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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 perform 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]

G-BLUP Additive

In the GBLUP, we will use the k matrix (additive) instead of the SNPs matrix. Thus, we will obtain the GEBV directly. Note that we will need to build the G matrix again, since some genotypes were dropped after our filtering.

For this purpose, we will use the sommer package [@Covarrubias-Pazaran_2014]. In the code below, y is for the vector with the means, K is for a covariance matrix 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.

K <- sommer::A.mat(geno-1)

Cross-validation

To prove that the prediction is accurate, we should perform 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 performance, 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_G_BLUP and, contains the results for each fold assignation that we built in the previous step. The second GEBVS_G_BLUP 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(K)) %>%
      mutate(ID = factor(1:nrow(.))) %>%
      droplevels()
    
    # Filtrar as linhas de Z com base em pheno2$ID_Clone
    K1 <-
      K[rownames(K) %in% pheno2$ID_Clone, rownames(K) %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"))
        
        GBLUP <-
          sommer::mmer(
            fixed,
            random = ~ sommer::vsr(ID_Clone, Gu = K1),
            data = train_data,
            rcov = ~ units
          )
        
        # Calcular herdabilidade
        narrow_sense <- sommer::vpredict(GBLUP, h2 ~ V1 / (V1 + V2)) # herdabilidade em sentido estrito
 
        
        # GETGV
        Pred <-
          data.frame(
            Yhat =  GBLUP$U$`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),
        narrow_sense = narrow_sense$Estimate,
      )
    })
  })
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.159   14:45:55      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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# Combinar todos os resultados da validação cruzada em uma única estrutura
results_cv_G_BLUP <- do.call(rbind, results_list)

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

Results

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

GEBVS_G_BLUP |>
  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 0.4396486 1.0945731 1.5367885 0.3575712 0.1320577 0.0218642 0.4637015 1.0041085 1.7281854 0.4522471 0.2773797 0.0615555
BGM0368.250437186 0.6183612 -0.4291852 0.5874587 0.1107249 -0.0221219 -0.0074425 -0.5080204 -0.5459849 -2.4883434 0.6245181 -0.0396337 -0.0388747
BGM0424.250437187 0.0738619 -0.1646794 0.0543841 -0.1523849 -0.0564455 0.0016752 -0.3826374 -0.4380215 -1.3788151 0.0924512 -0.0098418 -0.0160907
BGM0611.250437190 -0.8639430 -0.1746128 -0.4760090 -0.0025962 0.0412780 -0.0513404 -0.1812646 0.0714974 -0.6252969 -0.8570488 -0.0597242 -0.0697797
BGM0652.250437861 -0.1397058 -0.0686700 -0.3925016 -0.0765310 0.0314649 -0.0292519 -0.3950229 -0.1501383 0.0145408 -0.1387849 -0.0322588 -0.0207814
BGM0699.250437199 -0.1876035 -0.3585287 -0.8669334 -0.3302434 -0.0585199 -0.0095540 -0.3312754 -0.1395650 -0.5442389 -0.2016117 -0.0897525 0.0310219

Acuracy and MSPE for each trait and repetition:

results_cv_G_BLUP[-c(6:7)] |>
  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 0.3672 1.8078
Stem.D 3 1 0.3468 0.0076
FRY 3 1 0.3266 1.1526
ShY 3 1 0.3210 12.5394
Root.Di 3 1 0.3180 3.3210
StY 3 1 0.3104 0.0702
Plant.Height 3 1 0.2932 0.0074
Nstem.Plant 3 1 0.2722 0.0276
N_Roots 3 1 0.2542 0.8574
HI 3 1 0.2406 11.8996
StC 3 1 0.2212 5.8236
DMC 3 1 0.2200 5.8532

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).

G-BLUP Additive-dominant

In the GBLUP Additive-dominante, we will use the A (additive) and D(dominant) matrix instead of the SNPs matrix. Thus, we will obtain the GEBV directly. Note that we will need to build the G matrix again, since some genotypes were dropped after our filtering.

For this purpose, we will use the sommer package [@Covarrubias-Pazaran_2014]. In the code below, y is for the vector with the means, A is additive covariance matrix and D is dominance covariance matrix 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.

A <- sommer::A.mat(geno-1)
D <- sommer::D.mat(geno-1)

Cross-validation

To prove that the prediction is accurate, we should perform 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 performance, 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_G_BLUP and, contains the results for each fold assignation that we built in the previous step. The second GEBVS_G_BLUP 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(A)) %>%
      mutate(ID = factor(1:nrow(.)),
             IDD_Clone = ID_Clone) %>%
      droplevels()
    
    # Filtrar as linhas de A e D com base em pheno2$ID_Clone
    A1 <-
      A[rownames(A) %in% pheno2$ID_Clone, rownames(A) %in% pheno2$ID_Clone]
    
    D1 <-
      D[rownames(D) %in% pheno2$ID_Clone, rownames(D) %in% pheno2$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"))
        
        GBLUP_D <-
          sommer::mmer(
            fixed,
            random = ~ sommer::vsr(ID_Clone, Gu = A1) +
              sommer::vsr(IDD_Clone, Gu = D1),
            data = train_data,
            rcov = ~ units
          )
        
        # GETGV
        Pred <-
          data.frame(
            AD = GBLUP_D$U$`u:ID_Clone`[[j]],
            DOM =  GBLUP_D$U$`u:IDD_Clone`[[j]],
            Yhat = c(GBLUP_D$U$`u:ID_Clone`[[j]] +
                       GBLUP_D$U$`u:IDD_Clone`[[j]]),
            ID = train_data$ID,
            ID_Clone = train_data$ID_Clone
          ) %>%
          filter(ID %in% fold.list[[z]][[i]])
        
        result1 <-
          tibble(
            AD = Pred$AD,
            DOM =  Pred$DOM,
            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      -144.121   14:48:33      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -146.594   14:48:34      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.615   14:48:36      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.421   14:48:37      0           0
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    3      -143.666   14:48:37      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.739   14:48:39      1           0
    2      -144.667   14:48:39      1           0
    3      -144.622   14:48:39      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.703   14:48:40      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -143.517   14:48:41      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.443   14:47:16      1           0
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    3      -155.426   14:47:16      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -142.753   14:47:17      0           0
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    3      -141.954   14:47:18      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.775   14:47:19      0           0
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    3      -149.431   14:47:19      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.838   14:47:21      0           0
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    3      -151.701   14:47:22      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -146.22   14:47:23      0           0
    2      -145.232   14:47:23      0           0
    3      -144.504   14:47:24      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.3   14:47:26      0           0
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    3      -143.905   14:47:27      1           0
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    6      -143.708   14:47:28      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -146.968   14:47:29      1           0
    2      -146.668   14:47:29      1           0
    3      -146.64   14:47:29      1           0
    4      -146.635   14:47:30      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.768   14:47:31      0           0
    2      -147.346   14:47:31      0           0
    3      -147.153   14:47:31      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.168   14:47:33      0           0
    2      -152.149   14:47:34      1           0
    3      -152.138   14:47:34      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.185   14:47:35      0           0
    2      -151.869   14:47:36      1           0
    3      -151.686   14:47:36      1           1
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    6      -151.601   14:47:37      2           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.555   14:47:38      0           0
    2      -143.893   14:47:38      0           0
    3      -143.597   14:47:39      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.813   14:47:40      0           0
    2      -148.737   14:47:41      1           0
    3      -148.722   14:47:41      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.933   14:47:42      0           0
    2      -152.644   14:47:43      1           0
    3      -152.55   14:47:43      1           0
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    6      -152.519   14:47:44      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.015   14:47:44      0           0
    2      -148.889   14:47:45      1           0
    3      -148.809   14:47:45      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.989   14:47:47      0           0
    2      -147.612   14:47:47      0           0
    3      -147.428   14:47:48      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.707   14:47:49      0           0
    2      -145.298   14:47:50      1           0
    3      -145.199   14:47:50      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.444   14:47:52      1           0
    2      -152.266   14:47:52      1           0
    3      -152.196   14:47:52      1           0
    4      -152.171   14:47:52      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.232   14:47:54      1           0
    2      -147.694   14:47:54      1           0
    3      -147.337   14:47:54      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.955   14:47:56      0           0
    2      -147.378   14:47:56      0           0
    3      -147.046   14:47:57      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.545   14:47:58      0           0
    2      -149.401   14:47:59      1           0
    3      -149.356   14:47:59      1           0
    4      -149.348   14:47:59      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.29   14:48:0      0           0
    2      -147.062   14:48:0      0           0
    3      -146.961   14:48:1      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.657   14:48:2      0           0
    2      -143.567   14:48:2      0           0
    3      -143.114   14:48:3      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.265   14:48:5      1           0
    2      -148.048   14:48:5      1           0
    3      -147.935   14:48:5      1           0
    4      -147.903   14:48:6      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.563   14:48:7      0           0
    2      -152.266   14:48:7      0           0
    3      -152.136   14:48:7      0           0
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    5      -152.091   14:48:8      1           0
    6      -152.089   14:48:8      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.362   14:48:9      0           0
    2      -152.293   14:48:9      0           0
    3      -152.286   14:48:9      0           0
    4      -152.284   14:48:10      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.878   14:47:16      0           1
    2      -117.912   14:47:16      0           1
    3      -117.25   14:47:16      0           1
    4      -117.098   14:47:16      0           1
    5      -117.085   14:47:16      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.576   14:47:17      0           0
    2      -118.118   14:47:17      0           1
    3      -118.075   14:47:17      0           1
    4      -118.065   14:47:17      0           1
    5      -118.064   14:47:17      0           1
    6      -118.064   14:47:17      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.76   14:47:18      1           1
    2      -114.673   14:47:18      1           1
    3      -113.903   14:47:18      1           1
    4      -113.706   14:47:18      1           1
    5      -113.684   14:47:18      1           1
    6      -113.681   14:47:18      1           1
    7      -113.681   14:47:18      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.075   14:47:18      0           1
    2      -119.105   14:47:19      1           1
    3      -118.684   14:47:19      1           1
    4      -118.618   14:47:19      1           1
    5      -118.615   14:47:19      1           1
    6      -118.615   14:47:19      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.539   14:47:19      0           1
    2      -116.852   14:47:19      0           1
    3      -116.1   14:47:20      1           1
    4      -115.713   14:47:20      1           1
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    7      -115.553   14:47:20      1           1
    8      -115.551   14:47:20      1           1
    9      -115.55   14:47:20      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.059   14:47:20      0           0
    2      -118.502   14:47:21      1           1
    3      -118.193   14:47:21      1           1
    4      -118.186   14:47:21      1           1
    5      -118.186   14:47:21      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.951   14:47:21      0           1
    2      -118.948   14:47:21      0           1
    3      -118.487   14:47:21      0           1
    4      -118.343   14:47:22      1           1
    5      -118.321   14:47:22      1           1
    6      -118.317   14:47:22      1           1
    7      -118.317   14:47:22      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.047   14:47:22      0           0
    2      -116.737   14:47:22      0           1
    3      -116.621   14:47:22      0           1
    4      -116.594   14:47:22      0           1
    5      -116.589   14:47:23      1           1
    6      -116.588   14:47:23      1           1
    7      -116.588   14:47:23      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.273   14:47:23      0           1
    2      -115.049   14:47:23      0           1
    3      -114.23   14:47:23      0           1
    4      -114.04   14:47:23      0           1
    5      -114.021   14:47:24      1           1
    6      -114.019   14:47:24      1           1
    7      -114.019   14:47:24      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.004   14:47:24      0           1
    2      -115.455   14:47:24      0           1
    3      -114.871   14:47:24      0           1
    4      -114.671   14:47:25      1           1
    5      -114.631   14:47:25      1           1
    6      -114.622   14:47:25      1           1
    7      -114.62   14:47:25      1           1
    8      -114.62   14:47:25      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -123.498   14:47:25      0           0
    2      -121.841   14:47:25      0           1
    3      -121.38   14:47:26      1           1
    4      -121.337   14:47:26      1           1
    5      -121.332   14:47:26      1           1
    6      -121.331   14:47:26      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.637   14:47:26      0           0
    2      -115.578   14:47:26      0           1
    3      -115.366   14:47:26      0           1
    4      -115.261   14:47:27      1           1
    5      -115.238   14:47:27      1           1
    6      -115.232   14:47:27      1           1
    7      -115.231   14:47:27      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.734   14:47:27      0           1
    2      -117.928   14:47:27      0           1
    3      -117.457   14:47:28      1           1
    4      -117.296   14:47:28      1           1
    5      -117.269   14:47:28      1           1
    6      -117.264   14:47:28      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.251   14:47:28      0           1
    2      -115.89   14:47:28      0           1
    3      -115.216   14:47:29      1           1
    4      -115.107   14:47:29      1           1
    5      -115.1   14:47:29      1           1
    6      -115.099   14:47:29      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -111.567   14:47:29      0           0
    2      -109.074   14:47:30      1           1
    3      -108.546   14:47:30      1           1
    4      -108.328   14:47:30      1           1
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    6      -108.27   14:47:30      1           1
    7      -108.268   14:47:30      1           1
    8      -108.268   14:47:30      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.771   14:47:31      1           1
    2      -117.007   14:47:31      1           1
    3      -116.304   14:47:31      1           1
    4      -116.203   14:47:31      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.002   14:47:32      1           1
    2      -116.699   14:47:32      1           1
    3      -116.243   14:47:32      1           1
    4      -116.103   14:47:32      1           1
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    6      -116.075   14:47:32      1           1
    7      -116.074   14:47:32      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.285   14:47:33      0           1
    2      -119.063   14:47:33      0           1
    3      -118.681   14:47:33      0           1
    4      -118.515   14:47:33      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.113   14:47:34      0           0
    2      -116.867   14:47:34      0           1
    3      -116.783   14:47:34      0           1
    4      -116.78   14:47:34      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.076   14:47:34      0           1
    2      -116.625   14:47:35      1           1
    3      -115.876   14:47:35      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.813   14:47:35      0           1
    2      -118.719   14:47:35      0           1
    3      -118.338   14:47:36      1           1
    4      -118.228   14:47:36      1           1
    5      -118.212   14:47:36      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.368   14:47:36      0           0
    2      -116.481   14:47:36      0           1
    3      -116.337   14:47:37      1           1
    4      -116.337   14:47:37      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.735   14:47:37      0           1
    2      -115.175   14:47:37      0           1
    3      -114.162   14:47:37      0           1
    4      -113.805   14:47:37      0           1
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    6      -113.737   14:47:38      1           1
    7      -113.735   14:47:38      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.889   14:47:38      0           0
    2      -114.343   14:47:38      0           1
    3      -114.22   14:47:38      0           1
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    5      -114.181   14:47:39      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.284   14:47:39      0           1
    2      -119.273   14:47:39      0           1
    3      -118.975   14:47:39      0           1
    4      -118.908   14:47:39      0           1
    5      -118.901   14:47:39      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -110.589   14:47:48      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -110.24   14:47:51      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -109.212   14:47:54      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -107.903   14:47:55      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -106.582   14:47:56      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -110.512   14:47:57      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -109.792   14:47:58      0           0
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    3      -108.994   14:47:58      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -104.581   14:47:59      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -113.552   14:48:0      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -107.943   14:48:1      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -110.202   14:48:2      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -107.548   14:48:3      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -109.442   14:48:4      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -112.523   14:48:5      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.335   14:47:18      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.201   14:47:20      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.312   14:47:22      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.153   14:47:23      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.605   14:47:33      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -159.956   14:47:35      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.776   14:47:42      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.639   14:47:49      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.854   14:47:51      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.073   14:47:31      0           0
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    3      -152.025   14:47:32      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.266   14:47:33      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.622   14:47:35      0           0
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    3      -147.997   14:47:35      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.005   14:47:37      0           0
    2      -155.902   14:47:38      1           0
    3      -155.856   14:47:38      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.796   14:47:40      0           0
    2      -150.495   14:47:40      0           0
    3      -150.419   14:47:40      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.195   14:47:42      1           0
    2      -157.97   14:47:42      1           0
    3      -157.803   14:47:42      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.359   14:47:45      1           0
    2      -153.28   14:47:45      1           0
    3      -153.258   14:47:45      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.553   14:47:47      1           0
    2      -154.527   14:47:47      1           0
    3      -154.52   14:47:47      1           0
    4      -154.519   14:47:47      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.415   14:47:49      1           0
    2      -152.329   14:47:49      1           0
    3      -152.272   14:47:49      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.474   14:47:51      1           0
    2      -154.397   14:47:51      1           0
    3      -154.36   14:47:51      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -156.712   14:47:53      1           0
    2      -156.436   14:47:53      1           0
    3      -156.334   14:47:53      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.524   14:47:55      1           0
    2      -150.753   14:47:55      1           0
    3      -150.464   14:47:55      1           1
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    5      -150.419   14:47:55      1           1
    6      -150.417   14:47:56      2           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.478   14:47:57      1           0
    2      -152.105   14:47:57      1           0
    3      -151.984   14:47:57      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.249   14:47:59      1           0
    2      -152.904   14:47:59      1           0
    3      -152.844   14:47:59      1           0
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    5      -152.825   14:48:0      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.802   14:48:1      1           0
    2      -152.535   14:48:1      1           0
    3      -152.461   14:48:1      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -158.214   14:48:3      0           0
    2      -157.308   14:48:3      0           1
    3      -156.755   14:48:3      0           1
    4      -156.7   14:48:4      1           1
    5      -156.694   14:48:4      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.404   14:48:5      0           0
    2      -154.305   14:48:5      0           0
    3      -154.248   14:48:6      1           0
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    6      -154.215   14:48:6      1           0
    7      -154.214   14:48:7      2           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.538   14:48:7      0           0
    2      -148.72   14:48:7      0           0
    3      -148.208   14:48:8      1           0
    4      -148.037   14:48:8      1           0
    5      -148.014   14:48:8      1           0
    6      -148.011   14:48:8      1           0
    7      -148.011   14:48:8      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.776   14:48:9      0           0
    2      -151.767   14:48:9      0           0
    3      -151.763   14:48:9      0           0
    4      -151.762   14:48:10      1           0
    5      -151.762   14:48:10      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.858   14:47:17      0           1
    2      -117.851   14:47:17      0           1
    3      -117.195   14:47:17      0           1
    4      -117.047   14:47:17      0           1
    5      -117.035   14:47:17      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.662   14:47:18      0           1
    2      -118.628   14:47:18      0           1
    3      -118.228   14:47:18      0           1
    4      -118.124   14:47:18      0           1
    5      -118.112   14:47:18      0           1
    6      -118.11   14:47:18      0           1
    7      -118.11   14:47:18      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.781   14:47:19      0           1
    2      -114.606   14:47:19      0           1
    3      -113.837   14:47:19      0           1
    4      -113.649   14:47:19      0           1
    5      -113.628   14:47:19      0           1
    6      -113.626   14:47:19      0           1
    7      -113.625   14:47:19      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.09   14:47:20      0           1
    2      -119.069   14:47:20      0           1
    3      -118.639   14:47:20      0           1
    4      -118.573   14:47:20      0           1
    5      -118.571   14:47:20      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.539   14:47:20      0           1
    2      -116.773   14:47:21      1           1
    3      -116.025   14:47:21      1           1
    4      -115.648   14:47:21      1           1
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    7      -115.496   14:47:21      1           1
    8      -115.493   14:47:21      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.108   14:47:22      0           0
    2      -118.558   14:47:22      0           1
    3      -118.239   14:47:22      0           1
    4      -118.232   14:47:22      0           1
    5      -118.232   14:47:22      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.01   14:47:22      0           1
    2      -118.933   14:47:22      0           1
    3      -118.481   14:47:23      1           1
    4      -118.34   14:47:23      1           1
    5      -118.318   14:47:23      1           1
    6      -118.315   14:47:23      1           1
    7      -118.314   14:47:23      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.058   14:47:23      0           0
    2      -116.618   14:47:23      0           1
    3      -116.546   14:47:24      1           1
    4      -116.529   14:47:24      1           1
    5      -116.525   14:47:24      1           1
    6      -116.524   14:47:24      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.328   14:47:24      0           1
    2      -115.048   14:47:24      0           1
    3      -114.239   14:47:24      0           1
    4      -114.056   14:47:25      1           1
    5      -114.039   14:47:25      1           1
    6      -114.037   14:47:25      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.037   14:47:25      0           1
    2      -115.417   14:47:25      0           1
    3      -114.836   14:47:26      1           1
    4      -114.642   14:47:26      1           1
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    6      -114.596   14:47:26      1           1
    7      -114.594   14:47:26      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -123.538   14:47:26      0           0
    2      -121.791   14:47:27      1           1
    3      -121.372   14:47:27      1           1
    4      -121.317   14:47:27      1           1
    5      -121.311   14:47:27      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.665   14:47:27      0           0
    2      -115.505   14:47:27      0           1
    3      -115.298   14:47:28      1           1
    4      -115.211   14:47:28      1           1
    5      -115.192   14:47:28      1           1
    6      -115.188   14:47:28      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.742   14:47:28      0           1
    2      -117.894   14:47:29      1           1
    3      -117.427   14:47:29      1           1
    4      -117.272   14:47:29      1           1
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    6      -117.243   14:47:29      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.312   14:47:30      1           1
    2      -115.918   14:47:30      1           1
    3      -115.243   14:47:30      1           1
    4      -115.138   14:47:30      1           1
    5      -115.131   14:47:30      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -111.575   14:47:30      0           1
    2      -110.709   14:47:31      1           1
    3      -109.1   14:47:31      1           1
    4      -108.448   14:47:31      1           1
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    7      -108.266   14:47:31      1           1
    8      -108.265   14:47:31      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.719   14:47:32      0           1
    2      -116.899   14:47:32      0           1
    3      -116.185   14:47:32      0           1
    4      -116.085   14:47:32      0           1
    5      -116.081   14:47:32      0           1
    6      -116.08   14:47:32      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.027   14:47:33      0           1
    2      -116.645   14:47:33      0           1
    3      -116.194   14:47:33      0           1
    4      -116.059   14:47:33      0           1
    5      -116.037   14:47:33      0           1
    6      -116.033   14:47:33      0           1
    7      -116.032   14:47:33      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.294   14:47:34      0           1
    2      -119.057   14:47:34      0           1
    3      -118.674   14:47:34      0           1
    4      -118.51   14:47:34      0           1
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    6      -118.464   14:47:34      0           1
    7      -118.462   14:47:35      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.195   14:47:35      0           0
    2      -116.849   14:47:35      0           1
    3      -116.799   14:47:35      0           1
    4      -116.798   14:47:35      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.127   14:47:36      0           1
    2      -116.618   14:47:36      0           1
    3      -115.873   14:47:36      0           1
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    5      -115.744   14:47:36      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.834   14:47:37      1           1
    2      -118.716   14:47:37      1           1
    3      -118.337   14:47:37      1           1
    4      -118.23   14:47:37      1           1
    5      -118.215   14:47:37      1           1
    6      -118.213   14:47:37      1           1
    7      -118.213   14:47:37      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.344   14:47:38      0           0
    2      -116.393   14:47:38      0           1
    3      -116.262   14:47:38      0           1
    4      -116.262   14:47:38      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.739   14:47:38      0           1
    2      -115.13   14:47:39      1           1
    3      -114.128   14:47:39      1           1
    4      -113.779   14:47:39      1           1
    5      -113.722   14:47:39      1           1
    6      -113.713   14:47:39      1           1
    7      -113.712   14:47:39      1           1
    8      -113.711   14:47:39      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -115.908   14:47:40      0           1
    2      -115.48   14:47:40      0           1
    3      -114.469   14:47:40      0           1
    4      -114.155   14:47:40      0           1
    5      -114.11   14:47:40      0           1
    6      -114.104   14:47:40      0           1
    7      -114.103   14:47:40      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.245   14:47:41      1           1
    2      -119.175   14:47:41      1           1
    3      -118.867   14:47:41      1           1
    4      -118.799   14:47:41      1           1
    5      -118.793   14:47:41      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.064   14:47:42      0           0
    2      -148.6   14:47:42      0           0
    3      -148.467   14:47:43      1           0
    4      -148.459   14:47:43      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.695   14:47:44      0           0
    2      -147.589   14:47:44      0           0
    3      -147.55   14:47:44      0           0
    4      -147.543   14:47:44      0           0
    5      -147.543   14:47:45      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -139.052   14:47:46      1           0
    2      -138.69   14:47:46      1           0
    3      -138.602   14:47:46      1           0
    4      -138.595   14:47:46      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.478   14:47:47      0           0
    2      -144.396   14:47:48      1           0
    3      -144.382   14:47:48      1           0
    4      -144.382   14:47:48      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -142.63   14:47:49      0           0
    2      -142.069   14:47:49      0           1
    3      -142.016   14:47:49      0           1
    4      -141.877   14:47:50      1           1
    5      -141.876   14:47:50      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -140.492   14:47:51      0           0
    2      -140.283   14:47:51      0           0
    3      -140.223   14:47:52      1           0
    4      -140.216   14:47:52      1           0
    5      -140.216   14:47:52      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -141.688   14:47:53      1           0
    2      -141.235   14:47:53      1           0
    3      -141.1   14:47:53      1           0
    4      -141.087   14:47:53      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.799   14:47:54      0           0
    2      -150.494   14:47:55      1           0
    3      -150.376   14:47:55      1           0
    4      -150.359   14:47:55      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.05   14:47:56      0           0
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    3      -144.764   14:47:57      1           0
    4      -144.758   14:47:57      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -146.669   14:47:58      1           0
    2      -146.643   14:47:58      1           0
    3      -146.636   14:47:58      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -142.567   14:47:59      0           0
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    3      -142.29   14:48:0      1           0
    4      -142.267   14:48:0      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -140.993   14:48:1      0           0
    2      -140.545   14:48:1      0           0
    3      -140.394   14:48:2      1           0
    4      -140.374   14:48:2      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.783   14:48:3      0           0
    2      -147.645   14:48:3      0           0
    3      -147.609   14:48:4      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.067   14:48:5      0           0
    2      -144.99   14:48:5      0           0
    3      -144.966   14:48:5      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.936   14:48:7      1           0
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    3      -147.636   14:48:7      1           0
    4      -147.632   14:48:7      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.808   14:48:8      0           0
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    3      -148.655   14:48:9      1           0
    4      -148.654   14:48:9      1           0
    5      -148.654   14:48:9      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -143.909   14:48:10      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -135.304   14:48:11      0           0
    2      -134.063   14:48:11      0           0
    3      -133.658   14:48:11      0           0
    4      -133.611   14:48:11      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -143.23   14:48:12      0           0
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    3      -142.994   14:48:12      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.537   14:48:13      0           0
    2      -148.471   14:48:13      0           0
    3      -148.446   14:48:13      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.79   14:48:14      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -145.277   14:48:15      0           0
    2      -145.105   14:48:15      0           0
    3      -145.066   14:48:15      0           0
    4      -145.06   14:48:16      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -136.041   14:48:16      0           0
    2      -135.37   14:48:16      0           0
    3      -135.196   14:48:17      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.148   14:48:17      0           0
    2      -149.816   14:48:17      0           0
    3      -149.73   14:48:18      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.411   14:48:18      0           0
    2      -146.706   14:48:18      0           1
    3      -146.652   14:48:19      1           1
    4      -146.638   14:48:19      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -154.447   14:47:17      0           0
    2      -153.11   14:47:17      0           1
    3      -152.771   14:47:18      1           1
    4      -152.759   14:47:18      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.506   14:47:19      0           0
    2      -148.779   14:47:19      0           1
    3      -148.663   14:47:19      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.137   14:47:21      1           0
    2      -148.8   14:47:21      1           0
    3      -148.675   14:47:21      1           0
    4      -148.645   14:47:21      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.439   14:47:23      1           0
    2      -152.082   14:47:23      1           0
    3      -151.937   14:47:23      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.194   14:47:25      1           0
    2      -147.113   14:47:25      1           0
    3      -147.095   14:47:25      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.403   14:47:26      0           0
    2      -147.293   14:47:27      1           1
    3      -147.179   14:47:27      1           1
    4      -147.141   14:47:27      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.398   14:47:28      0           0
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    3      -150.707   14:47:29      1           0
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    5      -150.641   14:47:29      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.223   14:47:30      0           0
    2      -149.838   14:47:31      1           0
    3      -149.731   14:47:31      1           0
    4      -149.721   14:47:31      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.259   14:47:32      0           0
    2      -151.675   14:47:33      1           0
    3      -151.449   14:47:33      1           0
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    5      -151.397   14:47:33      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.761   14:47:34      0           0
    2      -152.367   14:47:35      1           0
    3      -152.19   14:47:35      1           0
    4      -152.151   14:47:35      1           0
    5      -152.148   14:47:35      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.479   14:47:36      0           0
    2      -149.03   14:47:37      1           0
    3      -148.888   14:47:37      1           0
    4      -148.87   14:47:37      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.411   14:47:38      0           0
    2      -151.184   14:47:39      1           0
    3      -151.098   14:47:39      1           0
    4      -151.078   14:47:39      1           0
    5      -151.075   14:47:39      1           0
    6      -151.075   14:47:40      2           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.972   14:47:40      0           0
    2      -151.663   14:47:41      1           0
    3      -151.547   14:47:41      1           0
    4      -151.522   14:47:41      1           0
    5      -151.52   14:47:41      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.353   14:47:43      0           0
    2      -148.104   14:47:43      0           0
    3      -148.036   14:47:43      0           0
    4      -148.027   14:47:43      0           0
    5      -148.027   14:47:44      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.994   14:47:44      0           0
    2      -151.515   14:47:45      1           1
    3      -151.119   14:47:45      1           1
    4      -151.113   14:47:45      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.323   14:47:46      0           0
    2      -150.081   14:47:47      1           0
    3      -149.973   14:47:47      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.903   14:47:48      0           0
    2      -146.879   14:47:49      1           1
    3      -146.736   14:47:49      1           1
    4      -146.658   14:47:49      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.642   14:47:50      0           0
    2      -152.092   14:47:50      0           0
    3      -151.919   14:47:51      1           0
    4      -151.892   14:47:51      1           0
    5      -151.89   14:47:51      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.015   14:47:52      0           0
    2      -152.799   14:47:52      0           0
    3      -152.707   14:47:53      1           0
    4      -152.684   14:47:53      1           0
    5      -152.681   14:47:53      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -148.511   14:47:54      0           0
    2      -147.621   14:47:54      0           1
    3      -147.491   14:47:55      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -149.585   14:47:56      0           0
    2      -149.237   14:47:56      0           0
    3      -149.114   14:47:56      0           0
    4      -149.084   14:47:57      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -146.778   14:47:58      0           0
    2      -146.473   14:47:58      0           0
    3      -146.446   14:47:58      0           0
    4      -146.445   14:47:58      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.006   14:47:59      0           0
    2      -149.077   14:48:0      1           1
    3      -148.985   14:48:0      1           1
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    5      -148.879   14:48:0      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.991   14:48:1      0           0
    2      -153.511   14:48:2      1           0
    3      -153.307   14:48:2      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.417   14:48:4      1           0
    2      -150.236   14:48:4      1           0
    3      -150.175   14:48:4      1           0
    4      -150.166   14:48:4      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.211   14:47:18      1           0
    2      -152.041   14:47:18      1           0
    3      -151.983   14:47:18      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.042   14:47:19      0           0
    2      -146.268   14:47:20      1           0
    3      -145.961   14:47:20      1           0
    4      -145.909   14:47:20      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.433   14:47:21      0           0
    2      -150.966   14:47:22      1           0
    3      -150.82   14:47:22      1           0
    4      -150.803   14:47:22      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.054   14:47:23      0           0
    2      -152.975   14:47:23      0           0
    3      -152.944   14:47:24      1           0
    4      -152.939   14:47:24      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.104   14:47:25      0           0
    2      -145.744   14:47:26      1           0
    3      -145.348   14:47:26      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.786   14:47:27      0           0
    2      -151.73   14:47:28      1           0
    3      -151.707   14:47:28      1           0
    4      -151.703   14:47:28      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.017   14:47:30      1           0
    2      -152.695   14:47:30      1           0
    3      -152.581   14:47:30      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -146.618   14:47:32      0           0
    2      -144.897   14:47:32      0           0
    3      -144.324   14:47:33      1           0
    4      -144.249   14:47:33      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.2   14:47:34      0           0
    2      -146.673   14:47:35      1           0
    3      -146.459   14:47:35      1           0
    4      -146.422   14:47:35      1           0
    5      -146.42   14:47:35      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.11   14:47:36      0           0
    2      -152.844   14:47:37      1           0
    3      -152.77   14:47:37      1           1
    4      -152.769   14:47:37      1           1
    5      -152.758   14:47:38      2           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.912   14:47:39      1           0
    2      -150.611   14:47:39      1           0
    3      -150.472   14:47:39      1           0
    4      -150.44   14:47:40      2           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.401   14:47:41      0           0
    2      -152.848   14:47:41      0           0
    3      -152.71   14:47:41      0           0
    4      -152.694   14:47:42      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.643   14:47:43      0           0
    2      -151.186   14:47:43      0           0
    3      -150.937   14:47:44      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.118   14:47:46      1           0
    2      -149.854   14:47:46      1           0
    3      -149.744   14:47:46      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.307   14:47:48      0           0
    2      -146.753   14:47:48      0           0
    3      -146.599   14:47:48      0           0
    4      -146.582   14:47:49      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.353   14:47:50      0           0
    2      -151.304   14:47:50      0           0
    3      -151.283   14:47:50      0           0
    4      -151.278   14:47:51      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -155.221   14:47:52      1           0
    2      -155.197   14:47:52      1           0
    3      -155.186   14:47:52      1           0
    4      -155.183   14:47:52      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.666   14:47:53      0           0
    2      -152.594   14:47:54      1           0
    3      -152.564   14:47:54      1           0
    4      -152.559   14:47:54      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -143.474   14:47:55      0           0
    2      -140.796   14:47:55      0           0
    3      -139.765   14:47:56      1           0
    4      -139.61   14:47:56      1           0
    5      -139.605   14:47:56      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -147.332   14:47:57      0           0
    2      -145.402   14:47:57      0           1
    3      -144.923   14:47:58      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -151.254   14:47:59      0           0
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    3      -150.813   14:48:0      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -150.513   14:48:1      0           0
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    3      -149.622   14:48:2      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -144.043   14:48:3      0           0
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    3      -142.582   14:48:4      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -153.865   14:48:5      0           0
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    3      -153.621   14:48:6      1           0
    4      -153.603   14:48:6      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -152.631   14:48:7      0           0
    2      -152.528   14:48:7      0           0
    3      -152.489   14:48:7      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.602   14:48:9      1           0
    2      -120.595   14:48:9      1           0
    3      -120.249   14:48:9      1           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.157   14:48:9      0           0
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    3      -120.787   14:48:10      1           0
    4      -120.765   14:48:10      1           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.9   14:48:10      0           0
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    3      -120.05   14:48:10      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.888   14:48:11      0           0
    2      -119.159   14:48:11      0           1
    3      -118.89   14:48:11      0           1
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.098   14:48:11      0           0
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    3      -120.098   14:48:11      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.758   14:48:12      0           0
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iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.437   14:48:12      0           0
    2      -118.889   14:48:12      0           0
    3      -118.727   14:48:12      0           0
    4      -118.702   14:48:13      1           0
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    6      -118.701   14:48:13      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.966   14:48:13      0           0
    2      -116.478   14:48:13      0           0
    3      -116.435   14:48:13      0           0
    4      -116.432   14:48:13      0           0
    5      -116.432   14:48:13      0           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -123.874   14:48:13      0           0
    2      -122.987   14:48:14      1           1
    3      -122.63   14:48:14      1           1
    4      -122.625   14:48:14      1           1
    5      -122.624   14:48:14      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -118.917   14:48:14      0           0
    2      -118.86   14:48:14      0           0
    3      -118.85   14:48:14      0           0
    4      -118.848   14:48:14      0           0
    5      -118.848   14:48:14      0           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.976   14:48:15      1           0
    2      -121.301   14:48:15      1           1
    3      -120.942   14:48:15      1           1
    4      -120.918   14:48:15      1           1
    5      -120.916   14:48:15      1           1
    6      -120.916   14:48:15      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.504   14:48:15      0           0
    2      -117.461   14:48:15      0           0
    3      -117.44   14:48:15      0           0
    4      -117.432   14:48:15      0           0
    5      -117.43   14:48:15      0           0
    6      -117.43   14:48:16      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.798   14:48:16      0           1
    2      -119.663   14:48:16      0           1
    3      -118.856   14:48:16      0           1
    4      -118.8   14:48:16      0           1
    5      -118.8   14:48:16      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -122.594   14:48:16      0           0
    2      -121.787   14:48:16      0           0
    3      -121.537   14:48:16      0           0
    4      -121.507   14:48:17      1           0
    5      -121.506   14:48:17      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.665   14:48:17      0           0
    2      -119.203   14:48:17      0           0
    3      -119.087   14:48:17      0           0
    4      -119.07   14:48:17      0           0
    5      -119.068   14:48:17      0           0
    6      -119.068   14:48:17      0           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.129   14:48:17      0           0
    2      -119.727   14:48:18      1           0
    3      -119.63   14:48:18      1           0
    4      -119.616   14:48:18      1           0
    5      -119.615   14:48:18      1           0
    6      -119.615   14:48:18      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -117.779   14:48:18      0           0
    2      -116.939   14:48:18      0           1
    3      -116.739   14:48:18      0           1
    4      -116.704   14:48:18      0           1
    5      -116.703   14:48:18      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -123.714   14:48:19      1           0
    2      -123.15   14:48:19      1           0
    3      -122.846   14:48:19      1           0
    4      -122.735   14:48:19      1           0
    5      -122.711   14:48:19      1           0
    6      -122.706   14:48:19      1           1
    7      -122.705   14:48:19      1           1
    8      -122.705   14:48:19      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -119.257   14:48:19      0           0
    2      -118.861   14:48:19      0           0
    3      -118.774   14:48:20      1           0
    4      -118.757   14:48:20      1           0
    5      -118.756   14:48:20      1           0
    6      -118.756   14:48:20      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.162   14:48:20      0           0
    2      -119.774   14:48:20      0           0
    3      -119.716   14:48:20      0           0
    4      -119.699   14:48:20      0           0
    5      -119.697   14:48:20      0           0
    6      -119.696   14:48:20      0           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -122.876   14:48:21      1           0
    2      -122.504   14:48:21      1           0
    3      -122.318   14:48:21      1           0
    4      -122.264   14:48:21      1           0
    5      -122.257   14:48:21      1           0
    6      -122.256   14:48:21      1           0
iteration    LogLik     wall    cpu(sec)   restrained
    1      -120.11   14:48:21      0           0
    2      -119.511   14:48:21      0           0
    3      -119.348   14:48:21      0           1
    4      -119.32   14:48:21      0           1
    5      -119.319   14:48:21      0           1
    6      -119.319   14:48:22      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -116.852   14:48:22      0           0
    2      -116.144   14:48:22      0           1
    3      -116.043   14:48:22      0           1
    4      -116.017   14:48:22      0           1
    5      -116.017   14:48:22      0           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -122.171   14:48:22      0           0
    2      -121.793   14:48:22      0           0
    3      -121.563   14:48:23      1           0
    4      -121.45   14:48:23      1           1
    5      -121.412   14:48:23      1           1
    6      -121.412   14:48:23      1           1
iteration    LogLik     wall    cpu(sec)   restrained
    1      -121.214   14:48:23      0           0
    2      -120.166   14:48:23      0           1
    3      -120.023   14:48:23      0           1
    4      -120.023   14:48:23      0           1
# Combinar todos os resultados da validação cruzada em uma única estrutura
results_cv_DOM <- do.call(rbind, results_list)

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

Results

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

GEBVS_DOM |>
  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 0.4396103 1.2603202 1.8005941 0.4638549 0.1626190 0.0185335 0.4637511 0.9340454 1.8777402 0.4522034 0.3290377 0.0528354
BGM0368.250437186 0.6182988 -0.4875003 0.7386014 0.0559251 -0.0222395 -0.0196118 -0.4864237 -0.6736069 -3.0870178 0.6243157 -0.0475617 -0.0425895
BGM0424.250437187 0.0740729 -0.1630034 0.0312075 -0.1574062 -0.0537993 -0.0067990 -0.3724140 -0.4054880 -1.2925178 0.0923974 -0.0105394 -0.0157553
BGM0611.250437190 -0.8635318 -0.1995060 -0.1799827 0.0135153 0.0344337 -0.0528794 -0.1603825 0.0008162 -0.7913598 -0.8565289 -0.0663013 -0.0707294
BGM0652.250437861 -0.1398403 -0.1107219 -0.4450446 -0.1098286 0.0281517 -0.0297611 -0.3908125 -0.1412208 -0.0367098 -0.1389182 -0.0437859 -0.0152233
BGM0699.250437199 -0.1875252 -0.2716831 -0.5937424 -0.2782195 -0.0560848 -0.0054131 -0.3179775 -0.1420196 -0.7187327 -0.2015375 -0.0688637 0.0107218

Acuracy and MSPE for each trait and repetition:

results_cv_DOM[-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 0.3624 1.8148
Stem.D 3 1 0.3534 0.0076
ShY 3 1 0.3216 12.5440
FRY 3 1 0.3210 1.1612
Root.Di 3 1 0.3150 3.3284
StY 3 1 0.2986 0.0710
Plant.Height 3 1 0.2956 0.0074
Nstem.Plant 3 1 0.2640 0.0278
N_Roots 3 1 0.2602 0.8548
HI 3 1 0.2308 11.9826
StC 3 1 0.2212 5.8236
DMC 3 1 0.2200 5.8532

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   Matrix_1.6-1      lifecycle_1.0.4  
[13] compiler_4.3.3    git2r_0.35.0      munsell_0.5.1     codetools_0.2-20 
[17] httpuv_1.6.15     htmltools_0.5.8.1 sass_0.4.9        yaml_2.3.10      
[21] crayon_1.5.3      later_1.4.1       pillar_1.10.1     jquerylib_0.1.4  
[25] MASS_7.3-60.0.1   cachem_1.1.0      parallelly_1.41.0 tidyselect_1.2.1 
[29] digest_0.6.37     stringi_1.8.4     sommer_4.3.6      listenv_0.9.1    
[33] rprojroot_2.0.4   fastmap_1.2.0     grid_4.3.3        colorspace_2.1-1 
[37] cli_3.6.3         magrittr_2.0.3    withr_3.0.2       scales_1.3.0     
[41] promises_1.3.2    timechange_0.3.0  rmarkdown_2.29    globals_0.16.3   
[45] workflowr_1.7.1   hms_1.1.3         evaluate_1.0.3    knitr_1.49       
[49] viridisLite_0.4.2 rlang_1.1.4       Rcpp_1.0.14       glue_1.8.0       
[53] xml2_1.3.6        svglite_2.1.3     rstudioapi_0.17.1 jsonlite_1.8.9   
[57] R6_2.5.1          systemfonts_1.1.0 fs_1.6.5         

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