library(car)
library(dae)
library(dplyr)
library(emmeans)
library(ggplot2)
library(lmerTest)
library(magrittr)
library(predictmeans)
data(DataExam6.2)
DataExam6.2.1 <-
DataExam6.2 %>%
filter(Province == "PNG")
# Pg. 94
fm6.3 <-
lm(
formula = Dbh.mean ~ Replication + Family
, data = DataExam6.2.1
)
b <- anova(fm6.3)
HM <- function(x){length(x)/sum(1/x)}
w <- HM(DataExam6.2.1$Dbh.count)
S2 <- b[["Mean Sq"]][length(b[["Mean Sq"]])]
Sigma2t <- mean(DataExam6.2.1$Dbh.variance)
sigma2m <- S2-(Sigma2t/w)
fm6.3.1 <-
lmer(
formula = Dbh.mean ~ 1 + Replication + (1|Family)
, data = DataExam6.2.1
, REML = TRUE
)
# Pg. 104
# summary(fm6.3.1)
varcomp(fm6.3.1)
vcov SE 2.5 % 97.5 %
Family.(Intercept) 0.2584 0.1286 0.0538 0.5767
residual 1.1667 0.1506 0.8954 1.4774
sigma2f <- 0.2584
h2 <- (sigma2f/(0.3))/(Sigma2t + sigma2m + sigma2f)
cbind(hmean = w, Sigma2t, sigma2m, sigma2f, h2)
hmean Sigma2t sigma2m sigma2f h2
[1,] 4.408602 3.920732 0.2773606 0.2584 0.1932761
fm6.4 <-
lm(
formula = Dbh.mean ~ Replication+Family
, data = DataExam6.2
)
b <- anova(fm6.4)
HM <- function(x){length(x)/sum(1/x)}
w <- HM(DataExam6.2$Dbh.count)
S2 <- b[["Mean Sq"]][length(b[["Mean Sq"]])]
Sigma2t <- mean(DataExam6.2$Dbh.variance)
sigma2m <- S2-(Sigma2t/w)
fm6.4.1 <-
lmer(
formula = Dbh.mean ~ 1 + Replication + Province + (1|Family)
, data = DataExam6.2
, REML = TRUE
)
# Pg. 107
varcomp(fm6.4.1)
vcov SE 2.5 % 97.5 %
Family.(Intercept) 0.3514 0.1358 0.1203 0.6361
residual 1.0951 0.1304 0.8584 1.3634
sigma2f <- 0.3514
h2 <- (sigma2f/(0.3))/(Sigma2t+sigma2m+sigma2f)
cbind(hmean = w, Sigma2t, sigma2m, sigma2f, h2)
hmean Sigma2t sigma2m sigma2f h2
[1,] 4.451314 3.860156 0.227873 0.3514 0.2638477
fm6.7.1 <-
lmer(
formula = Dbh.mean ~ 1+Replication+(1|Family)
, data = DataExam6.2.1
, REML = TRUE
)
# Pg. 116
varcomp(fm6.7.1)
vcov SE 2.5 % 97.5 %
Family.(Intercept) 0.2584 0.1286 0.0538 0.5767
residual 1.1667 0.1506 0.8954 1.4774
sigma2f[1] <- 0.2584
fm6.7.2<-
lmer(
formula = Ht.mean ~ 1 + Replication + (1|Family)
, data = DataExam6.2.1
, REML = TRUE
)
# Pg. 116
varcomp(fm6.7.2)
vcov SE 2.5 % 97.5 %
Family.(Intercept) 0.2711 0.1243 0.0743 0.5794
residual 1.0549 0.1362 0.8097 1.3359
sigma2f[2] <- 0.2711
fm6.7.3 <-
lmer(
formula = Sum.means ~ 1 + Replication + (1|Family)
, data = DataExam6.2.1
, REML = TRUE
, control = lmerControl()
)
# Pg. 116
varcomp(fm6.7.3)
vcov SE 2.5 % 97.5 %
Family.(Intercept) 0.8729 0.3907 0.2553 1.8421
residual 3.2428 0.4186 2.4888 4.1063
sigma2f[3] <- 0.873
sigma2xy <- 0.5*(sigma2f[3]-sigma2f[1]-sigma2f[2])
GenCorr <- sigma2xy/sqrt(sigma2f[1]*sigma2f[2])
cbind(
S2x = sigma2f[1]
, S2y = sigma2f[2]
, S2.x.plus.y = sigma2f[3]
, GenCorr
)
S2x S2y S2.x.plus.y GenCorr
[1,] 0.2584 0.2711 0.873 0.64891196 Variance Components and Genetics Concepts
6.1 Example 6.2 (Pg. 90)
Example 6.2 (Pg. 90)
A progeny trial of Acacia mangium was planted at Segaluid, Sabah, by the Sabah Forest Research Centre in 1994. The trial was designed to test 48 open-pollinated families collected from natural provenances in Papua New Guinea (PNG, 41 families) and far north Queensland (five families) and two families of the land race that had developed in Sabah after introduction of A. mangium in the 1960s. Based on the results of many previous trials (Harwood & Williams 1992), it was expected that the Sabah and Queensland families would perform more poorly than those from PNG. The trial was set out as an RCB design with four replicates each containing 48 five-tree plots. Spacing was 3m \(\times\) 3m between trees, and an external perimeter row surrounded the trial. Diameter at breast height (dbh) and height (ht) measurements were taken in 1997, 36 months after planting.