Bayesian Estimation of Genotype by Environment Interaction Model

Bayesian estimation method of linear–bilinear models for Genotype by Environment Interaction Model

# S3 method for default
bayes_ammi(.data, .y, .gen, .env, .rep, .nIter)

Arguments

.data	data.frame
.y	Response Variable
.gen	Genotypes Factor
.env	Environment Factor
.rep	Replication Factor
.nIter	Number of Iterations

Value

Genotype by Environment Interaction Model

References

Perez-Elizalde, S., Jarquin, D., and Crossa, J. (2011) A General Bayesian Estimation Method of Linear–Bilinear Models Applied to Plant Breeding Trials With Genotype × Environment Interaction. Journal of Agricultural, Biological, and Environmental Statistics, 17, 15–37. (doi:10.1007/s13253-011-0063-9)

Examples


library(baystability)
data(cultivo2008)
fm1 <-
   ge_ammi(
      .data  = cultivo2008
     , .y    = y
     , .gen  = entry
     , .env  = site
     , .rep  = rep
     )

r0 <- fm1$g
c0 <- fm1$e
n0 <- fm1$Rep
k0 <- fm1$k

mu0      <- fm1$mu
sigma20  <- fm1$sigma2
tau0     <- fm1$tau
tao0     <- fm1$tao
delta0   <- fm1$delta
lambdas0 <- fm1$lambdas
alphas0  <- fm1$alphas
gammas0  <- fm1$gammas

ge_means0 <- fm1$ge_means$ge_means

data(cultivo2008)

fm2 <-
 ge_ammi(
   .data = cultivo2009
   , .y    = y
   , .gen  = entry
   , .env  = site
   , .rep  = rep
  )

k        <- fm2$k
alphasa  <- fm2$alphas
gammasa  <- fm2$gammas

alphas1  <- tibble::as_tibble(fm2$alphas)
gammas1  <- tibble::as_tibble(fm2$gammas)



# Biplots OLS
library(ggplot2)
    BiplotOLS1 <-
      ggplot(data = alphas1, mapping = aes(x = V1, y = V2)) +
      geom_point() +
      geom_hline(yintercept = 0) +
      geom_vline(xintercept = 0) +
      geom_text(aes(label = 1:nrow(alphas1)), vjust = "inward", hjust = "inward") +
      scale_x_continuous(
               limits = c(-max(abs(c(range(alphas1[, 1:2]))))
                         , max(abs(c(range(alphas1[, 1:2])))))) +
      scale_y_continuous(
               limits = c(-max(abs(c(range(alphas1[, 1:2]))))
                         , max(abs(c(range(alphas1[, 1:2])))))) +
      labs(title = "OLS", x = expression(u[1]), y = expression(u[2])) +
      theme_bw() +
      theme(plot.title = element_text(hjust = 0.5))
      print(BiplotOLS1)


    BiplotOLS2 <-
      ggplot(data = gammas1, mapping = aes(x = V1, y = V2)) +
      geom_point() +
      geom_hline(yintercept = 0) +
      geom_vline(xintercept = 0) +
      geom_text(aes(label = 1:nrow(gammas1)), vjust = "inward", hjust = "inward") +
      scale_x_continuous(
                limits = c(-max(abs(c(range(gammas1[, 1:2]))))
                         , max(abs(c(range(gammas1[, 1:2])))))) +
      scale_y_continuous(
                limits = c(-max(abs(c(range(gammas1[, 1:2]))))
                          , max(abs(c(range(gammas1[, 1:2])))))) +
      labs(title = "OLS", x = expression(v[1]), y = expression(v[2])) +
      theme_bw() +
      theme(plot.title = element_text(hjust = 0.5))
      print(BiplotOLS2)


    BiplotOLS3 <-
      ggplot(data = alphas1, mapping = aes(x = V1, y = V2)) +
      geom_point() +
      geom_hline(yintercept = 0) +
      geom_vline(xintercept = 0) +
      geom_text(aes(label = 1:nrow(alphas1)), vjust = "inward", hjust = "inward") +
      geom_point(data = gammas1, mapping = aes(x = V1, y = V2)) +
      geom_segment(data = gammas1, aes(x = 0, y = 0, xend = V1, yend = V2),
                    arrow = arrow(length = unit(0.2, "cm")), alpha = 0.75, color = "red") +
      geom_text(data = gammas1,
              aes(x = V1, y = V2, label = paste0("E", 1:nrow(gammasa)))
             , vjust = "inward", hjust = "inward") +
      scale_x_continuous(
              limits = c(-max(abs(c(range(alphas1[, 1:2], gammas1[, 1:2]))))
                        , max(abs(c(range(alphas1[, 1:2], gammas1[, 1:2])))))) +
      scale_y_continuous(
              limits = c(-max(abs(c(range(alphas1[, 1:2], gammas1[, 1:2]))))
                       , max(abs(c(range(alphas1[, 1:2], gammas1[, 1:2])))))) +
      labs(title = "OLS", x = expression(PC[1]), y = expression(PC[2])) +
      theme_bw() +
      theme(plot.title = element_text(hjust = 0.5))
      print(BiplotOLS3)


data(cultivo2009)
fm3 <-
  bayes_ammi(
    .data = cultivo2009
    , .y     = y
    , .gen   = entry
    , .env   = site
    , .rep   = rep
    , .nIter = 200
  )
#> Error in bayes_ammi.default(.data = cultivo2009, .y = y, .gen = entry,     .env = site, .rep = rep, .nIter = 200): object 'n0' not found

 Mean_Alphas <- fm3$Mean_Alphas
#> Error in eval(expr, envir, enclos): object 'fm3' not found
 Mean_Gammas <- fm3$Mean_Gammas
#> Error in eval(expr, envir, enclos): object 'fm3' not found


# Biplots Bayesian
BiplotBayes1 <-
  ggplot(data = Mean_Alphas, mapping = aes(x = V1, y = V2)) +
  geom_point() +
  geom_hline(yintercept = 0) +
  geom_vline(xintercept = 0) +
  geom_text(aes(label = 1:nrow(Mean_Alphas)),
             vjust = "inward"
           , hjust = "inward") +
  scale_x_continuous(
     limits = c(-max(abs(c(range(Mean_Alphas[, 1:2]))))
               , max(abs(c(range(Mean_Alphas[, 1:2])))))) +
  scale_y_continuous(
      limits = c(-max(abs(c(range(Mean_Alphas[, 1:2]))))
                , max(abs(c(range(Mean_Alphas[, 1:2])))))) +
  labs(title = "Bayes", x = expression(u[1]), y = expression(u[2])) +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))
#> Error in ggplot(data = Mean_Alphas, mapping = aes(x = V1, y = V2)): object 'Mean_Alphas' not found

print(BiplotBayes1)
#> Error in print(BiplotBayes1): object 'BiplotBayes1' not found


BiplotBayes2 <-
  ggplot(data = Mean_Gammas, mapping = aes(x = V1, y = V2)) +
  geom_point() +
  geom_hline(yintercept = 0) +
  geom_vline(xintercept = 0) +
  geom_text(aes(label = 1:nrow(Mean_Gammas)), vjust = "inward", hjust = "inward") +
  scale_x_continuous(
            limits = c(-max(abs(c(range(Mean_Gammas[, 1:2]))))
                      , max(abs(c(range(Mean_Gammas[, 1:2])))))) +
  scale_y_continuous(
            limits = c(-max(abs(c(range(Mean_Gammas[, 1:2]))))
                      , max(abs(c(range(Mean_Gammas[, 1:2])))))) +
  labs(title = "Bayes", x = expression(v[1]), y = expression(v[2])) +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))
#> Error in ggplot(data = Mean_Gammas, mapping = aes(x = V1, y = V2)): object 'Mean_Gammas' not found

print(BiplotBayes2)
#> Error in print(BiplotBayes2): object 'BiplotBayes2' not found


BiplotBayes3 <-
  ggplot(data = Mean_Alphas, mapping = aes(x = V1, y = V2)) +
  geom_point() +
  geom_hline(yintercept = 0) +
  geom_vline(xintercept = 0) +
  geom_text(aes(label = 1:nrow(Mean_Alphas)),
             vjust = "inward", hjust = "inward") +
  geom_point(data = Mean_Gammas, mapping = aes(x = V1, y = V2)) +
  geom_segment(data = Mean_Gammas,
                aes(x = 0, y = 0, xend = V1, yend = V2),
               arrow = arrow(length = unit(0.2, "cm"))
               , alpha = 0.75, color = "red") +
  geom_text(data = Mean_Gammas,
            aes(x = V1, y = V2,
            label = paste0("E", 1:nrow(Mean_Gammas))),
            vjust = "inward", hjust = "inward") +
  scale_x_continuous(
            limits = c(-max(abs(c(range(Mean_Alphas[, 1:2], Mean_Gammas[, 1:2]))))
                      , max(abs(c(range(Mean_Alphas[, 1:2], Mean_Gammas[, 1:2])))))) +
  scale_y_continuous(
           limits = c(-max(abs(c(range(Mean_Alphas[, 1:2], Mean_Gammas[, 1:2]))))
                   , max(abs(c(range(Mean_Alphas[, 1:2], Mean_Gammas[, 1:2])))))) +
  labs(title = "Bayes", x = expression(PC[1]), y = expression(PC[2])) +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))
#> Error in ggplot(data = Mean_Alphas, mapping = aes(x = V1, y = V2)): object 'Mean_Alphas' not found

print(BiplotBayes3)
#> Error in print(BiplotBayes3): object 'BiplotBayes3' not found

Plot1Mu <-
  ggplot(data = fm3$mu1, mapping = aes(x = 1:nrow(fm3$mu1), y = mu)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(mu), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$mu1, mapping = aes(x = 1:nrow(fm3$mu1), y = mu)): object 'fm3' not found
print(Plot1Mu)
#> Error in print(Plot1Mu): object 'Plot1Mu' not found

Plot2Mu <-
  ggplot(data = fm3$mu1, mapping = aes(mu)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(mu)) +
  theme_bw()
#> Error in ggplot(data = fm3$mu1, mapping = aes(mu)): object 'fm3' not found
print(Plot2Mu)
#> Error in print(Plot2Mu): object 'Plot2Mu' not found


Plot1Sigma2 <-
  ggplot(data = fm3$tau1, mapping = aes(x = 1:nrow(fm3$tau1), y = tau)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(sigma^2), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$tau1, mapping = aes(x = 1:nrow(fm3$tau1), y = tau)): object 'fm3' not found
print(Plot1Sigma2)
#> Error in print(Plot1Sigma2): object 'Plot1Sigma2' not found


Plot2Sigma2 <-
  ggplot(data = fm3$tau1, mapping = aes(tau)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(sigma^2)) +
  theme_bw()
#> Error in ggplot(data = fm3$tau1, mapping = aes(tau)): object 'fm3' not found
print(Plot2Sigma2)
#> Error in print(Plot2Sigma2): object 'Plot2Sigma2' not found


# Plot of Alphas
Plot1Alpha1 <-
  ggplot(data = fm3$tao1, mapping = aes(x = 1:nrow(fm3$tao1), y = tao1)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(alpha[1]), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$tao1, mapping = aes(x = 1:nrow(fm3$tao1), y = tao1)): object 'fm3' not found
print(Plot1Alpha1)
#> Error in print(Plot1Alpha1): object 'Plot1Alpha1' not found

Plot2Alpha1 <-
  ggplot(data = fm3$tao1, mapping = aes(tao1)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(alpha[1])) +
  theme_bw()
#> Error in ggplot(data = fm3$tao1, mapping = aes(tao1)): object 'fm3' not found
print(Plot2Alpha1)
#> Error in print(Plot2Alpha1): object 'Plot2Alpha1' not found

Plot1Alpha2 <-
  ggplot(data = fm3$tao1, mapping = aes(x = 1:nrow(fm3$tao1), y = tao2)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(alpha[2]), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$tao1, mapping = aes(x = 1:nrow(fm3$tao1), y = tao2)): object 'fm3' not found
print(Plot1Alpha2)
#> Error in print(Plot1Alpha2): object 'Plot1Alpha2' not found

Plot2Alpha2 <-
  ggplot(data = fm3$tao1, mapping = aes(tao2)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(alpha[2])) +
  theme_bw()
#> Error in ggplot(data = fm3$tao1, mapping = aes(tao2)): object 'fm3' not found
print(Plot2Alpha2)
#> Error in print(Plot2Alpha2): object 'Plot2Alpha2' not found

# Plot of Betas
Plot1Beta1 <-
  ggplot(data = fm3$delta1, mapping = aes(x = 1:nrow(fm3$delta1), y = delta1)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(beta[1]), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$delta1, mapping = aes(x = 1:nrow(fm3$delta1),     y = delta1)): object 'fm3' not found
print(Plot1Beta1)
#> Error in print(Plot1Beta1): object 'Plot1Beta1' not found

Plot2Beta1 <-
  ggplot(data = fm3$delta1, mapping = aes(delta1)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(beta[1])) +
  theme_bw()
#> Error in ggplot(data = fm3$delta1, mapping = aes(delta1)): object 'fm3' not found
print(Plot2Beta1)
#> Error in print(Plot2Beta1): object 'Plot2Beta1' not found


Plot1Beta2 <-
  ggplot(data = fm3$delta1, mapping = aes(x = 1:nrow(fm3$delta1), y = delta2)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(beta[2]), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$delta1, mapping = aes(x = 1:nrow(fm3$delta1),     y = delta2)): object 'fm3' not found
print(Plot1Beta2)
#> Error in print(Plot1Beta2): object 'Plot1Beta2' not found

Plot2Beta2 <-
  ggplot(data = fm3$delta1, mapping = aes(delta2)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(beta[2])) +
  theme_bw()
#> Error in ggplot(data = fm3$delta1, mapping = aes(delta2)): object 'fm3' not found
print(Plot2Beta2)
#> Error in print(Plot2Beta2): object 'Plot2Beta2' not found


Plot1Beta3 <-
  ggplot(data = fm3$delta1, mapping = aes(x = 1:nrow(fm3$delta1), y = delta3)) +
  geom_line(color = "blue") +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = expression(beta[3]), x = "Iterations") +
  theme_bw()
#> Error in ggplot(data = fm3$delta1, mapping = aes(x = 1:nrow(fm3$delta1),     y = delta3)): object 'fm3' not found
print(Plot1Beta3)
#> Error in print(Plot1Beta3): object 'Plot1Beta3' not found

Plot2Beta3 <-
  ggplot(data = fm3$delta1, mapping = aes(delta3)) +
  geom_histogram() +
  scale_x_continuous(labels = scales::comma) +
  scale_y_continuous(labels = scales::comma) +
  labs(y = "Frequency", x = expression(beta[3])) +
  theme_bw()
#> Error in ggplot(data = fm3$delta1, mapping = aes(delta3)): object 'fm3' not found
print(Plot2Beta3)
#> Error in print(Plot2Beta3): object 'Plot2Beta3' not found

Bayesian Estimation of Genotype by Environment Interaction Model

Arguments

Value

References

Examples

Contents

Author