Combined cluster analysis

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Last updated: 2023-12-18

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Knit directory: bgc_argo_r_argodata/analysis/

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Tasks

Carried out cluster analysis having first set options and determined the data sets on which that cluster analysis should be based on.

Set directories

location of pre-prepared data

Category options

What category of data is the cluster analysis related to

# opt_category
opt_category <- "bgc_doxy"

Analysis options

Define options that are used to determine the nature of the cluster analysis that is carried out.

# Options

# opt_num_clusters
# How many clusters are used in the cluster analysis for each depth 1 (600 m), 2 (1000 m) and 3 (1500 m)
opt_num_clusters_min <- c(8, 8, 4)
opt_num_clusters_max <- c(8, 8, 5)
# Which profile range is used
opt_profile_range <- 3

# options relating to cluster analysis
opt_n_start <- 15
opt_max_iterations <- 500
opt_n_clusters <- 14 # Max number of clusters to try when determining optimal number of clusters

# opt_extreme_determination
# 1 - based on the trend of de-seasonal data - we believe this results in more summer extremes where variation tend to be greater.
# 2 - based on the trend of de-seasonal data by month. grouping is by lat, lon and month.
opt_extreme_determination <- 2

# Options associated with profiles under surface extreme conditions
extreme_type <- c('L', 'N', 'H')
opt_num_clusters_ext_min <- c(4, 4, 4)
opt_num_clusters_ext_max <- c(5, 5, 5)

# Option related to normalising the anomaly profiles.
# TRUE - anomaly profiles are normalised by the surface anomaly. Every depth anomaly is divided by the surface anomaly.
#      - The is only carried out for profiles where the abs(surface temp) > 1.
#      - This analysis is carried out in addition to the analysis on base anomaly profiles.  
# FALSE - The normalisation process is not carried out. 
opt_norm_anomaly <- TRUE

theme_set(theme_bw())

map <-
  read_rds(paste(path_emlr_utilities,
                 "map_landmask_WOA18.rds",
                 sep = ""))

Preparation

Prepare data for cluster analysis

if (opt_category == "bgc_doxy") {
  
  # ---------------------------------------------------------------------------------------------
  # spatial restrictions
  # ---------------------------------------------------------------------------------------------
  # global
  opt_lat_min <- -90
  opt_lat_max <- 90
  opt_lon_min <- 20
  opt_lon_max <- 380
  
  # Mapping latitude limits
  opt_map_lat_limit <- c(-85, 85) # global
  
  # ---------------------------------------------------------------------------------------------
  # read data - bgc oxygen must have a ph profile
  # ---------------------------------------------------------------------------------------------
  # read data, applying geographical limits and standardize field names.
  anomaly_va <-
    read_rds(file = paste0(path_argo_preprocessed, "/doxy_anomaly_va.rds")) %>%
    filter (lat >= opt_lat_min &
            lat <= opt_lat_max &
            lon >= opt_lon_min &
            lon <= opt_lon_max) %>%
    select(file_id,
           date,
           year,
           month,
           lat,
           lon,
           profile_range,
           depth, 
           prof_measure = doxy,
           clim_measure = clim_doxy,
           anomaly
           )
  
  # ---------------------------------------------------------------------------------------------
  # Associated data restrictions and formatting
  # ---------------------------------------------------------------------------------------------
  # What is the max depth of each profile_range
  opt_max_depth <- c(600, 1000, 1500)
  
  # opt_measure_label, opt_xlim and opt_xbreaks are associated with formatting
  opt_measure_label <- expression("dissolved oxygen anomaly ( µmol kg"^"-1"~")")
  opt_xlim <- c(-40, 40)
  opt_xbreaks <- c(-40, -20, 0, 20, 40)

  # adjusted to be in scale -1 to 1
  opt_measure_label_adjusted <- "adjusted oxygen anomaly"
  opt_xlim_adjusted <- c(-1, 1)
  opt_xbreaks_adjusted <- c(-1.0, -0.5, 0, 0.5, 1.0)

  # Under extreme analysis
  opt_extreme_analysis <- FALSE
  
}

Data preparation

# select profile based on profile_range and the appropriate max depth
anomaly_va <- anomaly_va %>% 
  filter(profile_range == opt_profile_range & depth <= opt_max_depth[opt_profile_range])

# Simplified table ready to pivot
anomaly_va_id <- anomaly_va %>%
  select(file_id,
         depth,
         anomaly,
         year, 
         month, 
         lat, 
         lon)

# wide table with each depth becoming a column
anomaly_va_wide <- anomaly_va_id %>%
  select(file_id, depth, anomaly) %>%
  pivot_wider(names_from = depth, values_from = anomaly)

# Drop any rows with missing values N/A caused by gaps in climatology data
anomaly_va_wide <- anomaly_va_wide %>% 
  drop_na()

# Table for cluster analysis
points <- anomaly_va_wide %>%
  column_to_rownames(var = "file_id")

# normalisation?
if (opt_norm_anomaly) {
  
  # Get the maximum anomaly for each profile - the normalisation will then fit -1 to 1
  anomaly_va_id_normalised <- anomaly_va_id %>%
    group_by(file_id) %>%
    mutate(abs_ma = max(abs(anomaly))) %>%
    ungroup()
  
  # divide each anomaly by the maximum anomaly
  anomaly_va_id_normalised <- anomaly_va_id_normalised %>%
    mutate(anomaly = anomaly/abs_ma)
    
  # wide table with each depth becoming a column
  anomaly_va_wide <- anomaly_va_id_normalised %>%
    select(file_id, depth, anomaly) %>%
    pivot_wider(names_from = depth, values_from = anomaly)
  
  # Drop any rows with missing values N/A caused by gaps in climatology data
  anomaly_va_wide <- anomaly_va_wide %>% 
    drop_na()
  
  # Table for cluster analysis
  points_normalised <- anomaly_va_wide %>%
    column_to_rownames(var = "file_id")

}

Cluster analysis

Cluster means

Based on all floats regardless of surface condition.

for (iType in 1:2) {
  for (inum_clusters in opt_num_clusters_min[opt_profile_range]:opt_num_clusters_max[opt_profile_range]) {
    if (iType == 1) {

      set.seed(1)
      kclusts <-
        tibble(k = inum_clusters) %>%
        mutate(kclust = map(k, ~ kmeans(points, .x, iter.max = opt_max_iterations, nstart = opt_n_start)),
          tidied = map(kclust, tidy),
          glanced = map(kclust, glance),
          augmented = map(kclust, augment, points)
        )
      
      profile_id <-
        kclusts %>%
        unnest(cols = c(augmented)) %>%
        select(file_id = .rownames,
               cluster = .cluster) %>%
        mutate(file_id = as.numeric(file_id),
               cluster = as.character(cluster))
      
      # Add cluster to anomaly_va_id
      anomaly_cluster <-
        full_join(anomaly_va_id, profile_id)
      
      # Add profile_type field
      anomaly_cluster <- anomaly_cluster %>%
        mutate(profile_type = 'base')
      
      # Check null clusters
      anomaly_cluster <- anomaly_cluster %>%
        filter(!is.na(cluster))
      
      # Create table to be used for later analysis and Set the number of clusters field
      if (!exists('anomaly_cluster_all')) {
        anomaly_cluster_all <- anomaly_cluster %>%
          mutate(num_clusters = inum_clusters)
      } else {
        anomaly_cluster_all <-
          rbind(
            anomaly_cluster_all,
            anomaly_cluster %>%
              mutate(num_clusters = inum_clusters)
          )
      }
      
    } else if (iType == 2 & opt_norm_anomaly) {

      set.seed(1)
      kclusts <-
        tibble(k = inum_clusters) %>%
        mutate(kclust = map(k, ~ kmeans(points_normalised, .x, iter.max = opt_max_iterations, nstart = opt_n_start)),
          tidied = map(kclust, tidy),
          glanced = map(kclust, glance),
          augmented = map(kclust, augment, points)
        )
      
      profile_id <-
        kclusts %>%
        unnest(cols = c(augmented)) %>%
        select(file_id = .rownames,
               cluster = .cluster) %>%
        mutate(file_id = as.numeric(file_id),
               cluster = as.character(cluster))
      
      # Add cluster to anomaly_va
      anomaly_cluster_norm <-
        full_join(anomaly_va_id_normalised %>% select(-c(abs_ma)) ,
                  profile_id)
      
      # Add profile_type field
      anomaly_cluster_norm <- anomaly_cluster_norm %>%
        mutate(profile_type = 'adjusted')
      
      # Check null clusters
      anomaly_cluster_norm <- anomaly_cluster_norm %>%
        filter(!is.na(cluster))
      
      # Create table to be used for later analysis and Set the number of clusters field
      if (!exists('anomaly_cluster_all')) {
        anomaly_cluster_all <- anomaly_cluster_norm %>%
          mutate(num_clusters = inum_clusters)
      } else {
        anomaly_cluster_all <-
          rbind(
            anomaly_cluster_all,
            anomaly_cluster_norm %>%
              mutate(num_clusters = inum_clusters)
          )
      }
      
    }
    
  }
}

# Prepare to plot cluster mean
anomaly_cluster_mean <- anomaly_cluster_all %>%
  group_by(profile_type, num_clusters, cluster, depth) %>%
  summarise(
    count_cluster = n(),
    anomaly_mean = mean(anomaly, na.rm = TRUE),
    anomaly_sd = sd(anomaly, na.rm = TRUE)
  ) %>%
  ungroup()

anomaly_cluster_mean_year <- anomaly_cluster_all %>%
  group_by(profile_type, num_clusters, cluster, depth, year) %>%
  summarise(
    count_cluster = n(),
    anomaly_mean = mean(anomaly, na.rm = TRUE),
    anomaly_sd = sd(anomaly, na.rm = TRUE)
  ) %>%
  ungroup()

anomaly_year_mean <- anomaly_cluster_all %>%
  group_by(profile_type, num_clusters, cluster, year) %>%
  summarise(
    count_cluster = n(),
    anomaly_mean = mean(anomaly, na.rm = TRUE),
    anomaly_sd = sd(anomaly, na.rm = TRUE)
  ) %>%
  ungroup()

anomaly_year_mean <- anomaly_year_mean %>%
  group_by(profile_type, num_clusters, year) %>%
  summarise(anomaly_mean = mean(anomaly_mean, na.rm = TRUE)) %>%
  ungroup ()

# Determine profile count by cluster and year
# Count the measurements
cluster_by_year <- anomaly_cluster_all %>% 
  count(profile_type, num_clusters, file_id, cluster, year,
        name = "count_cluster")

# Convert to profiles
cluster_by_year <- cluster_by_year %>% 
  count(profile_type, num_clusters, cluster, year,
        name = "count_cluster")

# total of each type of cluster
cluster_count <- cluster_by_year %>%
  group_by(profile_type, num_clusters, cluster) %>% 
  summarise(count_profiles = sum(count_cluster)) %>%
  ungroup()

anomaly_cluster_mean <- left_join(anomaly_cluster_mean, cluster_count)

Base profiles

# create figure of cluster mean profiles
anomaly_cluster_mean %>%
  filter (profile_type == "base") %>%
  group_split(profile_type, num_clusters) %>%
  map(
    ~ ggplot(data = .x,) +
      geom_path(aes(x = anomaly_mean,
                    y = depth)) +
      geom_ribbon(
        aes(
          xmax = anomaly_mean + anomaly_sd,
          xmin = anomaly_mean - anomaly_sd,
          y = depth
        ),
        alpha = 0.2
      ) +
      geom_vline(xintercept = 0) +
      scale_y_reverse() +
      facet_wrap(~ paste0(cluster, " (", formatC(count_profiles, big.mark=",") , ")")) +
      coord_cartesian(xlim = opt_xlim) +
      scale_x_continuous(breaks = opt_xbreaks) +
      labs(
        title = paste0(
          'Overall mean anomaly profiles by cluster \n',
          'type = ', unique(.x$profile_type), ', ', 
          'num clusters = ', unique(.x$num_clusters)
        ),
        x = opt_measure_label,
        y = 'depth (m)'
      )
  )

[[1]]

[[2]]

Adjusted profiles

if (opt_norm_anomaly) {

  # repeat for adjusted profiles profiles
  anomaly_cluster_mean %>%
    filter (profile_type == "adjusted") %>%
    group_split(profile_type, num_clusters) %>%
    map(
      ~ ggplot(data = .x,) +
        geom_path(aes(x = anomaly_mean,
                      y = depth)) +
        geom_ribbon(
          aes(
            xmax = anomaly_mean + anomaly_sd,
            xmin = anomaly_mean - anomaly_sd,
            y = depth
          ),
          alpha = 0.2
        ) +
        geom_vline(xintercept = 0) +
        scale_y_reverse() +
        facet_wrap(~ paste0(cluster, " (", formatC(count_profiles, big.mark=",") , ")")) +
        coord_cartesian(xlim = opt_xlim_adjusted) +
        scale_x_continuous(breaks = opt_xbreaks_adjusted) +
        labs(
          title = paste0(
            'Overall mean anomaly profiles by cluster \n',
            'type = ', unique(.x$profile_type), ', ', 
            'num clusters = ', unique(.x$num_clusters)
          ),
          x = opt_measure_label_adjusted,
          y = 'depth (m)'
        )
    )
}

[[1]]

[[2]]

Cluster mean by year

# cluster means by year
anomaly_cluster_mean_year %>%
  filter (profile_type == "base") %>%
  mutate(year = as.factor(year)) %>%
  group_split(profile_type, num_clusters) %>%
  map(
    ~ ggplot(data = .x, ) +
      geom_path(aes(
        x = anomaly_mean,
        y = depth,
        col = year
      )) +
      geom_vline(xintercept = 0) +
      scale_y_reverse() +
      facet_wrap(~ cluster) +
      coord_cartesian(xlim = opt_xlim) +
      scale_x_continuous(breaks = opt_xbreaks) +
      scale_color_viridis_d() +
      labs(
        title = paste0(
          'Overall mean anomaly profiles by cluster \n',
          'type = ', unique(.x$profile_type), ', ', 
          'num clusters = ', unique(.x$num_clusters)
        ),
        x = opt_measure_label,
        y = 'depth (m)'
      )
  )

[[1]]

[[2]]

Adjusted profiles

if (opt_norm_anomaly) {
  
  # Repeat for adjusted profiles
  anomaly_cluster_mean_year %>%
    filter (profile_type == "adjusted") %>%
    mutate(year = as.factor(year)) %>%
    group_split(profile_type, num_clusters) %>%
    map(
      ~ ggplot(data = .x, ) +
        geom_path(aes(
          x = anomaly_mean,
          y = depth,
          col = year
        )) +
        geom_vline(xintercept = 0) +
        scale_y_reverse() +
        facet_wrap(~ cluster) +
        coord_cartesian(xlim = opt_xlim_adjusted) +
        scale_x_continuous(breaks = opt_xbreaks_adjusted) +
        scale_color_viridis_d() +
        labs(
          title = paste0(
            'Overall mean anomaly profiles by cluster \n',
            'type = ', unique(.x$profile_type), ', ', 
            'num clusters = ', unique(.x$num_clusters)
          ),
          x = opt_measure_label_adjusted,
          y = 'depth (m)'
        )
    )
  
}

[[1]]

[[2]]

Cluster by year

count of each cluster by year

year_min <- min(cluster_by_year$year)
year_max <- max(cluster_by_year$year)

# create figure
cluster_by_year %>%
  filter (profile_type == "base") %>%
  group_split(profile_type, num_clusters) %>%
  map(
    ~ ggplot(data = .x, aes(
        x = year,
        y = count_cluster,
        col = cluster,
        group = cluster
      )) +
      geom_point() +
      geom_line() +
      scale_x_continuous(breaks = seq(year_min, year_max, 2)) +
      scale_color_brewer(palette = 'Dark2') +
      labs(
        title = paste0(
          'Count of profiles by year and cluster \n',
          'type = ', unique(.x$profile_type), ', ', 
          'num clusters = ', unique(.x$num_clusters)
        ),
        x = 'year',
        y = 'number of profiles',
        col = 'cluster'
      )
  )

[[1]]

[[2]]

Adjusted profiles

if (opt_norm_anomaly) {

  year_min <- min(cluster_by_year$year)
  year_max <- max(cluster_by_year$year)
  
  # create figure
  cluster_by_year %>%
    filter (profile_type == "adjusted") %>%
    group_split(profile_type, num_clusters) %>%
    map(
      ~ ggplot(data = .x, aes(
          x = year,
          y = count_cluster,
          col = cluster,
          group = cluster
        )) +
        geom_point() +
        geom_line() +
        scale_x_continuous(breaks = seq(year_min, year_max, 2)) +
        scale_color_brewer(palette = 'Dark2') +
        labs(
          title = paste0(
            'Count of profiles by year and cluster \n',
            'type = ', unique(.x$profile_type), ', ', 
            'num clusters = ', unique(.x$num_clusters)
          ),
          x = 'year',
          y = 'number of profiles',
          col = 'cluster'
        )
    )
  
}

[[1]]

[[2]]

Cluster by month

count of each cluster by month of year

# Determine profile count by cluster and year
# Count the measurements
cluster_by_year <- anomaly_cluster_all %>% 
  count(profile_type, num_clusters, file_id, cluster, month,
        name = "count_cluster")

# Convert to profiles
cluster_by_year <- cluster_by_year %>% 
  count(profile_type, num_clusters, cluster, month,
        name = "count_cluster")

# create figure
cluster_by_year %>%
  filter (profile_type == "base") %>%
  group_split(profile_type, num_clusters) %>%
  map(
    ~ ggplot(
      data = .x,
      aes(
        x = month,
        y = count_cluster,
        col = cluster,
        group = cluster
      )
    ) +
      geom_point() +
      geom_line() +
      scale_x_continuous(breaks = seq(1, 12, 2)) +
      scale_color_brewer(palette = 'Dark2') +
      labs(
        title = paste0(
          'Count of profiles by month and cluster \n',
          'type = ', unique(.x$profile_type), ', ', 
          'num clusters = ', unique(.x$num_clusters)
        ),
        x = 'month',
        y = 'number of profiles',
        col = 'cluster'
      )
  )

[[1]]

[[2]]

Adjusted profiles

if (opt_norm_anomaly) {

  # create figure
  cluster_by_year %>%
    filter (profile_type == "adjusted") %>%
    group_split(profile_type, num_clusters) %>%
    map(
      ~ ggplot(
        data = .x,
        aes(
          x = month,
          y = count_cluster,
          col = cluster,
          group = cluster
        )
      ) +
        geom_point() +
        geom_line() +
        scale_x_continuous(breaks = seq(1, 12, 2)) +
        scale_color_brewer(palette = 'Dark2') +
        labs(
          title = paste0(
            'Count of profiles by month and cluster \n',
            'type = ', unique(.x$profile_type), ', ', 
            'num clusters = ', unique(.x$num_clusters)
          ),
          x = 'month',
          y = 'number of profiles',
          col = 'cluster'
        )
    )
  
}

[[1]]

[[2]]

Cluster spatial

location of each cluster on map, spatial analysis

# create figure
anomaly_cluster_all %>%
  filter (profile_type == "base") %>%
  group_split(profile_type, num_clusters) %>%
  map(
    ~ map +
      geom_tile(data = .x,
                aes(
                  x = lon,
                  y = lat,
                  fill = cluster
                )) +
      lims(y = opt_map_lat_limit) +
      scale_fill_brewer(palette = 'Dark2') +
      labs(
        title = paste0(
          'cluster spatial distribution \n',
          'type = ', unique(.x$profile_type), ', ', 
          'num clusters = ', unique(.x$num_clusters)
        ),
      )
  )

[[1]]

[[2]]

Adjusted profiles

if (opt_norm_anomaly) {

  # create figure
  anomaly_cluster_all %>%
    filter (profile_type == "adjusted") %>%
    group_split(profile_type, num_clusters) %>%
    map(
      ~ map +
        geom_tile(data = .x,
                  aes(
                    x = lon,
                    y = lat,
                    fill = cluster
                  )) +
        lims(y = opt_map_lat_limit) +
        scale_fill_brewer(palette = 'Dark2') +
        labs(
          title = paste0(
            'cluster spatial distribution \n',
            'type = ', unique(.x$profile_type), ', ', 
            'num clusters = ', unique(.x$num_clusters)
          ),
        )
    )
  
}

[[1]]

[[2]]

Cluster spatial counts

count of measurements for each cluster on separate maps, spatial analysis

# Count profiles    
cluster_by_location <- anomaly_cluster_all %>%
  count(profile_type, num_clusters, file_id, lat, lon, cluster,
        name = "count_cluster")

# # Add cluster counts to 
cluster_by_location <- left_join(cluster_by_location, cluster_count)
    
# create figure
cluster_by_location %>%
  filter (profile_type == "base") %>%
  group_split(profile_type, num_clusters) %>%
  map(
    ~ map +
      geom_tile(data = .x %>%
                  count(lat, lon, cluster, count_profiles),
                aes(
                  x = lon,
                  y = lat,
                  fill = n
                )) +
      lims(y = opt_map_lat_limit) +
      scale_fill_gradient(low = "blue",
                          high = "red",
                          trans = "log10") +
      facet_wrap(~ paste0(cluster, " (", formatC(count_profiles, big.mark=",") , ")"), ncol = 2) +
      labs(
        title = paste0(
          'cluster spatial distribution \n',
          'type = ', unique(.x$profile_type), ', ', 
          'num clusters = ', unique(.x$num_clusters)
        )
      )
  )

[[1]]

[[2]]

Adjusted profiles

if (opt_norm_anomaly) {

  # create figure
  cluster_by_location %>%
    filter (profile_type == "adjusted") %>%
    group_split(profile_type, num_clusters) %>%
    map(
      ~ map +
        geom_tile(data = .x %>%
                    count(lat, lon, cluster, count_profiles),
                  aes(
                    x = lon,
                    y = lat,
                    fill = n
                  )) +
        lims(y = opt_map_lat_limit) +
        scale_fill_gradient(low = "blue",
                            high = "red",
                            trans = "log10") +
        facet_wrap(~ paste0(cluster, " (", formatC(count_profiles, big.mark=",") , ")"), ncol = 2) +
        labs(
          title = paste0(
            'cluster spatial distribution \n',
            'type = ', unique(.x$profile_type), ', ', 
            'num clusters = ', unique(.x$num_clusters)
          )
        )
    )
  
}

[[1]]

[[2]]

Session information

sessionInfo()

R version 4.2.2 (2022-10-31)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.5

Matrix products: default
BLAS:   /usr/local/R-4.2.2/lib64/R/lib/libRblas.so
LAPACK: /usr/local/R-4.2.2/lib64/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

other attached packages:
 [1] yardstick_1.2.0    workflowsets_1.0.1 workflows_1.1.3    tune_1.1.2        
 [5] rsample_1.2.0      recipes_1.0.8      parsnip_1.1.1      modeldata_1.2.0   
 [9] infer_1.0.5        dials_1.2.0        scales_1.2.1       broom_1.0.5       
[13] tidymodels_1.1.1   ggpmisc_0.5.4-1    ggpp_0.5.5         ggforce_0.4.1     
[17] gsw_1.1-1          gridExtra_2.3      lubridate_1.9.0    timechange_0.1.1  
[21] argodata_0.1.0     forcats_0.5.2      stringr_1.5.0      dplyr_1.1.3       
[25] purrr_1.0.2        readr_2.1.3        tidyr_1.3.0        tibble_3.2.1      
[29] ggplot2_3.4.4      tidyverse_1.3.2   

loaded via a namespace (and not attached):
  [1] googledrive_2.0.0   colorspace_2.0-3    ellipsis_0.3.2     
  [4] class_7.3-20        rprojroot_2.0.3     fs_1.5.2           
  [7] rstudioapi_0.15.0   furrr_0.3.1         listenv_0.8.0      
 [10] farver_2.1.1        MatrixModels_0.5-1  prodlim_2019.11.13 
 [13] fansi_1.0.3         xml2_1.3.3          codetools_0.2-18   
 [16] splines_4.2.2       cachem_1.0.6        knitr_1.41         
 [19] polyclip_1.10-4     polynom_1.4-1       jsonlite_1.8.3     
 [22] workflowr_1.7.0     dbplyr_2.2.1        compiler_4.2.2     
 [25] httr_1.4.4          backports_1.4.1     assertthat_0.2.1   
 [28] Matrix_1.5-3        fastmap_1.1.0       gargle_1.2.1       
 [31] cli_3.6.1           later_1.3.0         tweenr_2.0.2       
 [34] htmltools_0.5.3     quantreg_5.94       tools_4.2.2        
 [37] gtable_0.3.1        glue_1.6.2          Rcpp_1.0.10        
 [40] cellranger_1.1.0    jquerylib_0.1.4     RNetCDF_2.6-1      
 [43] DiceDesign_1.9      vctrs_0.6.4         iterators_1.0.14   
 [46] timeDate_4021.106   xfun_0.35           gower_1.0.0        
 [49] globals_0.16.2      rvest_1.0.3         lifecycle_1.0.3    
 [52] googlesheets4_1.0.1 future_1.29.0       MASS_7.3-58.1      
 [55] ipred_0.9-13        hms_1.1.2           promises_1.2.0.1   
 [58] parallel_4.2.2      SparseM_1.81        RColorBrewer_1.1-3 
 [61] yaml_2.3.6          sass_0.4.4          rpart_4.1.19       
 [64] stringi_1.7.8       highr_0.9           foreach_1.5.2      
 [67] lhs_1.1.6           hardhat_1.3.0       lava_1.7.0         
 [70] rlang_1.1.1         pkgconfig_2.0.3     evaluate_0.18      
 [73] lattice_0.20-45     labeling_0.4.2      tidyselect_1.2.0   
 [76] here_1.0.1          parallelly_1.32.1   magrittr_2.0.3     
 [79] R6_2.5.1            generics_0.1.3      DBI_1.1.3          
 [82] pillar_1.9.0        haven_2.5.1         whisker_0.4        
 [85] withr_2.5.0         survival_3.4-0      nnet_7.3-18        
 [88] future.apply_1.10.0 modelr_0.1.10       crayon_1.5.2       
 [91] utf8_1.2.2          tzdb_0.3.0          rmarkdown_2.18     
 [94] grid_4.2.2          readxl_1.4.1        git2r_0.30.1       
 [97] reprex_2.0.2        digest_0.6.30       httpuv_1.6.6       
[100] GPfit_1.0-8         munsell_0.5.0       viridisLite_0.4.1  
[103] bslib_0.4.1