Exam6.2 {eda4treeR}

Example 6.2 from Experimental Design and Analysis for Tree Improvement

Description

Exam 6.2 Dbh mean, Dbh varince and number of trees per plot from 3 provinces("PNG","Sabah","Queensland") with 4 replications of 48 families.

Author(s)

1. Muhammad Yaseen ([e-mail])

2. Sami Ullah ([e-mail])

References

1. E.R. Williams, C.E. Harwood and A.C. Matheson (2023). Experimental Design and Analysis for Tree Improvement. CSIRO Publishing (https://www.publish.csiro.au/book/3145/).

See Also

DataExam6.2

Examples

library(car)
library(dae)
library(dplyr)
library(emmeans)
library(ggplot2)
library(lmerTest)
library(magrittr)
library(predictmeans)
library(supernova)

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)
sigma2f <- 0.2584
h2 <- (sigma2f/(0.3))/(Sigma2t + sigma2m + sigma2f)
cbind(hmean = w, Sigma2t, sigma2m, sigma2f, h2)

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)
sigma2f <- 0.3514
h2 <- (sigma2f/(0.3))/(Sigma2t+sigma2m+sigma2f)
cbind(hmean = w, Sigma2t, sigma2m, sigma2f, h2)

fm6.7.1 <-
  lmer(
      formula   = Dbh.mean ~ 1+Replication+(1|Family)
    , data      = DataExam6.2.1
    , REML      = TRUE
    )

# Pg. 116
varcomp(fm6.7.1)
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)
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)
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)