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Knit directory: Genomic-Selection-for-Drought-Tolerance-Using-Genome-Wide-SNPs-in-Casava/

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Configurations and packages

To peRKHSorm the analyses, we will need the following packages:

library(furrr)
library(tidyverse)
library(cvTools)
library(kableExtra)

Data

geno<- readRDS("data/geno.rds")
pheno<-readRDS("data/pheno.rds")
traits <- colnames(pheno)[-1]

RKHS

We can also use the eigenvalues of the G covariance matrix Gaussian Kernel (GK) to perform the analyses. But first, we have to build GK.

For this purpose, we will use the sommer package [@Covarrubias-Pazaran_2014]. In the code below, y is for the vector with the means, GK is G covariance matrix Gaussian Kernel for the random effects, which will be and identity matrix by default; and X is a design matrix for the fixed effects, which will be a vector of ones (1) by default. Note that we are returning to the “1, 0, -1” codification in the SNPs matrix. This is a requirement of the sommer package.

dist <- as.matrix(dist(scale(geno, center = TRUE, scale = TRUE))) ^ 2
GK <- exp(-dist / median(dist))
GK[1:5,1:5]
                      Alagoana363.250437472 Arari424.250437476  BGM_2042
Alagoana363.250437472             1.0000000          0.4278287 0.3892939
Arari424.250437476                0.4278287          1.0000000 0.3832281
BGM_2042                          0.3892939          0.3832281 1.0000000
BGM0290.250581760                 0.3548060          0.3448635 0.3622436
BGM0368.250437186                 0.3195954          0.3273520 0.3875223
                      BGM0290.250581760 BGM0368.250437186
Alagoana363.250437472         0.3548060         0.3195954
Arari424.250437476            0.3448635         0.3273520
BGM_2042                      0.3622436         0.3875223
BGM0290.250581760             1.0000000         0.3404986
BGM0368.250437186             0.3404986         1.0000000

Cross-validation

To prove that the prediction is accurate, we should peRKHSorm a cross-validation (CV) scheme. For this purpose, we divide the data into a training set and a validation set.

First we separate the data into k folds. Then, we attribute NA for one fold and try to predict the data from this fold based on the others. When selecting the number of folds, one must prioritize the balance between the number of observations in each fold.

In addition, this process should be repeated for further validation. The step-by-step below will guide the CV in the data we are analysing.

1. Determine the number of folds and repetitions

nfolds = 5
nrept = 5

Since we defined 5 folds, our data will be divided into 5 parts with 83 observations each.

2. Match the order of the data and the rows of the SNP matrix

The order is decreasing or increasing (numeric or alphabetical) regarding the name of the genotypes.

pheno <- pheno[order(pheno$ID_Clone, decreasing = F),]
geno <- geno[order(row.names(geno)),]
all(rownames(geno) == pheno$ID_Clone)
[1] TRUE

3. Add a column indicating a number for each observation

This will be useful to assign each observation for a fold, which will be the next step.

pheno$ID <- factor(1:nrow(pheno))

4. Folds assignment

In this step, we will assign each observation to a fold. Bear in mind that for each repetition, the folds will comprise different observations. The purpose of the repetition is to make sure of the randomness of the assignment step.

In this step, we will use the cvTools package [@cvTools]

For better peRKHSormance, we included this step in the loop of the next step.

Run model

The next step is the very CV. Here, we will define the linear predictor and the lists that will be useful in the loop. The first list, here called results_cv_RKHS and, contains the results for each fold assignation that we built in the previous step. The second GEBVS_RKHS contains the GEBVs.

Then, we will construct the loop. Each iteration will assign NA for a different fold, and we will use the other folds to predict the missing values. Note that the folds vary for each repetition and trait.

Set up parallel processing. Define and run multiple models to get the GEBVs ATTENTION: This process is time-consuming.

# Planejar o processamento em várias sessões para paralelização
plan(multisession)

# Iniciar uma lista para armazenar os resultados
results_list <-
  future_map(traits, .options = furrr_options(seed = 100), function(j)  {
    # Pré-processamento dos dados
    pheno2 <- pheno %>%
      select(ID_Clone, all_of(j)) %>%
      na.omit() %>%
      ungroup() %>%
      filter(ID_Clone %in% rownames(GK)) %>%
      mutate(ID = factor(1:nrow(.))) %>%
      droplevels()
    
    # Filtrar as linhas de Z com base em pheno2$ID_Clone
    GK1 <-
      GK[rownames(GK) %in% pheno2$ID_Clone, rownames(GK) %in% pheno2$ID_Clone]
    
    #Semente para reprodução
    set.seed(100)
    
    # Listas das folds
    fold.list <- lapply(1:nrept, function(a) {
      folds <- cvFolds(nlevels(pheno2$ID),
                       type = "random",
                       K = nfolds)
      
      split(folds$subsets, f = folds$which)
    })
    
    # Usar future_map_dfr para criar dobras cruzadas em paralelo
    future_map_dfr(1:length(fold.list), function(z) {
      for (i in 1:nfolds) {
        # Conjunto de treinamento
        train_data <- pheno2
        
        # Conjunto de validação
        train_data[train_data$ID %in% fold.list[[z]][[i]], j] <- NA
        
        # Fitting model
        fixed <- formula(paste(j, " ~ 1"))
        
        RKHS <-
          sommer::mmer(
            fixed,
            random = ~ sommer::vsr(ID_Clone, Gu = GK1),
            data = train_data,
            rcov = ~ units
          )
        
        # GETGV
        Pred <-
          data.frame(
            Yhat =  RKHS$U$`u:ID_Clone`[[j]],
            ID = train_data$ID,
            ID_Clone = train_data$ID_Clone
          ) %>%
          filter(ID %in% fold.list[[z]][[i]])
        
        result1 <-
          tibble(
            GEBV = Pred$Yhat,
            ID = Pred$ID,
            ID_Clone = Pred$ID_Clone,
            Trait = j,
            rep = z,
            fold = i
          )
        
        
        # Resultados da previsão
        if (i == 1) {
          result <- result1
        } else {
          result <- rbind(result, result1)
        }
      }
      
      #Ordenando os resultados de acordo com o ID
      result <- result[order(result$ID, decreasing = F),]
      
      # Resultados da validação cruzada
      result_cv <- tibble(
        Trait = j,
        rep = z,
        Log = all(result$ID == pheno2$ID),
        Ac = round(cor(result$GEBV, pheno2[[j]], use = "na.or.complete"), 3),
        MSPE = round(mean((
          result$GEBV - pheno2[[j]]
        ) ^ 2, na.rm = TRUE), 3),
        result = list(result)
      )
    })
  })
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.193   14:51:49      0           0
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    3      -144.893   14:51:49      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.335   14:51:50      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.768   14:51:51      0           0
    2      -147.232   14:51:52      1           0
    3      -144.835   14:51:52      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.64   14:51:52      0           0
    2      -146.461   14:51:53      1           0
    3      -143.414   14:51:53      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.057   14:51:54      0           0
    2      -146.803   14:51:54      0           0
    3      -145.342   14:51:54      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.641   14:51:55      1           0
    2      -147.632   14:51:55      1           0
    3      -145.246   14:51:55      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.976   14:51:56      0           0
    2      -146.417   14:51:56      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.287   14:51:57      1           0
    2      -145.537   14:51:57      1           0
    3      -141.915   14:51:57      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.34   14:51:58      1           0
    2      -145.165   14:51:58      1           0
    3      -143.634   14:51:58      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.909   14:51:58      0           0
    2      -149.319   14:51:59      1           0
    3      -147.222   14:51:59      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.369   14:52:0      1           0
    2      -148.722   14:52:0      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.816   14:52:1      0           0
    2      -146.223   14:52:1      0           0
    3      -144.045   14:52:1      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.4   14:52:2      0           0
    2      -146.471   14:52:2      0           0
    3      -145.297   14:52:2      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.974   14:52:3      1           0
    2      -147.867   14:52:3      1           0
    3      -144.189   14:52:3      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.466   14:52:4      1           0
    2      -145.723   14:52:4      1           0
    3      -144.453   14:52:4      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.439   14:51:0      0           0
    2      -156.437   14:51:0      0           0
    3      -155.338   14:51:0      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.888   14:51:2      0           0
    2      -143.671   14:51:2      0           0
    3      -142.49   14:51:2      0           0
    4      -142.398   14:51:3      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.25   14:51:3      0           0
    2      -151.296   14:51:4      1           0
    3      -149.495   14:51:4      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.805   14:51:5      0           0
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    3      -152.063   14:51:6      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.492   14:51:7      0           0
    2      -148.761   14:51:7      0           0
    3      -145.488   14:51:8      1           0
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    8      -143.399   14:51:9      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.676   14:51:9      0           0
    2      -146.892   14:51:10      1           0
    3      -143.572   14:51:10      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.683   14:51:12      1           0
    2      -148.98   14:51:12      1           0
    3      -147.606   14:51:12      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.769   14:51:14      1           0
    2      -149.761   14:51:14      1           0
    3      -147.653   14:51:14      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.632   14:51:16      1           0
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    3      -152.6   14:51:16      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.259   14:51:18      0           0
    2      -154.272   14:51:18      0           0
    3      -152.825   14:51:18      0           0
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    8      -152.131   14:51:20      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.464   14:51:20      0           0
    2      -147.13   14:51:20      0           0
    3      -144.525   14:51:21      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.784   14:51:22      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.672   14:51:24      0           0
    2      -154.653   14:51:24      0           0
    3      -152.882   14:51:24      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.062   14:51:26      0           0
    2      -150.687   14:51:26      0           0
    3      -149.01   14:51:26      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.256   14:51:28      1           0
    2      -150.211   14:51:28      1           0
    3      -147.976   14:51:28      1           0
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    5      -147.332   14:51:29      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.611   14:51:29      0           0
    2      -146.113   14:51:30      1           0
    3      -145.14   14:51:30      1           0
    4      -145.004   14:51:30      1           0
    5      -144.997   14:51:30      1           0
    6      -144.996   14:51:31      2           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.411   14:51:31      0           0
    2      -154.477   14:51:32      1           0
    3      -152.729   14:51:32      1           0
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    6      -151.856   14:51:32      1           0
    7      -151.852   14:51:33      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.257   14:51:33      0           0
    2      -150.523   14:51:33      0           0
    3      -147.998   14:51:34      1           0
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    8      -146.637   14:51:35      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.351   14:51:35      0           0
    2      -149.857   14:51:35      0           0
    3      -147.059   14:51:36      1           0
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    6      -146.017   14:51:36      1           0
    7      -146.016   14:51:37      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.647   14:51:37      0           0
    2      -151.987   14:51:37      0           0
    3      -150.599   14:51:38      1           0
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    6      -150.204   14:51:38      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.137   14:51:39      0           0
    2      -149.093   14:51:39      0           0
    3      -146.995   14:51:39      0           0
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    6      -146.304   14:51:40      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.032   14:51:40      0           0
    2      -146.698   14:51:40      0           0
    3      -143.894   14:51:41      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.656   14:51:42      0           0
    2      -149.862   14:51:42      0           0
    3      -147.997   14:51:42      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.54   14:51:43      0           0
    2      -154.181   14:51:43      0           0
    3      -152.305   14:51:44      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.631   14:51:45      0           0
    2      -153.977   14:51:45      0           0
    3      -153.146   14:51:46      1           0
    4      -152.925   14:51:46      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.911   14:51:0      0           0
    2      -118.677   14:51:0      0           0
    3      -118.224   14:51:0      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.036   14:51:1      0           0
    2      -118.963   14:51:1      0           0
    3      -118.519   14:51:1      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.109   14:51:1      0           0
    2      -115.543   14:51:2      1           0
    3      -114.736   14:51:2      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.408   14:51:2      0           0
    2      -119.771   14:51:2      0           0
    3      -119.554   14:51:2      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.811   14:51:3      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.957   14:51:4      0           0
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    3      -119.213   14:51:4      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.975   14:51:4      0           0
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    3      -118.533   14:51:5      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.132   14:51:5      0           0
    2      -118.594   14:51:5      0           0
    3      -117.622   14:51:5      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.484   14:51:6      0           0
    2      -116.129   14:51:6      0           0
    3      -115.183   14:51:6      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.04   14:51:7      1           0
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    3      -115.891   14:51:7      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.459   14:51:8      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.269   14:51:9      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.435   14:51:10      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.796   14:51:10      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.141   14:51:11      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.03   14:51:12      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.538   14:51:13      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.813   14:51:14      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.054   14:51:14      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.345   14:51:15      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.444   14:51:16      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.041   14:51:17      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.499   14:51:18      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.581   14:51:18      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.128   14:51:19      0           0
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    3      -108.736   14:51:19      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -114.88   14:51:20      0           0
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    3      -105.467   14:51:20      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.332   14:51:21      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -114.802   14:51:21      0           0
    2      -109.396   14:51:22      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.935   14:51:22      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.02   14:51:23      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -114.776   14:51:24      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.198   14:51:25      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.662   14:51:25      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.732   14:51:26      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.062   14:51:27      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.191   14:51:28      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.163   14:51:29      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.404   14:51:29      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.327   14:51:30      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -114.201   14:51:31      0           0
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    3      -106.392   14:51:31      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.455   14:51:32      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.177   14:51:33      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -113.855   14:51:33      0           0
    2      -105.355   14:51:33      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.003   14:51:34      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.398   14:51:35      0           0
    2      -109.491   14:51:35      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.942   14:51:36      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -114.388   14:51:37      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.684   14:51:37      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.5   14:51:38      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -159.608   14:51:1      1           0
    2      -158.548   14:51:1      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.155   14:51:2      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.613   14:51:4      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.427   14:51:6      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.616   14:51:7      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.277   14:51:9      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -159.085   14:51:11      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.648   14:51:15      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -161.352   14:51:17      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.675   14:51:19      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.747   14:51:21      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.847   14:51:23      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -160.191   14:51:24      0           0
    2      -159.097   14:51:25      1           0
    3      -158.487   14:51:25      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -161.179   14:51:26      0           0
    2      -160.215   14:51:26      0           0
    3      -159.531   14:51:27      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -159.317   14:51:28      0           0
    2      -157.509   14:51:28      0           0
    3      -156.329   14:51:28      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.748   14:51:30      0           0
    2      -154.403   14:51:30      0           0
    3      -152.331   14:51:30      0           0
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    6      -151.64   14:51:31      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.586   14:51:32      0           0
    2      -156.598   14:51:32      0           0
    3      -155.558   14:51:32      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.634   14:51:34      0           0
    2      -155.418   14:51:34      0           0
    3      -153.579   14:51:34      0           0
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    6      -153.095   14:51:35      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -159.662   14:51:36      1           0
    2      -157.293   14:51:36      1           0
    3      -155.871   14:51:36      1           0
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    6      -155.432   14:51:37      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.843   14:51:37      0           0
    2      -156.199   14:51:38      1           0
    3      -154.528   14:51:38      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.147   14:51:39      0           0
    2      -153.06   14:51:39      0           0
    3      -150.567   14:51:39      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.671   14:51:40      0           0
    2      -156.078   14:51:41      1           0
    3      -154.465   14:51:41      1           0
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    6      -153.899   14:51:41      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -159.283   14:51:42      0           0
    2      -156.564   14:51:42      0           0
    3      -154.868   14:51:42      0           0
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    6      -154.29   14:51:43      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.348   14:51:43      0           0
    2      -156.322   14:51:43      0           0
    3      -155.647   14:51:43      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.894   14:51:1      0           0
    2      -154.812   14:51:1      0           0
    3      -153.652   14:51:1      0           0
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    6      -153.323   14:51:2      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.803   14:51:3      1           0
    2      -158.303   14:51:3      1           0
    3      -158.038   14:51:3      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.709   14:51:4      0           0
    2      -150.363   14:51:5      1           0
    3      -148.293   14:51:5      1           0
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    6      -147.809   14:51:5      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.045   14:51:6      0           0
    2      -154.111   14:51:6      0           0
    3      -152.034   14:51:6      0           0
    4      -151.236   14:51:7      1           0
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    6      -151.1   14:51:7      1           0
    7      -151.098   14:51:7      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.307   14:51:8      0           0
    2      -155.257   14:51:8      0           0
    3      -154.018   14:51:8      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.064   14:51:10      1           0
    2      -155.527   14:51:10      1           0
    3      -154.721   14:51:10      1           0
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    6      -154.452   14:51:11      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.883   14:51:12      1           0
    2      -153.186   14:51:12      1           0
    3      -152.054   14:51:12      1           0
    4      -151.873   14:51:12      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.135   14:51:13      0           0
    2      -155.254   14:51:13      0           0
    3      -154.372   14:51:13      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.075   14:51:15      1           0
    2      -152.226   14:51:15      1           0
    3      -149.146   14:51:15      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.799   14:51:17      0           0
    2      -156.033   14:51:17      0           0
    3      -154.954   14:51:17      0           0
    4      -154.605   14:51:18      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.526   14:51:19      0           0
    2      -152.013   14:51:19      0           0
    3      -150.114   14:51:19      0           0
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    6      -149.647   14:51:20      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.331   14:51:20      0           0
    2      -157.487   14:51:21      1           0
    3      -156.963   14:51:21      1           0
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    6      -156.729   14:51:21      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.213   14:51:22      0           0
    2      -154.978   14:51:22      0           0
    3      -153.716   14:51:23      1           0
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    6      -153.317   14:51:23      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.314   14:51:24      0           0
    2      -155.4   14:51:24      0           0
    3      -154.329   14:51:24      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.387   14:51:25      0           0
    2      -153.343   14:51:26      1           0
    3      -151.448   14:51:26      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.261   14:51:27      0           0
    2      -155.48   14:51:27      0           0
    3      -154.424   14:51:28      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.992   14:51:29      0           0
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    3      -156.295   14:51:29      0           0
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    6      -156.067   14:51:30      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.835   14:51:31      0           0
    2      -152.209   14:51:31      0           0
    3      -149.955   14:51:31      0           0
    4      -149.247   14:51:32      1           0
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    6      -149.162   14:51:32      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.809   14:51:33      1           0
    2      -152.753   14:51:33      1           0
    3      -151.469   14:51:33      1           0
    4      -151.226   14:51:33      1           0
    5      -151.213   14:51:33      1           0
    6      -151.212   14:51:34      2           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.051   14:51:34      0           0
    2      -154.733   14:51:34      0           0
    3      -153.446   14:51:34      0           0
    4      -153.057   14:51:35      1           0
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    6      -153   14:51:35      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.338   14:51:36      1           0
    2      -153.855   14:51:36      1           0
    3      -152.43   14:51:36      1           0
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    6      -151.971   14:51:37      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -157.786   14:51:37      0           0
    2      -156.715   14:51:37      0           0
    3      -156.196   14:51:38      1           0
    4      -156.077   14:51:38      1           0
    5      -156.068   14:51:38      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.53   14:51:38      0           0
    2      -154.52   14:51:39      1           0
    3      -153.51   14:51:39      1           0
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    6      -153.163   14:51:39      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.205   14:51:40      0           0
    2      -152.1   14:51:40      0           0
    3      -149.062   14:51:40      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.246   14:51:41      0           0
    2      -153.372   14:51:42      1           0
    3      -152.119   14:51:42      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.873   14:51:1      0           0
    2      -118.619   14:51:1      0           0
    3      -118.163   14:51:1      0           0
    4      -118.089   14:51:1      0           0
    5      -118.085   14:51:1      0           0
    6      -118.085   14:51:2      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.07   14:51:2      0           0
    2      -119.023   14:51:2      0           0
    3      -118.591   14:51:2      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.063   14:51:2      0           0
    2      -115.473   14:51:2      0           0
    3      -114.684   14:51:3      1           0
    4      -114.555   14:51:3      1           0
    5      -114.548   14:51:3      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.383   14:51:3      0           0
    2      -119.734   14:51:3      0           0
    3      -119.516   14:51:3      0           0
    4      -119.487   14:51:3      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.764   14:51:4      0           0
    2      -118.02   14:51:4      0           0
    3      -116.781   14:51:4      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.982   14:51:5      0           0
    2      -119.387   14:51:5      0           0
    3      -119.252   14:51:5      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.968   14:51:5      0           0
    2      -118.934   14:51:5      0           0
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    5      -118.44   14:51:6      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.095   14:51:6      0           0
    2      -118.532   14:51:6      0           0
    3      -117.563   14:51:6      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.472   14:51:7      0           0
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    3      -115.199   14:51:7      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.017   14:51:7      0           0
    2      -116.881   14:51:7      0           0
    3      -115.87   14:51:8      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.964   14:51:8      0           0
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    3      -121.806   14:51:8      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.437   14:51:9      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.236   14:51:10      0           0
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    3      -118.674   14:51:10      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.443   14:51:11      1           0
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    3      -116.068   14:51:11      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.768   14:51:11      0           0
    2      -111.72   14:51:11      0           0
    3      -109.206   14:51:11      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.08   14:51:12      0           0
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    3      -116.994   14:51:12      0           0
    4      -116.938   14:51:12      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.997   14:51:13      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.538   14:51:13      0           0
    2      -119.678   14:51:14      1           0
    3      -119.155   14:51:14      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.797   14:51:14      0           0
    2      -118.27   14:51:14      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.053   14:51:15      0           0
    2      -117.523   14:51:15      0           0
    3      -117.078   14:51:15      0           0
    4      -117.029   14:51:15      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.341   14:51:16      0           0
    2      -119.387   14:51:16      0           0
    3      -118.944   14:51:16      0           0
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    6      -118.818   14:51:16      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.406   14:51:17      0           0
    2      -117.87   14:51:17      0           0
    3      -117.266   14:51:17      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.012   14:51:18      1           0
    2      -116.695   14:51:18      1           0
    3      -115.473   14:51:18      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.468   14:51:18      0           0
    2      -115.803   14:51:18      0           0
    3      -114.702   14:51:18      0           0
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    6      -114.437   14:51:19      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.531   14:51:19      0           0
    2      -120.008   14:51:19      0           0
    3      -119.824   14:51:19      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.217   14:51:20      0           0
    2      -150.452   14:51:20      0           0
    3      -149.932   14:51:20      0           0
    4      -149.901   14:51:20      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.663   14:51:21      0           0
    2      -148.823   14:51:21      0           0
    3      -147.843   14:51:22      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.676   14:51:23      1           0
    2      -140.961   14:51:23      1           0
    3      -139.642   14:51:23      1           0
    4      -139.564   14:51:23      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.864   14:51:24      0           0
    2      -146.074   14:51:24      0           0
    3      -145.315   14:51:24      0           0
    4      -145.271   14:51:24      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.755   14:51:25      0           0
    2      -145.269   14:51:25      0           0
    3      -143.775   14:51:25      0           0
    4      -143.558   14:51:26      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.234   14:51:27      1           0
    2      -142.903   14:51:27      1           0
    3      -141.684   14:51:27      1           0
    4      -141.595   14:51:27      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.027   14:51:28      0           0
    2      -143.626   14:51:28      0           0
    3      -142.094   14:51:28      0           0
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    5      -141.918   14:51:29      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.455   14:51:29      0           0
    2      -151.022   14:51:30      1           0
    3      -150.526   14:51:30      1           0
    4      -150.478   14:51:30      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.171   14:51:31      1           0
    2      -147.725   14:51:31      1           0
    3      -146.496   14:51:31      1           0
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    5      -146.317   14:51:32      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.046   14:51:32      0           0
    2      -148.119   14:51:33      1           0
    3      -147.372   14:51:33      1           0
    4      -147.318   14:51:33      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.27   14:51:34      1           0
    2      -144.248   14:51:34      1           0
    3      -142.921   14:51:34      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.932   14:51:35      0           0
    2      -143.744   14:51:35      0           0
    3      -142.331   14:51:35      0           0
    4      -142.168   14:51:35      0           0
    5      -142.164   14:51:36      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.794   14:51:36      0           0
    2      -149.286   14:51:36      0           0
    3      -148.391   14:51:37      1           0
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    5      -148.279   14:51:37      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.153   14:51:38      1           0
    2      -147.691   14:51:38      1           0
    3      -146.538   14:51:38      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.649   14:51:39      0           0
    2      -148.277   14:51:39      0           0
    3      -147.861   14:51:39      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.286   14:51:40      0           0
    2      -150.338   14:51:40      0           0
    3      -149.785   14:51:40      0           0
    4      -149.754   14:51:40      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.586   14:51:41      0           0
    2      -145.35   14:51:41      0           0
    3      -144.264   14:51:41      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.625   14:51:42      0           0
    2      -138.067   14:51:42      0           0
    3      -135.647   14:51:42      0           0
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    5      -135.341   14:51:43      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.583   14:51:43      0           0
    2      -144.726   14:51:43      0           0
    3      -143.384   14:51:43      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.755   14:51:44      0           0
    2      -149.612   14:51:45      1           0
    3      -148.865   14:51:45      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.311   14:51:46      0           0
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    3      -145.736   14:51:46      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.515   14:51:47      0           0
    2      -147.217   14:51:47      0           0
    3      -146.226   14:51:47      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.138   14:51:48      0           0
    2      -138.244   14:51:48      0           0
    3      -136.448   14:51:48      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.571   14:51:49      1           0
    2      -150.912   14:51:49      1           0
    3      -150.486   14:51:49      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.106   14:51:49      0           0
    2      -149.357   14:51:49      0           0
    3      -148.086   14:51:50      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.556   14:51:2      1           0
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    3      -153.442   14:51:2      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.815   14:51:3      0           0
    2      -150.402   14:51:3      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.217   14:51:4      0           0
    2      -149.912   14:51:5      1           0
    3      -149.142   14:51:5      1           0
    4      -149.074   14:51:5      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.641   14:51:6      1           0
    2      -152.42   14:51:6      1           0
    3      -151.874   14:51:6      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.961   14:51:7      0           0
    2      -148.714   14:51:7      0           0
    3      -147.373   14:51:7      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.018   14:51:8      0           0
    2      -149.178   14:51:8      0           0
    3      -148.157   14:51:9      1           0
    4      -148.084   14:51:9      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.952   14:51:10      1           0
    2      -151.615   14:51:10      1           0
    3      -151.158   14:51:10      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.952   14:51:11      0           0
    2      -151.934   14:51:11      0           0
    3      -150.448   14:51:12      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.328   14:51:13      0           0
    2      -151.931   14:51:13      0           0
    3      -151.369   14:51:13      0           0
    4      -151.316   14:51:14      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.816   14:51:14      0           0
    2      -152.544   14:51:14      0           0
    3      -151.95   14:51:15      1           0
    4      -151.893   14:51:15      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.694   14:51:16      1           0
    2      -150.267   14:51:16      1           0
    3      -149.168   14:51:16      1           0
    4      -149.044   14:51:16      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.736   14:51:17      0           0
    2      -152.137   14:51:18      1           0
    3      -151.076   14:51:18      1           0
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    6      -150.82   14:51:18      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.147   14:51:19      0           0
    2      -153.128   14:51:19      0           0
    3      -152.576   14:51:19      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.58   14:51:21      1           0
    2      -148.666   14:51:21      1           0
    3      -147.994   14:51:21      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.436   14:51:22      0           0
    2      -152.505   14:51:22      0           0
    3      -152.083   14:51:22      0           0
    4      -152.049   14:51:23      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.806   14:51:23      0           0
    2      -151.087   14:51:23      0           0
    3      -150.452   14:51:24      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.501   14:51:24      0           0
    2      -148.423   14:51:25      1           0
    3      -147.644   14:51:25      1           0
    4      -147.616   14:51:25      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.938   14:51:26      1           0
    2      -152.684   14:51:26      1           0
    3      -151.972   14:51:26      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.683   14:51:27      0           0
    2      -153.462   14:51:27      0           0
    3      -152.545   14:51:27      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.71   14:51:29      1           0
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    3      -148.202   14:51:29      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.876   14:51:30      0           0
    2      -150.748   14:51:30      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.705   14:51:32      0           0
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    3      -146.924   14:51:32      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.261   14:51:33      0           0
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    3      -149.941   14:51:34      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.952   14:51:34      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.529   14:51:36      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.156   14:51:2      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.122   14:51:4      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.294   14:51:5      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.385   14:51:7      0           0
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# Combinar todos os resultados da validação cruzada em uma única estrutura
results_cv_RKHS <- do.call(rbind, results_list)

# Extrair os GEBVs (Valores Genômicos Empíricos Melhorados) em uma estrutura separada
GEBVS_RKHS <- do.call(rbind, results_cv_RKHS$result)

Results

The object “GEBVS_RKHS” contains the GEBVs for each trait and clone. The table above shows the first five clones and their GEBVs for each trait.

GEBVS_RKHS |>
  group_by(Trait, ID_Clone) |>
  summarise(GEBV = mean(GEBV)) %>%
  pivot_wider(names_from = Trait, values_from = GEBV) %>%
  head() %>%
  kbl(escape = F, align = 'c') |>
  kable_classic("hover", full_width = F, position = "center", fixed_thead = T)
`summarise()` has grouped output by 'Trait'. You can override using the
`.groups` argument.
ID_Clone DMC FRY HI N_Roots Nstem.Plant Plant.Height Root.Di Root.Le ShY StC StY Stem.D
BGM_2042 0.8851626 1.3775816 1.3504393 0.6349606 0.2436677 0.0377981 0.5743877 1.3658880 2.5388808 0.8840124 0.3752536 0.0794001
BGM0368.250437186 1.0559030 -0.3675476 0.3446849 0.2653845 0.0682762 0.0043035 -0.3011155 -0.2631986 -2.2886017 1.0532570 -0.0273292 -0.0151872
BGM0424.250437187 0.3769805 -0.0584124 -0.6649231 0.0488446 0.0440244 0.0168310 -0.1650248 -0.0106796 -0.4532117 0.3828497 0.0125693 0.0170974
BGM0611.250437190 -0.3807381 0.0447070 -0.3671337 0.2625928 0.0984610 -0.0341276 0.2121542 0.5576522 -0.0286580 -0.3846556 -0.0397691 -0.0440015
BGM0652.250437861 0.3289363 0.1283697 -0.5251662 0.1961288 0.1018050 0.0031698 -0.0252586 0.5300556 0.8376198 0.3238434 0.0160116 0.0235057
BGM0699.250437199 0.1243751 -0.1788720 -1.0288358 -0.0047164 0.0343550 0.0108437 -0.0565137 0.2842844 0.2205706 0.1122764 -0.0277006 0.0437123

Acuracy and MSPE for each trait and repetition:

results_cv_RKHS[-6] |>
  group_by(Trait) %>% 
  summarise_all(mean) %>% 
  arrange(desc(Ac), MSPE) %>% 
  kbl(escape = F, align = 'c') |>
  kable_classic("hover", full_width = F, position = "center", fixed_thead = T)
Trait rep Log Ac MSPE
Root.Le 3 1 0.3714 1.9894
Stem.D 3 1 0.3512 0.0084
ShY 3 1 0.3288 13.2408
FRY 3 1 0.3280 1.1972
Root.Di 3 1 0.3170 3.3912
StY 3 1 0.3090 0.0724
Plant.Height 3 1 0.3032 0.0080
HI 3 1 0.2640 11.7624
Nstem.Plant 3 1 0.2600 0.0330
N_Roots 3 1 0.2484 0.9312
StC 3 1 0.1908 6.0810
DMC 3 1 0.1900 6.1150

The object “result_cv” is divided by repetition. In the “result_cv” objects for each repetition, “Rep” is the number of the repetition, “Log” is a diagnostic indicating if the order of the predicted breeding values matches the order of the adjusted means, “Ac” is the prediction accuracy (correlation between the GEBV and adjusted means), and “MSPE” is the mean square prediction error (the lower, the better).

Let’s now move on to processing each model. Since this can be time-consuming, I’ve separated it into parallel processing and each model into each script:


sessionInfo()
R version 4.3.3 (2024-02-29 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19045)

Matrix products: default


locale:
[1] LC_COLLATE=Portuguese_Brazil.utf8  LC_CTYPE=Portuguese_Brazil.utf8   
[3] LC_MONETARY=Portuguese_Brazil.utf8 LC_NUMERIC=C                      
[5] LC_TIME=Portuguese_Brazil.utf8    

time zone: America/Sao_Paulo
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] kableExtra_1.4.0    cvTools_0.3.3       robustbase_0.99-4-1
 [4] lattice_0.22-6      lubridate_1.9.4     forcats_1.0.0      
 [7] stringr_1.5.1       dplyr_1.1.4         purrr_1.0.2        
[10] readr_2.1.5         tidyr_1.3.1         tibble_3.2.1       
[13] ggplot2_3.5.1       tidyverse_2.0.0     furrr_0.3.1        
[16] future_1.34.0      

loaded via a namespace (and not attached):
 [1] gtable_0.3.6      xfun_0.50         bslib_0.8.0       tzdb_0.4.0       
 [5] vctrs_0.6.5       tools_4.3.3       generics_0.1.3    parallel_4.3.3   
 [9] DEoptimR_1.1-3-1  pkgconfig_2.0.3   lifecycle_1.0.4   compiler_4.3.3   
[13] git2r_0.35.0      munsell_0.5.1     codetools_0.2-20  httpuv_1.6.15    
[17] htmltools_0.5.8.1 sass_0.4.9        yaml_2.3.10       later_1.4.1      
[21] pillar_1.10.1     jquerylib_0.1.4   cachem_1.1.0      parallelly_1.41.0
[25] tidyselect_1.2.1  digest_0.6.37     stringi_1.8.4     listenv_0.9.1    
[29] rprojroot_2.0.4   fastmap_1.2.0     grid_4.3.3        colorspace_2.1-1 
[33] cli_3.6.3         magrittr_2.0.3    withr_3.0.2       scales_1.3.0     
[37] promises_1.3.2    timechange_0.3.0  rmarkdown_2.29    globals_0.16.3   
[41] workflowr_1.7.1   hms_1.1.3         evaluate_1.0.3    knitr_1.49       
[45] viridisLite_0.4.2 rlang_1.1.4       Rcpp_1.0.14       glue_1.8.0       
[49] xml2_1.3.6        svglite_2.1.3     rstudioapi_0.17.1 jsonlite_1.8.9   
[53] R6_2.5.1          systemfonts_1.1.0 fs_1.6.5         

  1. Weverton Gomes da Costa, Pós-Doutorando, Embrapa Mandioca e Fruticultura, ↩︎