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = saturation)Warning: Redundant predictors dropped from the model.summary(M2.2)# interaction not significant
Multivariate Meta-Analysis Model (k = 105; method: REML)
logLik Deviance AIC BIC AICc
8.8067 -17.6134 16.3866 59.0712 24.7701
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 13 no tip_label
sigma^2.2 0.0137 0.1171 27 no Study_no
sigma^2.3 0.0144 0.1201 105 no es_ID
Test for Residual Heterogeneity:
QE(df = 91) = 248.1211, p-val < .0001
Test of Moderators (coefficients 2:14):
QM(df = 13) = 23.0519, p-val = 0.0411
Model Results:
estimate se zval
intrcpt -0.0034 0.1971 -0.0172
colour_typemelanin-based 0.2411 0.1840 1.3100
colour_typestructural 0.3094 0.1117 2.7693
pollution_typepersistent_organic_pollutants 0.0935 0.0877 1.0659
pollution_typeurbanisation 0.0107 0.0778 0.1381
sexM -0.0146 0.1317 -0.1106
sexM/F -0.1043 0.1545 -0.6751
ageJUV -0.0261 0.0922 -0.2834
ageMIXED 0.0613 0.1538 0.3983
measured_partfeathers 0.0407 0.1002 0.4060
study_typeO 0.0570 0.1085 0.5254
raw_or_modelraw 0.0228 0.0869 0.2620
methodspectro -0.1714 0.1064 -1.6116
colour_typestructural:pollution_typeurbanisation 0.1827 0.2368 0.7716
pval ci.lb ci.ub
intrcpt 0.9863 -0.3896 0.3829
colour_typemelanin-based 0.1902 -0.1196 0.6017
colour_typestructural 0.0056 0.0904 0.5283 **
pollution_typepersistent_organic_pollutants 0.2865 -0.0784 0.2655
pollution_typeurbanisation 0.8902 -0.1417 0.1631
sexM 0.9120 -0.2728 0.2437
sexM/F 0.4996 -0.4072 0.1986
ageJUV 0.7769 -0.2069 0.1546
ageMIXED 0.6904 -0.2401 0.3626
measured_partfeathers 0.6847 -0.1557 0.2371
study_typeO 0.5993 -0.1557 0.2697
raw_or_modelraw 0.7933 -0.1476 0.1932
methodspectro 0.1071 -0.3799 0.0371
colour_typestructural:pollution_typeurbanisation 0.4403 -0.2813 0.6467
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M2.2 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+sex+age+measured_part
+study_type +raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = saturation)
summary(M2.2)
Multivariate Meta-Analysis Model (k = 105; method: REML)
logLik Deviance AIC BIC AICc
8.9908 -17.9816 14.0184 54.3670 21.2718
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 13 no tip_label
sigma^2.2 0.0128 0.1131 27 no Study_no
sigma^2.3 0.0146 0.1207 105 no es_ID
Test for Residual Heterogeneity:
QE(df = 92) = 249.0711, p-val < .0001
Test of Moderators (coefficients 2:13):
QM(df = 12) = 23.0733, p-val = 0.0271
Model Results:
estimate se zval pval
intrcpt -0.0395 0.1903 -0.2077 0.8354
colour_typemelanin-based 0.2457 0.1829 1.3428 0.1793
colour_typestructural 0.3547 0.0930 3.8125 0.0001
pollution_typepersistent_organic_pollutants 0.1029 0.0868 1.1860 0.2356
pollution_typeurbanisation 0.0235 0.0759 0.3095 0.7569
sexM -0.0255 0.1305 -0.1952 0.8452
sexM/F -0.1149 0.1532 -0.7504 0.4530
ageJUV 0.0009 0.0845 0.0107 0.9915
ageMIXED 0.0742 0.1491 0.4974 0.6189
measured_partfeathers 0.0352 0.0990 0.3558 0.7220
study_typeO 0.0838 0.1017 0.8239 0.4100
raw_or_modelraw 0.0479 0.0791 0.6059 0.5446
methodspectro -0.1659 0.1048 -1.5836 0.1133
ci.lb ci.ub
intrcpt -0.4124 0.3334
colour_typemelanin-based -0.1129 0.6042
colour_typestructural 0.1724 0.5370 ***
pollution_typepersistent_organic_pollutants -0.0671 0.2729
pollution_typeurbanisation -0.1252 0.1722
sexM -0.2813 0.2304
sexM/F -0.4151 0.1853
ageJUV -0.1647 0.1665
ageMIXED -0.2181 0.3664
measured_partfeathers -0.1589 0.2294
study_typeO -0.1156 0.2832
raw_or_modelraw -0.1071 0.2029
methodspectro -0.3712 0.0394
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1brightness <- subset(mydata, HSB == "brightness")
# summary(brightness)
M2.3<- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+colour_type:pollution_type+sex+age+measured_part+ study_type +raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = brightness)Warning: Redundant predictors dropped from the model.summary(M2.3)# interaction significant
Multivariate Meta-Analysis Model (k = 96; method: REML)
logLik Deviance AIC BIC AICc
13.4732 -26.9463 11.0537 56.3122 23.7203
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0229 0.1514 13 no tip_label
sigma^2.2 0.0750 0.2739 17 no Study_no
sigma^2.3 0.0030 0.0552 95 no es_ID
Test for Residual Heterogeneity:
QE(df = 80) = 126.9029, p-val = 0.0007
Test of Moderators (coefficients 2:16):
QM(df = 15) = 25.3802, p-val = 0.0451
Model Results:
estimate
intrcpt -0.0003
colour_typemelanin-based 0.1185
colour_typestructural -0.0958
pollution_typepersistent_organic_pollutants 0.2689
pollution_typeurbanisation 0.1515
sexM -0.1778
sexM/F -0.0422
ageJUV -0.1763
ageMIXED 0.0437
measured_partfeathers -0.0597
study_typeO -0.2047
raw_or_modelraw 0.0890
methodspectro 0.2689
colour_typemelanin-based:pollution_typepersistent_organic_pollutants -0.7469
colour_typemelanin-based:pollution_typeurbanisation -0.0404
colour_typestructural:pollution_typeurbanisation -0.0571
se
intrcpt 0.6445
colour_typemelanin-based 0.0739
colour_typestructural 0.1126
pollution_typepersistent_organic_pollutants 0.0920
pollution_typeurbanisation 0.3675
sexM 0.1153
sexM/F 0.1883
ageJUV 0.2128
ageMIXED 0.3390
measured_partfeathers 0.0837
study_typeO 0.3673
raw_or_modelraw 0.3618
methodspectro 0.4400
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.3892
colour_typemelanin-based:pollution_typeurbanisation 0.6103
colour_typestructural:pollution_typeurbanisation 0.6024
zval
intrcpt -0.0004
colour_typemelanin-based 1.6042
colour_typestructural -0.8509
pollution_typepersistent_organic_pollutants 2.9230
pollution_typeurbanisation 0.4122
sexM -1.5415
sexM/F -0.2241
ageJUV -0.8288
ageMIXED 0.1290
measured_partfeathers -0.7124
study_typeO -0.5574
raw_or_modelraw 0.2460
methodspectro 0.6112
colour_typemelanin-based:pollution_typepersistent_organic_pollutants -1.9193
colour_typemelanin-based:pollution_typeurbanisation -0.0661
colour_typestructural:pollution_typeurbanisation -0.0947
pval
intrcpt 0.9997
colour_typemelanin-based 0.1087
colour_typestructural 0.3948
pollution_typepersistent_organic_pollutants 0.0035
pollution_typeurbanisation 0.6802
sexM 0.1232
sexM/F 0.8227
ageJUV 0.4072
ageMIXED 0.8973
measured_partfeathers 0.4762
study_typeO 0.5773
raw_or_modelraw 0.8057
methodspectro 0.5411
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.0549
colour_typemelanin-based:pollution_typeurbanisation 0.9473
colour_typestructural:pollution_typeurbanisation 0.9246
ci.lb
intrcpt -1.2634
colour_typemelanin-based -0.0263
colour_typestructural -0.3166
pollution_typepersistent_organic_pollutants 0.0886
pollution_typeurbanisation -0.5687
sexM -0.4039
sexM/F -0.4113
ageJUV -0.5934
ageMIXED -0.6206
measured_partfeathers -0.2238
study_typeO -0.9247
raw_or_modelraw -0.6201
methodspectro -0.5935
colour_typemelanin-based:pollution_typepersistent_organic_pollutants -1.5096
colour_typemelanin-based:pollution_typeurbanisation -1.2365
colour_typestructural:pollution_typeurbanisation -1.2378
ci.ub
intrcpt 1.2629
colour_typemelanin-based 0.2634
colour_typestructural 0.1249
pollution_typepersistent_organic_pollutants 0.4492
pollution_typeurbanisation 0.8717
sexM 0.0483
sexM/F 0.3269
ageJUV 0.2407
ageMIXED 0.7081
measured_partfeathers 0.1045
study_typeO 0.5152
raw_or_modelraw 0.7982
methodspectro 1.1313
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.0158
colour_typemelanin-based:pollution_typeurbanisation 1.1557
colour_typestructural:pollution_typeurbanisation 1.1237
intrcpt
colour_typemelanin-based
colour_typestructural
pollution_typepersistent_organic_pollutants **
pollution_typeurbanisation
sexM
sexM/F
ageJUV
ageMIXED
measured_partfeathers
study_typeO
raw_or_modelraw
methodspectro
colour_typemelanin-based:pollution_typepersistent_organic_pollutants .
colour_typemelanin-based:pollution_typeurbanisation
colour_typestructural:pollution_typeurbanisation
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1other <- subset(mydata, HSB == "other")
# summary(other)
M2.4<- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+colour_type:pollution_type
+sex+age+measured_part+ study_type +raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = other)Warning: Redundant predictors dropped from the model.summary(M2.4)# interaction not significant
Multivariate Meta-Analysis Model (k = 125; method: REML)
logLik Deviance AIC BIC AICc
-8.0858 16.1717 60.1717 118.7673 72.3644
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 20 no tip_label
sigma^2.2 0.0232 0.1523 32 no Study_no
sigma^2.3 0.0217 0.1473 125 no es_ID
Test for Residual Heterogeneity:
QE(df = 106) = 214.7590, p-val < .0001
Test of Moderators (coefficients 2:19):
QM(df = 18) = 43.4694, p-val = 0.0007
Model Results:
estimate
intrcpt -0.4828
colour_typemelanin-based 0.4200
colour_typestructural 0.4827
pollution_typeother -0.0760
pollution_typepersistent_organic_pollutants -0.2350
pollution_typeurbanisation 0.2683
sexM -0.0261
sexM/F -0.0243
ageJUV 0.1667
ageMIXED 0.0706
measured_partfeathers -0.2260
study_typeO 0.1839
raw_or_modelraw 0.1229
methodphoto 0.2194
methodspectro 0.2333
colour_typestructural:pollution_typeother -0.1422
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.3514
colour_typestructural:pollution_typepersistent_organic_pollutants 0.3385
colour_typemelanin-based:pollution_typeurbanisation -0.3407
se
intrcpt 0.1553
colour_typemelanin-based 0.1810
colour_typestructural 0.1943
pollution_typeother 0.2641
pollution_typepersistent_organic_pollutants 0.1630
pollution_typeurbanisation 0.1819
sexM 0.0848
sexM/F 0.1124
ageJUV 0.1151
ageMIXED 0.1522
measured_partfeathers 0.1429
study_typeO 0.1035
raw_or_modelraw 0.0914
methodphoto 0.0944
methodspectro 0.1049
colour_typestructural:pollution_typeother 0.3263
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.2545
colour_typestructural:pollution_typepersistent_organic_pollutants 0.3187
colour_typemelanin-based:pollution_typeurbanisation 0.2079
zval
intrcpt -3.1081
colour_typemelanin-based 2.3205
colour_typestructural 2.4850
pollution_typeother -0.2876
pollution_typepersistent_organic_pollutants -1.4417
pollution_typeurbanisation 1.4750
sexM -0.3079
sexM/F -0.2163
ageJUV 1.4481
ageMIXED 0.4641
measured_partfeathers -1.5813
study_typeO 1.7772
raw_or_modelraw 1.3444
methodphoto 2.3251
methodspectro 2.2233
colour_typestructural:pollution_typeother -0.4357
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 1.3809
colour_typestructural:pollution_typepersistent_organic_pollutants 1.0624
colour_typemelanin-based:pollution_typeurbanisation -1.6387
pval
intrcpt 0.0019
colour_typemelanin-based 0.0203
colour_typestructural 0.0130
pollution_typeother 0.7737
pollution_typepersistent_organic_pollutants 0.1494
pollution_typeurbanisation 0.1402
sexM 0.7581
sexM/F 0.8288
ageJUV 0.1476
ageMIXED 0.6425
measured_partfeathers 0.1138
study_typeO 0.0755
raw_or_modelraw 0.1788
methodphoto 0.0201
methodspectro 0.0262
colour_typestructural:pollution_typeother 0.6631
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.1673
colour_typestructural:pollution_typepersistent_organic_pollutants 0.2881
colour_typemelanin-based:pollution_typeurbanisation 0.1013
ci.lb
intrcpt -0.7872
colour_typemelanin-based 0.0652
colour_typestructural 0.1020
pollution_typeother -0.5937
pollution_typepersistent_organic_pollutants -0.5545
pollution_typeurbanisation -0.0882
sexM -0.1924
sexM/F -0.2446
ageJUV -0.0589
ageMIXED -0.2276
measured_partfeathers -0.5061
study_typeO -0.0189
raw_or_modelraw -0.0563
methodphoto 0.0345
methodspectro 0.0276
colour_typestructural:pollution_typeother -0.7818
colour_typemelanin-based:pollution_typepersistent_organic_pollutants -0.1473
colour_typestructural:pollution_typepersistent_organic_pollutants -0.2860
colour_typemelanin-based:pollution_typeurbanisation -0.7481
ci.ub
intrcpt -0.1783
colour_typemelanin-based 0.7747
colour_typestructural 0.8635
pollution_typeother 0.4418
pollution_typepersistent_organic_pollutants 0.0845
pollution_typeurbanisation 0.6248
sexM 0.1401
sexM/F 0.1960
ageJUV 0.3923
ageMIXED 0.3689
measured_partfeathers 0.0541
study_typeO 0.3867
raw_or_modelraw 0.3021
methodphoto 0.4044
methodspectro 0.4389
colour_typestructural:pollution_typeother 0.4974
colour_typemelanin-based:pollution_typepersistent_organic_pollutants 0.8501
colour_typestructural:pollution_typepersistent_organic_pollutants 0.9631
colour_typemelanin-based:pollution_typeurbanisation 0.0668
intrcpt **
colour_typemelanin-based *
colour_typestructural *
pollution_typeother
pollution_typepersistent_organic_pollutants
pollution_typeurbanisation
sexM
sexM/F
ageJUV
ageMIXED
measured_partfeathers
study_typeO .
raw_or_modelraw
methodphoto *
methodspectro *
colour_typestructural:pollution_typeother
colour_typemelanin-based:pollution_typepersistent_organic_pollutants
colour_typestructural:pollution_typepersistent_organic_pollutants
colour_typemelanin-based:pollution_typeurbanisation
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M2.4<- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~colour_type+pollution_type+sex+age+measured_part+study_type
+raw_or_model+ method,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = other)
summary(M2.4)
Multivariate Meta-Analysis Model (k = 125; method: REML)
logLik Deviance AIC BIC AICc
-11.0174 22.0347 58.0347 106.6434 65.5512
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0001 20 no tip_label
sigma^2.2 0.0388 0.1970 32 no Study_no
sigma^2.3 0.0209 0.1447 125 no es_ID
Test for Residual Heterogeneity:
QE(df = 110) = 275.3088, p-val < .0001
Test of Moderators (coefficients 2:15):
QM(df = 14) = 30.7969, p-val = 0.0059
Model Results:
estimate se zval pval
intrcpt -0.5089 0.1546 -3.2912 0.0010
colour_typemelanin-based 0.3030 0.1535 1.9741 0.0484
colour_typestructural 0.3601 0.1696 2.1233 0.0337
pollution_typeother -0.1289 0.2161 -0.5965 0.5508
pollution_typepersistent_organic_pollutants -0.1240 0.1294 -0.9584 0.3378
pollution_typeurbanisation 0.0495 0.1215 0.4069 0.6841
sexM -0.0341 0.0837 -0.4074 0.6837
sexM/F -0.0051 0.1196 -0.0425 0.9661
ageJUV 0.2139 0.1221 1.7513 0.0799
ageMIXED -0.0121 0.1492 -0.0812 0.9353
measured_partfeathers -0.1268 0.1501 -0.8448 0.3982
study_typeO 0.2114 0.1007 2.0994 0.0358
raw_or_modelraw 0.1517 0.0948 1.6006 0.1095
methodphoto 0.2166 0.0997 2.1726 0.0298
methodspectro 0.2657 0.1164 2.2814 0.0225
ci.lb ci.ub
intrcpt -0.8119 -0.2058 ***
colour_typemelanin-based 0.0022 0.6038 *
colour_typestructural 0.0277 0.6924 *
pollution_typeother -0.5524 0.2946
pollution_typepersistent_organic_pollutants -0.3777 0.1296
pollution_typeurbanisation -0.1888 0.2877
sexM -0.1982 0.1300
sexM/F -0.2395 0.2293
ageJUV -0.0255 0.4533 .
ageMIXED -0.3046 0.2804
measured_partfeathers -0.4210 0.1674
study_typeO 0.0140 0.4088 *
raw_or_modelraw -0.0341 0.3376
methodphoto 0.0212 0.4119 *
methodspectro 0.0374 0.4939 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1carotenoids <- subset(mydata, colour_type == "carotenoid-based")
M3.0 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~ pollution_type + measured_part:carotenoids_type+HSB+sex+age +measured_part
+study_type + raw_or_model+carotenoids_type,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = carotenoids)Warning: 29 rows with NAs omitted from model fitting.Warning: Redundant predictors dropped from the model.summary(M3.0) # interaction not significant
Multivariate Meta-Analysis Model (k = 256; method: REML)
logLik Deviance AIC BIC AICc
17.4166 -34.8332 1.1668 63.8931 4.2479
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0175 0.1323 8 no tip_label
sigma^2.2 0.0308 0.1755 34 no Study_no
sigma^2.3 0.0133 0.1153 243 no es_ID
Test for Residual Heterogeneity:
QE(df = 241) = 620.8080, p-val < .0001
Test of Moderators (coefficients 2:15):
QM(df = 14) = 28.3620, p-val = 0.0127
Model Results:
estimate se zval
intrcpt -0.0438 0.1354 -0.3232
pollution_typepersistent_organic_pollutants 0.1272 0.0562 2.2635
pollution_typeurbanisation -0.0004 0.0695 -0.0051
HSBhue -0.1203 0.0363 -3.3153
HSBother -0.0327 0.0938 -0.3486
HSBsaturation -0.1376 0.0360 -3.8164
sexM -0.0640 0.0632 -1.0120
sexM/F 0.0406 0.0782 0.5196
ageJUV -0.0034 0.0897 -0.0380
ageMIXED 0.1243 0.1993 0.6236
measured_partfeathers -0.0189 0.0853 -0.2215
study_typeO 0.0365 0.1108 0.3293
raw_or_modelraw -0.0245 0.0731 -0.3350
carotenoids_typedietary -0.0742 0.0446 -1.6646
measured_partfeathers:carotenoids_typedietary -0.0079 0.1873 -0.0424
pval ci.lb ci.ub
intrcpt 0.7466 -0.3091 0.2216
pollution_typepersistent_organic_pollutants 0.0236 0.0171 0.2373 *
pollution_typeurbanisation 0.9959 -0.1366 0.1359
HSBhue 0.0009 -0.1915 -0.0492 ***
HSBother 0.7274 -0.2165 0.1511
HSBsaturation 0.0001 -0.2082 -0.0669 ***
sexM 0.3115 -0.1879 0.0599
sexM/F 0.6033 -0.1127 0.1940
ageJUV 0.9697 -0.1792 0.1724
ageMIXED 0.5329 -0.2663 0.5149
measured_partfeathers 0.8247 -0.1861 0.1483
study_typeO 0.7419 -0.1808 0.2538
raw_or_modelraw 0.7376 -0.1677 0.1187
carotenoids_typedietary 0.0960 -0.1616 0.0132 .
measured_partfeathers:carotenoids_typedietary 0.9662 -0.3751 0.3592
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M3.0 <- rma.mv(yi = ES_biol, V = Z_var,
method = "REML",
mods = ~ pollution_type +HSB+sex+age +measured_part
+study_type + raw_or_model+carotenoids_type,
random = list(~1|tip_label,
~1|Study_no,
~1|es_ID),
control=list(optimizer="optim",optmethod="Nelder-Mead"),
data = carotenoids)Warning: 29 rows with NAs omitted from model fitting.
Warning: Redundant predictors dropped from the model.summary(M3.0)
Multivariate Meta-Analysis Model (k = 256; method: REML)
logLik Deviance AIC BIC AICc
17.2500 -34.5000 -0.5000 58.8120 2.2322
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0087 0.0935 8 no tip_label
sigma^2.2 0.0315 0.1776 34 no Study_no
sigma^2.3 0.0133 0.1152 243 no es_ID
Test for Residual Heterogeneity:
QE(df = 242) = 621.0423, p-val < .0001
Test of Moderators (coefficients 2:14):
QM(df = 13) = 28.6042, p-val = 0.0074
Model Results:
estimate se zval pval
intrcpt -0.0585 0.1282 -0.4566 0.6480
pollution_typepersistent_organic_pollutants 0.1270 0.0555 2.2884 0.0221
pollution_typeurbanisation -0.0021 0.0685 -0.0307 0.9755
HSBhue -0.1210 0.0363 -3.3378 0.0008
HSBother -0.0363 0.0927 -0.3918 0.6952
HSBsaturation -0.1375 0.0360 -3.8171 0.0001
sexM -0.0625 0.0628 -0.9956 0.3194
sexM/F 0.0380 0.0773 0.4914 0.6232
ageJUV 0.0013 0.0873 0.0150 0.9880
ageMIXED 0.1207 0.1987 0.6076 0.5434
measured_partfeathers -0.0250 0.0773 -0.3231 0.7466
study_typeO 0.0547 0.1060 0.5162 0.6057
raw_or_modelraw -0.0288 0.0729 -0.3957 0.6923
carotenoids_typedietary -0.0721 0.0433 -1.6679 0.0953
ci.lb ci.ub
intrcpt -0.3098 0.1927
pollution_typepersistent_organic_pollutants 0.0182 0.2357 *
pollution_typeurbanisation -0.1364 0.1322
HSBhue -0.1921 -0.0500 ***
HSBother -0.2179 0.1453
HSBsaturation -0.2081 -0.0669 ***
sexM -0.1855 0.0605
sexM/F -0.1135 0.1894
ageJUV -0.1697 0.1723
ageMIXED -0.2687 0.5101
measured_partfeathers -0.1764 0.1265
study_typeO -0.1530 0.2624
raw_or_modelraw -0.1717 0.1140
carotenoids_typedietary -0.1569 0.0126 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M4.0 <- run.model(mydata, ~sqrt(Z_var))
summary(M4.0)
Multivariate Meta-Analysis Model (k = 421; method: REML)
logLik Deviance AIC BIC AICc
-35.9087 71.8173 83.8173 108.0445 84.0212
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0142 0.1191 25 no tip_label
sigma^2.2 0.0060 0.0773 59 no Study_no
sigma^2.3 0.0343 0.1851 402 no es_ID
sigma^2.4 0.0000 0.0001 25 no research_group
Test for Residual Heterogeneity:
QE(df = 419) = 1832.0103, p-val < .0001
Test of Moderators (coefficient 2):
QM(df = 1) = 0.1482, p-val = 0.7002
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.0397 0.0559 -0.7106 0.4773 -0.1492 0.0698
sqrt(Z_var) -0.1206 0.3131 -0.3850 0.7002 -0.7343 0.4932
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1M5.0 <- run.model(mydata, ~date)
summary(M5.0)
Multivariate Meta-Analysis Model (k = 421; method: REML)
logLik Deviance AIC BIC AICc
-31.4363 62.8725 74.8725 99.0997 75.0764
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0127 0.1127 25 no tip_label
sigma^2.2 0.0000 0.0000 59 no Study_no
sigma^2.3 0.0344 0.1855 402 no es_ID
sigma^2.4 0.0000 0.0001 25 no research_group
Test for Residual Heterogeneity:
QE(df = 419) = 1809.3232, p-val < .0001
Test of Moderators (coefficient 2):
QM(df = 1) = 11.9257, p-val = 0.0006
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -24.9964 7.2242 -3.4601 0.0005 -39.1556 -10.8372 ***
date 0.0124 0.0036 3.4534 0.0006 0.0054 0.0194 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1pred_year_model <- predict.rma(M5.0)
plot_continuous(mydata, M5.0, mydata$date, "Publication year")Warning: The `size` argument of `element_rect()` is deprecated as of ggplot2 3.4.0.
ℹ Please use the `linewidth` argument instead.
pred_Egger_reg <- predict.rma(M4.0)
plot_continuous(mydata, M4.0, sqrt(mydata$Z_var), "Standard error")
sessionInfo()R version 4.3.1 (2023-06-16)
Platform: x86_64-apple-darwin20 (64-bit)
Running under: macOS Sonoma 14.1
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: Europe/Warsaw
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] metaAidR_0.0.0.9000 orchaRd_2.0 emmeans_1.10.0
[4] R.rsp_0.45.0 ape_5.7-1 lubridate_1.9.3
[7] forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
[10] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1
[13] tibble_3.2.1 tidyverse_2.0.0 patchwork_1.1.3
[16] devtools_2.4.5 usethis_2.2.2 metafor_4.4-0
[19] numDeriv_2016.8-1.1 metadat_1.2-0 Matrix_1.6-1
[22] packcircles_0.3.6 ggpubr_0.6.0 ggplot2_3.4.4
[25] here_1.0.1
loaded via a namespace (and not attached):
[1] remotes_2.4.2.1 sandwich_3.1-0 rlang_1.1.3 magrittr_2.0.3
[5] multcomp_1.4-25 compiler_4.3.1 callr_3.7.3 vctrs_0.6.5
[9] profvis_0.3.8 pkgconfig_2.0.3 crayon_1.5.2 fastmap_1.1.1
[13] backports_1.4.1 ellipsis_0.3.2 labeling_0.4.3 utf8_1.2.4
[17] promises_1.2.1 rmarkdown_2.25 sessioninfo_1.2.2 tzdb_0.4.0
[21] ggbeeswarm_0.7.2 ps_1.7.6 xfun_0.42 cachem_1.0.8
[25] jsonlite_1.8.8 later_1.3.1 broom_1.0.5 parallel_4.3.1
[29] prettyunits_1.2.0 R6_2.5.1 stringi_1.8.3 car_3.1-2
[33] pkgload_1.3.2.1 estimability_1.4.1 Rcpp_1.0.12 knitr_1.45
[37] zoo_1.8-12 pacman_0.5.1 R.utils_2.12.2 splines_4.3.1
[41] httpuv_1.6.11 R.cache_0.16.0 timechange_0.3.0 tidyselect_1.2.0
[45] abind_1.4-5 yaml_2.3.8 codetools_0.2-19 miniUI_0.1.1.1
[49] curl_5.2.0 processx_3.8.3 pkgbuild_1.4.2 lattice_0.21-8
[53] shiny_1.7.5 withr_3.0.0 coda_0.19-4.1 evaluate_0.23
[57] desc_1.4.2 survival_3.5-5 urlchecker_1.0.1 pillar_1.9.0
[61] carData_3.0-5 generics_0.1.3 rprojroot_2.0.3 mathjaxr_1.6-0
[65] hms_1.1.3 munsell_0.5.0 scales_1.3.0 xtable_1.8-4
[69] glue_1.7.0 tools_4.3.1 ggsignif_0.6.4 fs_1.6.3
[73] mvtnorm_1.2-4 grid_4.3.1 colorspace_2.1-0 nlme_3.1-162
[77] beeswarm_0.4.0 vipor_0.4.7 latex2exp_0.9.6 cli_3.6.2
[81] fansi_1.0.6 gtable_0.3.4 R.methodsS3_1.8.2 rstatix_0.7.2
[85] digest_0.6.34 TH.data_1.1-2 farver_2.1.1 htmlwidgets_1.6.2
[89] memoise_2.0.1 htmltools_0.5.7 R.oo_1.25.0 lifecycle_1.0.4
[93] mime_0.12 MASS_7.3-60