Last updated: 2021-03-04

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1 Required data

Required are:

  • cleaned and prepared GLODAP-based synthetic model subsetting file
GLODAP <-
  read_csv(paste(path_version_data,
                 "GLODAPv2.2020_MLR_fitting_ready.csv",
                 sep = ""))

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

  • sal, temp, aou, nitrate, silicate, phosphate, phosphate_star
# the following code is a workaround to find all predictor combinations
# using the olsrr package and fit all models for one era, slab, and basin

i_basin <- unique(GLODAP$basin)[1]
i_era   <- unique(GLODAP$era)[1]

# subset one basin and era for fitting
GLODAP_basin_era <- GLODAP %>%
  filter(basin == i_basin, era == i_era)

i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
print(i_gamma_slab)

# subset one gamma slab
GLODAP_basin_era_slab <- GLODAP_basin_era %>%
  filter(gamma_slab == i_gamma_slab)

# fit the full linear model, i.e. all predictor combinations
lm_full <- lm(paste(
  params_local$MLR_target,
  paste(params_local$MLR_predictors, collapse = " + "),
  sep = " ~ "
),
data = GLODAP_basin_era_slab)

# fit linear models for all possible predictor combinations
# unfortunately, this functions does not provide model coefficients (yet)
lm_all <- ols_step_all_possible(lm_full)

# convert to tibble
lm_all <- as_tibble(lm_all)

# extract relevant columns and format model formula
lm_all <- lm_all %>% 
  select(n, predictors) %>% 
  mutate(lm_coeff = str_replace_all(predictors, " ", " + "),
         lm_coeff = paste(params_local$MLR_target, "~", lm_coeff))

# remove certain predictor combinations
# lm_rm_ph <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "oxygen") &
#       str_detect(lm_coeff_filter, "phosphate")
#   )

# lm_rm_si <- lm_all %>%
#   filter(str_detect(lm_coeff, "silicate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "silicate_star")) %>%
#   filter(str_detect(lm_coeff_filter, "silicate"))

# lm_rm_o2 <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "phosphate") &
#       str_detect(lm_coeff_filter, "oxygen")
#   )

# lm_rm <- bind_rows(lm_rm_ph, lm_rm_o2) %>%
#   select(-lm_coeff_filter) %>%
#   unique()


# remove temp sal predictor combination
lm_all <- lm_all %>%
  # filter(!(
  #   str_detect(lm_coeff, "temp") &
  #     str_detect(lm_coeff, "phosphate_star")
  # )) %>%
  mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
  filter(!(str_detect(lm_coeff_filter, "nitrate") &
             str_detect(lm_coeff_filter, "phosphate")
  )) %>%
  filter(!(
    str_detect(lm_coeff_filter, "temp") &
      str_detect(lm_coeff_filter, "sal")
  )) %>%
  filter(!(
    str_detect(lm_coeff_filter, "oxygen") &
      str_detect(lm_coeff_filter, "aou")
  )) %>%
  select(-lm_coeff_filter)

# lm_rm <- lm_rm_ph %>%
#   select(-lm_coeff_filter) %>%
#   unique()
# 
# lm_all <- anti_join(lm_all, lm_rm)

# remove helper objects
rm(
  i_gamma_slab,
  i_era,
  i_basin,
  GLODAP_basin_era,
  GLODAP_basin_era_slab,
  lm_full,
  lm_rm_ph,
  lm_rm_si,
  lm_rm_o2,
  lm_rm
)

3 Apply predictor threshold

Select combinations with a total number of predictors in the range:

  • Minimum: 3
  • Maximum: 9
lm_all <- lm_all %>% 
  filter(n >= params_local$MLR_predictors_min,
         n <= params_local$MLR_predictors_max)

This results in a total number of MLR models of:

  • 45

4 Fit all models

Individual linear regression models were fitted for the chosen target variable:

  • cstar_tref

as a function of each predictor combination. Fitting was performed separately within each basin, era, and slab. Model diagnostics, such as the root mean squared error (RMSE), were calculated for each fitted model.

# loop across all basins, era, gamma slabs, and MLRs
# fit all MLR models
for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {
    #i_basin <- unique(GLODAP$basin)[1]
    #i_era   <- unique(GLODAP$era)[1]
    print(i_basin)
    print(i_era)
    
    GLODAP_basin_era <- GLODAP %>%
      filter(basin == i_basin, era == i_era)
    
    for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
      #i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
      print(i_gamma_slab)
      
      GLODAP_basin_era_slab <- GLODAP_basin_era %>%
        filter(gamma_slab == i_gamma_slab)
      
      # number of observations used for each fitting model
      i_nr_obs = nrow(GLODAP_basin_era_slab)
      
      for (i_predictors in unique(lm_all$predictors)) {
        #i_predictors <- unique(lm_all$predictors)[1]
        
        # extract one model definition
        i_lm <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(lm_coeff) %>%
          pull()
        
        # extract number of predictors
        i_n_predictors <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(n) %>%
          pull()
        
        if (i_nr_obs > i_n_predictors) {
          # fit model
          if (params_local$MLR_type == "rlm") {
            i_lm_fit <- MASS::rlm(as.formula(i_lm),
                                  data = GLODAP_basin_era_slab)
          }
          
          if (params_local$MLR_type == "lm") {
            i_lm_fit <- lm(as.formula(i_lm),
                           data = GLODAP_basin_era_slab)
          }
          
          # find max predictor correlation
          i_cor_max <- GLODAP_basin_era_slab %>%
            select(!!!syms(str_split(i_predictors, " ",
                                     simplify = TRUE))) %>%
            correlate(quiet = TRUE) %>%
            select(-term) %>%
            abs() %>%
            max(na.rm = TRUE)
          
          # calculate root mean squared error
          i_rmse <- sqrt(c(crossprod(i_lm_fit$residuals)) /
                           length(i_lm_fit$residuals))
          
          # calculate maximum residual
          i_resid_max <- max(abs(i_lm_fit$residuals))
          
          # calculate Akaike information criterion aic
          i_aic <- AIC(i_lm_fit)
          
          # collect model coefficients and diagnostics
          coefficients <- tidy(i_lm_fit)
          
          coefficients <- coefficients %>%
            mutate(
              basin = i_basin,
              era = i_era,
              gamma_slab = i_gamma_slab,
              model = i_lm,
              nr_obs = i_nr_obs,
              rmse = i_rmse,
              aic = i_aic,
              resid_max = i_resid_max,
              n_predictors = i_n_predictors,
              na_predictor = anyNA(coefficients$estimate),
              cor_max = i_cor_max
            )
          
          if (exists("lm_all_fitted")) {
            lm_all_fitted <- bind_rows(lm_all_fitted, coefficients)
          }
          
          if (!exists("lm_all_fitted")) {
            lm_all_fitted <- coefficients
          }
        }
      }
    }
  }
}

rm(
  i_lm_fit,
  coefficients,
  i_rmse,
  GLODAP_basin_era,
  GLODAP_basin_era_slab,
  i_lm,
  i_basin,
  i_era,
  i_gamma_slab,
  i_nr_obs,
  i_predictors,
  i_aic,
  i_n_predictors,
  i_resid_max
)

5 Prepare coeffcients

Coefficients are prepared for the mapping of Cant and the chosen target variable.

5.1 Formatting

# select relevant columns
lm_all_fitted <- lm_all_fitted %>%
  select(
    basin,
    gamma_slab,
    era,
    model,
    nr_obs,
    n_predictors,
    term,
    estimate,
    rmse,
    aic,
    resid_max,
    na_predictor,
    cor_max
  )

# set coefficient to zero if not fitted (=NA)
lm_all_fitted <- lm_all_fitted %>%
  mutate(estimate = if_else(is.na(estimate), 0, estimate))

# Prepare model coefficients for mapping of target variable
lm_all_fitted_wide <- lm_all_fitted %>%
  pivot_wider(
    values_from = estimate,
    names_from = term,
    names_prefix = "coeff_",
    values_fill = 0
  )

5.2 Predictor selection

Within each basin and slab, the following number of best linear regression models was selected:

  • 5

The criterion used to select the best models was:

  • aic

The criterion was summed up for two adjacent eras, and the models with lowest summed values were selected.

Please note, that currently the lm() function produces NAs for some predictors. It is not yet entirely clear when this happens, but presumably it is caused by some form of collinearity between predictors, such that including another predictor does not help to explain the target variable any better. The issues also expresses as exactly identical rmse values of different models. As an interim solution, models with fitted NA predictors were not included.

# remove models with predictors fitted as NA

lm_all_fitted_wide <- lm_all_fitted_wide %>%
  filter(na_predictor == FALSE)
# calculate RMSE sum for adjacent eras
lm_all_fitted_wide_eras <- lm_all_fitted_wide  %>%
  select(basin, gamma_slab, model, era, nr_obs, rmse, aic, resid_max) %>%
  arrange(era) %>%
  group_by(basin, gamma_slab, model) %>%
  mutate(
    eras = paste(lag(era), era, sep = " --> "),
    rmse_sum = rmse + lag(rmse),
    aic_sum = aic + lag(aic)
  ) %>%
  ungroup() %>%
  select(-c(era)) %>%
  drop_na()

# subset models with lowest summed criterion
# chose which criterion is applied

if (params_local$MLR_criterion == "aic") {
  lm_best <- lm_all_fitted_wide_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = aic_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
} else {
  lm_best <- lm_all_fitted_wide_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = rmse_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
}

5.3 RMSE tables

5.3.1 per model

lm_best %>%
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
basin gamma_slab model nr_obs rmse aic resid_max eras rmse_sum aic_sum
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate_star 124 1.5807480 477.4555 6.522283 1982-2000 –> 2001-2010 3.2616043 1350.0349
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 124 1.0668019 379.9337 4.237628 1982-2000 –> 2001-2010 2.3972549 1148.7131
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 124 1.0665290 381.8703 4.204572 1982-2000 –> 2001-2010 2.3963330 1152.4330
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 124 1.4713158 459.6637 7.006217 1982-2000 –> 2001-2010 3.1175359 1322.9984
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 124 1.4579175 459.3950 6.615827 1982-2000 –> 2001-2010 3.1034850 1324.5536
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 92 1.2425411 313.0419 3.684842 2001-2010 –> 2011-2019 2.3093430 692.9756
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 92 1.1737104 304.5560 3.337674 2001-2010 –> 2011-2019 2.2402394 686.4263
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate_star 92 1.7091191 371.7047 4.482545 2001-2010 –> 2011-2019 3.2834003 848.1435
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 92 1.5863943 357.9940 6.073868 2001-2010 –> 2011-2019 3.0577101 817.6577
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 92 1.5384000 354.3414 5.490783 2001-2010 –> 2011-2019 2.9963175 813.7364
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 822 3.5759506 4441.5708 13.571055 1982-2000 –> 2001-2010 7.0219043 12987.0900
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 822 4.2553451 4725.5361 10.458058 1982-2000 –> 2001-2010 8.4116141 13871.0390
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 822 4.0724443 4653.3111 12.387382 1982-2000 –> 2001-2010 8.1508205 13738.0466
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 822 4.0631204 4651.5428 12.919751 1982-2000 –> 2001-2010 8.1394412 13736.6592
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 822 4.3618184 4768.1645 13.130655 1982-2000 –> 2001-2010 8.5911338 13971.6280
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 710 3.5876836 3842.9523 11.056693 2001-2010 –> 2011-2019 7.1636342 8284.5231
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 710 4.0777394 4022.7635 12.865584 2001-2010 –> 2011-2019 8.3330845 8748.2995
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 710 3.9167692 3965.5721 16.808870 2001-2010 –> 2011-2019 7.9892135 8618.8831
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 710 3.9000219 3961.4874 18.379640 2001-2010 –> 2011-2019 7.9631423 8613.0302
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 710 4.1918274 4063.9469 11.602249 2001-2010 –> 2011-2019 8.5536459 8832.1115
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1090 3.2754353 5691.7487 10.887201 1982-2000 –> 2001-2010 6.3678701 15854.5714
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 1090 3.2650067 5684.7967 10.029957 1982-2000 –> 2001-2010 6.4191843 15926.3794
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1090 3.2002314 5643.1124 10.279690 1982-2000 –> 2001-2010 6.2584880 15763.6581
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1090 3.2654795 5687.1124 10.220265 1982-2000 –> 2001-2010 6.4086257 15916.7370
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1090 3.1572866 5613.6603 10.001595 1982-2000 –> 2001-2010 6.1346605 15627.4215
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 868 3.6003392 4699.1420 11.802729 2001-2010 –> 2011-2019 6.8757745 10390.8907
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 868 3.5314345 4665.5957 11.416965 2001-2010 –> 2011-2019 6.7964411 10350.3924
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 868 3.5028068 4653.4654 11.671917 2001-2010 –> 2011-2019 6.7030382 10296.5778
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 868 3.5201255 4662.0275 9.397928 2001-2010 –> 2011-2019 6.7856050 10349.1399
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 868 3.4940939 4649.1419 11.129108 2001-2010 –> 2011-2019 6.6513805 10262.8022
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1822 2.1248401 7929.0822 14.759493 1982-2000 –> 2001-2010 3.7996578 20806.4574
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1822 2.0314866 7767.3621 14.059395 1982-2000 –> 2001-2010 3.6862083 20566.4615
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1822 2.2235130 8096.4900 15.400293 1982-2000 –> 2001-2010 4.0198755 21441.7606
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 1822 2.2260401 8098.6293 15.241001 1982-2000 –> 2001-2010 4.0143645 21412.0763
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1822 2.1229030 7927.7588 16.155894 1982-2000 –> 2001-2010 3.6446994 20169.9784
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1654 2.5494966 7801.7924 27.697323 2001-2010 –> 2011-2019 4.6743366 15730.8745
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 1654 2.4887515 7722.0208 24.985488 2001-2010 –> 2011-2019 4.7147748 15820.6226
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1654 2.4378718 7655.6917 26.094232 2001-2010 –> 2011-2019 4.4693584 15423.0537
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1654 2.5970570 7864.9341 23.518921 2001-2010 –> 2011-2019 4.8205700 15961.4241
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1654 2.1639596 7261.4252 22.660033 2001-2010 –> 2011-2019 4.2868627 15189.1840
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1552 2.0955352 6714.7523 9.837575 1982-2000 –> 2001-2010 4.3116870 19029.2561
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1552 1.9221229 6444.6327 9.160166 1982-2000 –> 2001-2010 3.6264500 17298.6456
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1552 1.8997568 6410.3024 9.550953 1982-2000 –> 2001-2010 3.4591179 16772.5970
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1552 2.0570227 6657.1751 13.518443 1982-2000 –> 2001-2010 3.7360282 17430.0519
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1552 2.3187569 7028.9461 13.576293 1982-2000 –> 2001-2010 4.3890491 18965.3197
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1455 2.2352316 6483.7546 11.845042 2001-2010 –> 2011-2019 4.3307668 13198.5069
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1455 2.2644017 6519.4849 13.764140 2001-2010 –> 2011-2019 4.1865246 12964.1177
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1455 2.2629528 6519.6223 13.921405 2001-2010 –> 2011-2019 4.1627096 12929.9247
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 1455 2.3287999 6601.0886 15.070391 2001-2010 –> 2011-2019 4.4695849 13380.1534
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1455 2.4732508 6778.2133 19.985420 2001-2010 –> 2011-2019 4.5302734 13435.3884
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 1572 2.5272621 7388.0600 13.344877 1982-2000 –> 2001-2010 5.1384234 21919.8500
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1572 2.4408050 7280.6216 13.255119 1982-2000 –> 2001-2010 4.9770428 21636.7043
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1572 2.7074971 7606.6442 21.317688 1982-2000 –> 2001-2010 4.8628150 20969.3400
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 1572 2.3720740 7188.8189 11.059121 1982-2000 –> 2001-2010 4.1034456 19212.5903
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1572 2.2092614 6967.2602 15.249969 1982-2000 –> 2001-2010 3.9379144 18983.4398
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate_star 1388 2.9677724 6970.7385 21.519349 2001-2010 –> 2011-2019 5.7140874 14620.1387
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 1388 2.9418952 6946.4273 16.058883 2001-2010 –> 2011-2019 5.4691573 14334.4873
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1388 2.7521896 6763.3870 17.076695 2001-2010 –> 2011-2019 5.1929946 14044.0086
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 1388 3.0777910 7071.7862 11.915546 2001-2010 –> 2011-2019 5.4498650 14260.6051
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1388 2.7598039 6771.0565 16.780096 2001-2010 –> 2011-2019 4.9690652 13738.3167
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 2162 2.7964448 10592.0709 13.783745 1982-2000 –> 2001-2010 5.2660619 28972.3678
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 2162 2.7797968 10568.2520 14.208983 1982-2000 –> 2001-2010 5.0399422 28249.6317
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2162 2.4631463 10045.3146 13.875210 1982-2000 –> 2001-2010 4.8244810 28073.0480
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2162 2.4052497 9944.4649 14.632668 1982-2000 –> 2001-2010 4.5001000 27027.2554
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2162 3.1043060 11047.6750 16.223029 1982-2000 –> 2001-2010 5.4891704 29155.8179
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate 1937 3.2145883 10032.6349 16.577579 2001-2010 –> 2011-2019 6.0403932 20671.8672
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1937 3.1752800 9986.9713 14.945718 2001-2010 –> 2011-2019 5.9973203 20622.4391
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 1937 3.3297137 10168.9495 14.066023 2001-2010 –> 2011-2019 6.1095106 20737.2016
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 1937 2.8098769 9511.3548 15.377731 2001-2010 –> 2011-2019 5.2730231 19556.6694
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1937 2.8042018 9505.5226 15.279124 2001-2010 –> 2011-2019 5.2094514 19449.9874
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 785 1.8855233 3235.4360 13.349427 1982-2000 –> 2001-2010 3.8964658 9134.2029
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 785 1.8258772 3186.9685 14.242551 1982-2000 –> 2001-2010 3.7837528 9013.3885
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 785 1.9708245 3304.9031 12.481851 1982-2000 –> 2001-2010 3.6583538 8716.2303
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 785 1.7033214 3075.8842 12.310184 1982-2000 –> 2001-2010 3.5153221 8685.0533
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 785 1.5146745 2893.5984 12.891500 1982-2000 –> 2001-2010 3.1159869 8161.1370
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 694 2.0171038 2955.3945 12.602743 2001-2010 –> 2011-2019 3.9026271 6190.8305
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 694 2.0083437 2951.3535 12.900020 2001-2010 –> 2011-2019 3.8342209 6138.3220
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 694 2.3686529 3178.3888 11.418228 2001-2010 –> 2011-2019 4.3394774 6483.2919
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 694 1.8392362 2827.2650 11.670593 2001-2010 –> 2011-2019 3.5425575 5903.1492
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 694 1.7303093 2744.5274 12.029848 2001-2010 –> 2011-2019 3.2449838 5638.1257
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 750 3.3364134 3947.7524 34.657618 1982-2000 –> 2001-2010 6.2083339 10921.3618
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 750 3.3228087 3941.6234 29.238932 1982-2000 –> 2001-2010 6.0445845 10764.1311
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 750 3.3098149 3937.7462 27.040745 1982-2000 –> 2001-2010 6.0315906 10762.2538
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 750 2.9541554 3765.2270 21.443241 1982-2000 –> 2001-2010 5.8594535 10771.3523
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 750 2.9422333 3761.1612 21.234297 1982-2000 –> 2001-2010 5.8010723 10723.9237
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 731 3.7755824 4028.8350 24.278071 2001-2010 –> 2011-2019 7.1119959 7976.5875
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 731 3.4079754 3879.0732 31.539245 2001-2010 –> 2011-2019 6.7307842 7820.6967
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 731 3.3293057 3846.9288 30.295708 2001-2010 –> 2011-2019 6.6391206 7784.6750
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 731 3.6982911 3998.5953 22.983455 2001-2010 –> 2011-2019 6.6524465 7763.8223
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 731 3.6706108 3989.6117 24.150702 2001-2010 –> 2011-2019 6.6128441 7750.7728
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 924 4.7604439 5517.7084 26.013108 1982-2000 –> 2001-2010 9.5363645 16075.9179
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 924 4.6749284 5486.2096 25.087518 1982-2000 –> 2001-2010 9.3658088 15982.8896
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 924 4.1940970 5283.6354 22.150822 1982-2000 –> 2001-2010 8.2222752 15239.7612
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 924 3.9985432 5197.3972 24.814968 1982-2000 –> 2001-2010 7.5507949 14710.9327
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 924 4.6469816 5475.1291 21.659193 1982-2000 –> 2001-2010 9.4448907 16051.5810
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 854 4.3034100 4930.2154 24.473348 2001-2010 –> 2011-2019 8.9783384 10416.4250
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 854 3.8115314 4720.9041 22.515294 2001-2010 –> 2011-2019 8.0056284 10004.5395
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 854 3.4333251 4544.4149 26.895103 2001-2010 –> 2011-2019 7.4318684 9741.8122
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 854 4.4106534 4972.2580 22.938388 2001-2010 –> 2011-2019 9.0576350 10447.3871
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate_star 854 4.4116486 4970.6434 23.326605 2001-2010 –> 2011-2019 9.1170344 10466.8537
Atlantic (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 625 1.1915521 2004.7441 10.369923 1982-2000 –> 2001-2010 2.1503088 5144.8803
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 625 1.0583111 1856.5161 7.080725 1982-2000 –> 2001-2010 1.9609969 4859.7355
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 625 1.0195181 1811.8358 6.026932 1982-2000 –> 2001-2010 1.9217241 4815.8470
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 625 1.1353075 1944.3026 10.661233 1982-2000 –> 2001-2010 2.0802819 5051.5414
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 625 1.0777521 1881.2701 11.573628 1982-2000 –> 2001-2010 1.9221628 4734.8662
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 553 1.1578690 1745.4649 7.747201 2001-2010 –> 2011-2019 2.2788683 3675.9137
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 553 1.0938294 1680.5373 9.449358 2001-2010 –> 2011-2019 2.1521405 3537.0534
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 553 1.0491050 1636.3648 8.200998 2001-2010 –> 2011-2019 2.0686231 3448.2006
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 553 1.1005139 1687.2756 13.167362 2001-2010 –> 2011-2019 2.2358214 3631.5783
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 553 1.0518980 1639.3054 13.891084 2001-2010 –> 2011-2019 2.1296501 3520.5754
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 730 0.8316656 1814.5359 10.908166 1982-2000 –> 2001-2010 1.5404495 4758.4101
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 730 0.8281911 1810.4237 7.666230 1982-2000 –> 2001-2010 1.5452432 4787.9368
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 730 0.7586142 1680.3079 6.943802 1982-2000 –> 2001-2010 1.4371203 4505.0850
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 730 0.7442971 1654.4904 6.811637 1982-2000 –> 2001-2010 1.3827121 4315.1191
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 730 0.7465013 1658.8077 10.996359 1982-2000 –> 2001-2010 1.3698086 4254.1037
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 634 0.9257911 1715.4428 7.538886 2001-2010 –> 2011-2019 1.7539822 3525.8665
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 634 0.8400290 1590.1777 6.642030 2001-2010 –> 2011-2019 1.5986432 3270.4856
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 634 0.8391551 1590.8579 6.641684 2001-2010 –> 2011-2019 1.5834522 3245.3484
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 634 0.9112747 1693.4030 11.656765 2001-2010 –> 2011-2019 1.7375224 3498.3967
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 634 0.8256471 1570.2807 12.116337 2001-2010 –> 2011-2019 1.5721484 3229.0884
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1187 0.5984880 2161.8700 2.366104 1982-2000 –> 2001-2010 1.1309089 5850.4058
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1187 0.5473862 1951.9860 2.058856 1982-2000 –> 2001-2010 1.0642219 5504.0161
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 1187 0.6012769 2172.9070 2.164382 1982-2000 –> 2001-2010 1.1626119 6107.9849
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 1187 0.5697070 2044.8693 2.170583 1982-2000 –> 2001-2010 1.1178257 5868.8707
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1187 0.5553026 1986.0732 2.299378 1982-2000 –> 2001-2010 1.1028603 5807.3008
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1065 0.7329106 2372.4808 5.199994 2001-2010 –> 2011-2019 1.3313986 4534.3508
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1065 0.7275030 2358.7071 5.749767 2001-2010 –> 2011-2019 1.2748892 4310.6931
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 1065 0.8596180 2712.1399 9.457165 2001-2010 –> 2011-2019 1.4608949 4885.0469
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 1065 0.8514553 2691.8173 10.098604 2001-2010 –> 2011-2019 1.4211623 4736.6867
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1065 0.8513703 2693.6049 10.031960 2001-2010 –> 2011-2019 1.4066729 4679.6781
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 2075 0.3613902 1674.7368 1.956822 1982-2000 –> 2001-2010 0.6665844 3504.1839
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 2075 0.3550275 1603.0206 1.931437 1982-2000 –> 2001-2010 0.6566067 3341.0744
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 2075 0.3607754 1669.6717 1.955102 1982-2000 –> 2001-2010 0.6647962 3470.9247
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2075 0.3464217 1503.1862 1.892131 1982-2000 –> 2001-2010 0.6454337 3176.2308
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2075 0.5252661 3230.6162 3.159045 1982-2000 –> 2001-2010 0.9842505 8262.5004
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 1967 0.4147946 2130.2948 2.430540 2001-2010 –> 2011-2019 0.7761847 3805.0316
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 1967 0.3962301 1952.1633 2.371006 2001-2010 –> 2011-2019 0.7512575 3555.1839
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 1967 0.4077495 2064.9043 2.421900 2001-2010 –> 2011-2019 0.7685250 3734.5760
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1967 0.3876841 1868.3856 2.430333 2001-2010 –> 2011-2019 0.7341058 3371.5718
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1967 0.6964403 4172.8882 9.154760 2001-2010 –> 2011-2019 1.2217064 7403.5044
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 4077 6.2423624 26514.9237 30.007691 1982-2000 –> 2001-2010 12.7729567 76617.5583
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4077 6.2014106 26463.2547 29.570480 1982-2000 –> 2001-2010 12.6811456 76449.0504
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4077 7.1680889 27644.4618 31.671143 1982-2000 –> 2001-2010 14.6957444 79908.7989
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4077 7.2968233 27789.6032 29.238432 1982-2000 –> 2001-2010 14.8724117 80150.4204
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4077 7.3823263 27882.5949 28.571764 1982-2000 –> 2001-2010 15.0955286 80515.0490
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 3620 5.9822711 23236.0290 24.783697 2001-2010 –> 2011-2019 12.2246335 49750.9526
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3620 5.9125324 23153.1324 24.045503 2001-2010 –> 2011-2019 12.1139430 49616.3871
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3620 7.0143253 24390.3058 25.654692 2001-2010 –> 2011-2019 14.1824142 52034.7676
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3620 7.0552862 24432.4615 25.263739 2001-2010 –> 2011-2019 14.3521095 52222.0647
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3620 7.1801867 24557.5108 24.268755 2001-2010 –> 2011-2019 14.5625130 52440.1057
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4220 4.8481760 25311.2467 41.407552 1982-2000 –> 2001-2010 9.4790502 73382.5687
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4220 4.4768482 24640.7199 44.950576 1982-2000 –> 2001-2010 8.7109155 71255.4582
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4220 4.7028378 25056.3632 49.169658 1982-2000 –> 2001-2010 9.0977168 72278.0445
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4220 4.8543645 25322.0131 39.590413 1982-2000 –> 2001-2010 9.4588005 73300.1132
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4220 4.8402050 25299.3590 40.775879 1982-2000 –> 2001-2010 9.4444784 73278.8839
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3794 4.9439290 22905.7463 41.470670 2001-2010 –> 2011-2019 9.7921049 48216.9931
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3794 4.6050429 22368.9348 44.026694 2001-2010 –> 2011-2019 9.0818911 47009.6547
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3794 4.7582837 22617.3285 47.149314 2001-2010 –> 2011-2019 9.4611215 47673.6916
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 3794 4.9331516 22889.1871 40.344940 2001-2010 –> 2011-2019 9.7875161 48211.2003
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3794 4.9294606 22885.5075 40.824625 2001-2010 –> 2011-2019 9.7696656 48184.8665
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3488 3.9936193 19570.1678 21.854404 1982-2000 –> 2001-2010 7.9426839 56710.1481
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3488 3.8865143 19382.5237 19.967572 1982-2000 –> 2001-2010 7.6476919 55876.3686
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3488 3.9371842 19472.8847 28.744685 1982-2000 –> 2001-2010 7.9390219 56791.3683
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3488 3.9056251 19416.7421 22.936500 1982-2000 –> 2001-2010 7.7808115 56307.6276
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3488 3.9374337 19471.3267 28.456319 1982-2000 –> 2001-2010 8.0073863 57012.2158
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3143 4.3952443 18238.0159 24.561008 2001-2010 –> 2011-2019 8.3888635 37808.1836
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3143 4.2668415 18053.6406 24.765936 2001-2010 –> 2011-2019 8.1533558 37436.1643
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3143 4.3240503 18137.3618 31.696967 2001-2010 –> 2011-2019 8.2612345 37610.2465
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3143 4.2646943 18050.4766 22.795115 2001-2010 –> 2011-2019 8.1703194 37467.2187
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3143 4.3368573 18153.9523 34.262429 2001-2010 –> 2011-2019 8.2742910 37625.2789
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4075 4.4903153 23817.0208 18.274731 1982-2000 –> 2001-2010 8.4951577 68299.9128
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4075 4.2636121 23394.8003 21.453879 1982-2000 –> 2001-2010 7.9665783 66635.8405
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4075 4.2446394 23360.4526 20.527811 1982-2000 –> 2001-2010 7.9333507 66542.3744
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4075 4.1678976 23209.7547 22.715098 1982-2000 –> 2001-2010 7.8610003 66408.5298
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4075 4.1293884 23136.1029 20.985678 1982-2000 –> 2001-2010 7.7946425 66216.9355
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3755 4.9077345 22615.2297 19.517122 2001-2010 –> 2011-2019 9.3980497 46432.2505
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 3755 4.6853329 22266.9500 21.537757 2001-2010 –> 2011-2019 8.9489450 45661.7503
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3755 4.6745542 22251.6532 20.722111 2001-2010 –> 2011-2019 8.9191936 45612.1058
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 3755 4.5848207 22104.0884 17.762636 2001-2010 –> 2011-2019 8.7527183 45313.8431
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3755 4.5607657 22066.5823 16.916459 2001-2010 –> 2011-2019 8.6901541 45202.6852
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5035 4.3102276 29014.8876 46.155819 1982-2000 –> 2001-2010 7.9128855 79497.8945
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5035 4.0038801 28272.4587 56.307607 1982-2000 –> 2001-2010 7.4447808 77896.9651
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 5035 4.2955079 28978.4390 49.201148 1982-2000 –> 2001-2010 7.9416121 79683.4662
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5035 3.9360765 28100.4681 34.337169 1982-2000 –> 2001-2010 7.2554038 77052.7463
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5035 4.3655118 29141.2268 77.949507 1982-2000 –> 2001-2010 7.9801620 79684.3386
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4394 5.0667861 26741.9784 31.695512 2001-2010 –> 2011-2019 9.4295109 55876.7744
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4394 5.0220198 26665.9892 33.949988 2001-2010 –> 2011-2019 9.3322474 55680.8768
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4394 4.8756983 26406.1379 36.885352 2001-2010 –> 2011-2019 8.8795784 54678.5967
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 4394 5.0361214 26688.6309 40.506889 2001-2010 –> 2011-2019 9.3316293 55667.0699
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4394 4.4115113 25526.9337 26.045742 2001-2010 –> 2011-2019 8.3475878 53627.4018
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4525 3.4799839 24140.9942 32.135758 1982-2000 –> 2001-2010 6.3873651 65594.8305
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4525 3.7505502 24818.6119 32.274426 1982-2000 –> 2001-2010 6.8082863 67112.8828
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 4525 3.7656904 24853.0713 31.549125 1982-2000 –> 2001-2010 6.8240442 67148.7093
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4525 3.6715997 24626.0722 32.686045 1982-2000 –> 2001-2010 6.7386442 66971.0070
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4525 3.3799370 23877.0001 33.076763 1982-2000 –> 2001-2010 6.2894729 65343.1851
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4007 3.8895971 22270.8344 30.979101 2001-2010 –> 2011-2019 7.3695811 46411.8286
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4007 4.2014468 22888.9009 32.220987 2001-2010 –> 2011-2019 7.9519970 47707.5128
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 4007 4.2453334 22970.1777 30.526464 2001-2010 –> 2011-2019 8.0110238 47823.2489
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4007 4.1765503 22841.2712 31.079200 2001-2010 –> 2011-2019 7.8481500 47467.3434
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4007 3.7690403 22018.5122 33.027470 2001-2010 –> 2011-2019 7.1489773 45895.5123
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4480 3.2279559 23227.4570 23.413050 1982-2000 –> 2001-2010 5.5484190 61940.2109
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4480 3.2082778 23172.6685 9.520468 1982-2000 –> 2001-2010 5.5549541 62077.7119
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 4480 3.3382148 23526.3975 21.820643 1982-2000 –> 2001-2010 5.7056523 62580.2189
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4480 3.3689421 23608.4944 28.724988 1982-2000 –> 2001-2010 5.7635414 62857.5936
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4480 3.3907556 23666.3222 24.766375 1982-2000 –> 2001-2010 5.7750174 62841.3636
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4006 3.9723248 22433.8999 26.174799 2001-2010 –> 2011-2019 7.2002807 45661.3569
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4006 3.8155457 22111.2740 10.753469 2001-2010 –> 2011-2019 7.0238235 45283.9425
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 4006 4.1351566 22753.7714 24.548760 2001-2010 –> 2011-2019 7.4733714 46280.1689
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4006 4.1639733 22809.4111 32.338700 2001-2010 –> 2011-2019 7.5329154 46417.9055
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4006 4.0318574 22553.0836 20.361122 2001-2010 –> 2011-2019 7.3689300 46078.4146
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1772 2.7599137 8638.5849 21.254361 1982-2000 –> 2001-2010 4.7332261 22468.1101
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1772 2.7584715 8638.7324 21.555579 1982-2000 –> 2001-2010 4.7259624 22450.8055
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1772 2.7577040 8637.7463 21.618971 1982-2000 –> 2001-2010 4.7371972 22489.8618
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 1772 2.7719110 8653.9572 20.827350 1982-2000 –> 2001-2010 4.7562740 22520.2503
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1772 2.6644514 8515.8317 21.069300 1982-2000 –> 2001-2010 4.6161467 22274.8333
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1648 3.1007702 8420.7415 30.298833 2001-2010 –> 2011-2019 5.8580176 17057.9010
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1648 3.1316820 8453.4369 29.493657 2001-2010 –> 2011-2019 5.8901534 17092.1693
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1648 3.1100170 8428.5559 28.314959 2001-2010 –> 2011-2019 5.8672645 17063.7154
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 1648 3.0782123 8394.6758 30.602797 2001-2010 –> 2011-2019 5.8351309 17029.4125
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1648 3.0255771 8339.8291 27.765869 2001-2010 –> 2011-2019 5.6900285 16855.6608
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 2176 2.8139345 10689.7287 26.269590 1982-2000 –> 2001-2010 4.9632767 29209.7952
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 2176 2.8056180 10676.8474 25.811713 1982-2000 –> 2001-2010 5.0081207 29403.9546
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2176 2.8024815 10673.9795 25.619696 1982-2000 –> 2001-2010 4.9506525 29191.4270
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 2176 2.8507228 10744.2564 30.642369 1982-2000 –> 2001-2010 5.0026643 29272.5646
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2176 2.8347495 10721.8025 29.563474 1982-2000 –> 2001-2010 4.9857992 29248.5984
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate 2046 3.1312405 10487.0250 35.046588 2001-2010 –> 2011-2019 5.9470284 21177.6192
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 2046 3.1228292 10478.0181 35.215964 2001-2010 –> 2011-2019 5.9367637 21167.7467
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 2046 3.1187952 10472.7286 34.654059 2001-2010 –> 2011-2019 5.9244131 21149.5760
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2046 3.1112502 10464.8172 34.828329 2001-2010 –> 2011-2019 5.9137317 21138.7967
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2046 3.0550292 10390.1976 39.731544 2001-2010 –> 2011-2019 5.9343874 21181.9515
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1910 2.2359997 8506.2550 8.252999 1982-2000 –> 2001-2010 4.1617415 23846.9607
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1910 2.1869449 8423.5165 8.473373 1982-2000 –> 2001-2010 4.0818379 23646.8818
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1910 2.2389081 8513.2204 8.073343 1982-2000 –> 2001-2010 4.1776861 23905.7840
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 1910 2.2509584 8531.7255 8.303155 1982-2000 –> 2001-2010 4.1876636 23914.3837
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1910 2.1669641 8388.4550 7.912503 1982-2000 –> 2001-2010 4.0448198 23545.0755
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 1759 2.4104487 8099.0076 8.219622 2001-2010 –> 2011-2019 4.5988824 16523.1237
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1759 2.4042735 8091.9835 8.383840 2001-2010 –> 2011-2019 4.5756335 16488.1798
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1759 2.4709066 8188.1563 8.414649 2001-2010 –> 2011-2019 4.6578516 16611.6727
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 1759 2.4660466 8179.2299 8.996953 2001-2010 –> 2011-2019 4.6931974 16670.3373
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1759 2.4261389 8123.8329 8.758843 2001-2010 –> 2011-2019 4.5931030 16512.2878
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1321 1.9459542 5519.7535 8.761522 1982-2000 –> 2001-2010 3.5789895 15815.6687
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1321 1.8457950 5382.1440 9.399175 1982-2000 –> 2001-2010 3.4548955 15600.5344
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1321 1.9477084 5522.1341 8.912383 1982-2000 –> 2001-2010 3.6005421 15882.9548
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1321 1.8644415 5408.6999 10.139916 1982-2000 –> 2001-2010 3.4829412 15658.4598
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1321 1.8164242 5339.7657 9.293231 1982-2000 –> 2001-2010 3.4508411 15642.2356
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1224 2.0621585 5257.3095 10.073863 2001-2010 –> 2011-2019 3.9481582 10694.3832
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1224 2.0058896 5191.5841 9.838746 2001-2010 –> 2011-2019 3.8516846 10573.7281
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1224 2.0461176 5240.1928 10.585784 2001-2010 –> 2011-2019 3.9105591 10648.8928
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 1224 2.0743598 5271.7510 10.122214 2001-2010 –> 2011-2019 3.9694929 10721.5884
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1224 1.9585274 5133.0896 9.225019 2001-2010 –> 2011-2019 3.7749515 10472.8553
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 11307 1.4250021 40109.1506 13.558260 1982-2000 –> 2001-2010 2.7006050 111369.7919
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 11307 1.3268182 38496.7473 16.035475 1982-2000 –> 2001-2010 2.4993190 106147.1458
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 11307 1.3629573 39104.4548 12.897592 1982-2000 –> 2001-2010 2.4882887 104994.9681
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 11307 1.3789342 39368.0002 16.828107 1982-2000 –> 2001-2010 2.6219522 109521.5676
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 11307 1.5541757 42071.4136 17.274570 1982-2000 –> 2001-2010 2.8856234 115168.5156
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 10029 1.6342281 38326.9691 9.304087 2001-2010 –> 2011-2019 3.1484753 79811.8101
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 10029 1.5705643 37527.9526 10.813075 2001-2010 –> 2011-2019 2.9955664 77637.1032
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 10029 1.4904452 36479.7127 12.918817 2001-2010 –> 2011-2019 2.8172634 74976.4600
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 10029 1.5745823 37581.2007 11.169511 2001-2010 –> 2011-2019 2.9375395 76685.6555
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 10029 1.5486196 37247.7156 14.043850 2001-2010 –> 2011-2019 2.9275538 76615.7158

5.3.2 per fitting unit

lm_best %>%
  group_by(basin, gamma_slab, eras) %>% 
  summarise(rmse_sum_mean = mean(rmse_sum),
            ais_sum_mean = mean(aic_sum)) %>% 
  ungroup() %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
basin gamma_slab eras rmse_sum_mean ais_sum_mean
Atlantic (-Inf,26] 1982-2000 –> 2001-2010 2.8552426 1259.7466
Atlantic (-Inf,26] 2001-2010 –> 2011-2019 2.7774021 771.7879
Atlantic (26,26.5] 1982-2000 –> 2001-2010 8.0629828 13660.8926
Atlantic (26,26.5] 2001-2010 –> 2011-2019 8.0005441 8619.3695
Atlantic (26.5,26.75] 1982-2000 –> 2001-2010 6.3177657 15817.7535
Atlantic (26.5,26.75] 2001-2010 –> 2011-2019 6.7624479 10329.9606
Atlantic (26.75,27] 1982-2000 –> 2001-2010 3.8329611 20879.3469
Atlantic (26.75,27] 2001-2010 –> 2011-2019 4.5931805 15625.0318
Atlantic (27,27.25] 1982-2000 –> 2001-2010 3.9044665 17899.1740
Atlantic (27,27.25] 2001-2010 –> 2011-2019 4.3359719 13181.6182
Atlantic (27.25,27.5] 1982-2000 –> 2001-2010 4.6039282 20544.3849
Atlantic (27.25,27.5] 2001-2010 –> 2011-2019 5.3590339 14199.5113
Atlantic (27.5,27.75] 1982-2000 –> 2001-2010 5.0239511 28295.6242
Atlantic (27.5,27.75] 2001-2010 –> 2011-2019 5.7259397 20207.6329
Atlantic (27.75,27.85] 1982-2000 –> 2001-2010 3.5939763 8742.0024
Atlantic (27.75,27.85] 2001-2010 –> 2011-2019 3.7727733 6070.7439
Atlantic (27.85,27.95] 1982-2000 –> 2001-2010 5.9890069 10788.6045
Atlantic (27.85,27.95] 2001-2010 –> 2011-2019 6.7494383 7819.3109
Atlantic (27.95,28.05] 1982-2000 –> 2001-2010 8.8240268 15612.2165
Atlantic (27.95,28.05] 2001-2010 –> 2011-2019 8.5181009 10215.4035
Atlantic (28.05,28.1] 1982-2000 –> 2001-2010 2.0070949 4921.3741
Atlantic (28.05,28.1] 2001-2010 –> 2011-2019 2.1730207 3562.6643
Atlantic (28.1,28.15] 1982-2000 –> 2001-2010 1.4550667 4524.1309
Atlantic (28.1,28.15] 2001-2010 –> 2011-2019 1.6491497 3353.8371
Atlantic (28.15,28.2] 1982-2000 –> 2001-2010 1.1156857 5827.7157
Atlantic (28.15,28.2] 2001-2010 –> 2011-2019 1.3790036 4629.2911
Atlantic (28.2, Inf] 1982-2000 –> 2001-2010 0.7235343 4350.9828
Atlantic (28.2, Inf] 2001-2010 –> 2011-2019 0.8503559 4373.9735
Indo-Pacific (-Inf,26] 1982-2000 –> 2001-2010 14.0235574 78728.1754
Indo-Pacific (-Inf,26] 2001-2010 –> 2011-2019 13.4871226 51212.8556
Indo-Pacific (26,26.5] 1982-2000 –> 2001-2010 9.2381923 72699.0137
Indo-Pacific (26,26.5] 2001-2010 –> 2011-2019 9.5784598 47859.2812
Indo-Pacific (26.5,26.75] 1982-2000 –> 2001-2010 7.8635191 56539.5457
Indo-Pacific (26.5,26.75] 2001-2010 –> 2011-2019 8.2496128 37589.4184
Indo-Pacific (26.75,27] 1982-2000 –> 2001-2010 8.0101459 66820.7186
Indo-Pacific (26.75,27] 2001-2010 –> 2011-2019 8.9418122 45644.5270
Indo-Pacific (27,27.25] 1982-2000 –> 2001-2010 7.7069688 78763.0822
Indo-Pacific (27,27.25] 2001-2010 –> 2011-2019 9.0641108 55106.1439
Indo-Pacific (27.25,27.5] 1982-2000 –> 2001-2010 6.6095626 66434.1229
Indo-Pacific (27.25,27.5] 2001-2010 –> 2011-2019 7.6659458 47061.0892
Indo-Pacific (27.5,27.75] 1982-2000 –> 2001-2010 5.6695168 62459.4198
Indo-Pacific (27.5,27.75] 2001-2010 –> 2011-2019 7.3198642 45944.3577
Indo-Pacific (27.75,27.85] 1982-2000 –> 2001-2010 4.7137613 22440.7722
Indo-Pacific (27.75,27.85] 2001-2010 –> 2011-2019 5.8281190 17019.7718
Indo-Pacific (27.85,27.95] 1982-2000 –> 2001-2010 4.9821027 29265.2680
Indo-Pacific (27.85,27.95] 2001-2010 –> 2011-2019 5.9312649 21163.1380
Indo-Pacific (27.95,28.05] 1982-2000 –> 2001-2010 4.1307498 23771.8172
Indo-Pacific (27.95,28.05] 2001-2010 –> 2011-2019 4.6237336 16561.1203
Indo-Pacific (28.05,28.1] 1982-2000 –> 2001-2010 3.5136419 15719.9707
Indo-Pacific (28.05,28.1] 2001-2010 –> 2011-2019 3.8909693 10622.2896
Indo-Pacific (28.1, Inf] 1982-2000 –> 2001-2010 2.6391577 109440.3978
Indo-Pacific (28.1, Inf] 2001-2010 –> 2011-2019 2.9652797 77145.3489

5.4 Target variable coefficients

A data frame to map the target variable is prepared.

# create table with two era belonging to one eras
eras_forward <- lm_all_fitted_wide %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(era, lead(era), sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_backward <- lm_all_fitted_wide %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_era <- full_join(eras_backward, eras_forward) %>% 
  filter(str_detect(eras, "NA") == FALSE)

# extend best model selection from eras to era
lm_best_target <- full_join(
  lm_best %>% select(basin, gamma_slab, model, eras),
  eras_era)

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.5 Plot selected model residuals

# plot model diagnostics, if activated
if (params_local$plot_all_figures == "y") {
  # mutate predictors column
  lm_best_plot <- lm_best_target %>%
    select(basin, gamma_slab, model, eras, era) %>%
    mutate(
      predictors = str_remove(model, paste(params_local$MLR_target, "~ ")),
      predictors = str_replace_all(predictors, "\\+ ", "")
    )
  
  # loop across all basins, era, gamma slabs, and MLRs
  # fit all MLR models
  for (i_basin in unique(GLODAP$basin)) {
    for (i_era in unique(GLODAP$era)) {
      #i_basin <- unique(GLODAP$basin)[1]
      #i_era   <- unique(GLODAP$era)[2]
      print(i_basin)
      print(i_era)
      
      GLODAP_basin_era <- GLODAP %>%
        filter(basin == i_basin, era == i_era)
      
      for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
        #i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
        print(i_gamma_slab)
        
        GLODAP_basin_era_slab <- GLODAP_basin_era %>%
          filter(gamma_slab == i_gamma_slab)
        
        lm_best_basin_era_slab <- lm_best_plot %>%
          filter(basin == i_basin, era == i_era, gamma_slab == i_gamma_slab)
        
        for (i_eras in unique(lm_best_basin_era_slab$eras)) {
          #i_eras <- unique(lm_best_basin_era_slab$eras)[1]
          print(i_eras)
          
          lm_best_basin_era_slab_eras <- lm_best_basin_era_slab %>%
            filter(eras == i_eras)
          
          for (i_predictors in unique(lm_best_basin_era_slab_eras$predictors)) {
            #i_predictors <- unique(lm_best_basin_era_slab$predictors)[1]
            print(i_predictors)
            # extract one model definition
            i_lm <- lm_all %>%
              filter(predictors == i_predictors) %>%
              select(lm_coeff) %>%
              pull()
            
             # fit model
          if (params_local$MLR_type == "rlm") {
            i_lm_fit <- MASS::rlm(as.formula(i_lm),
                                  data = GLODAP_basin_era_slab)
          }
          
          if (params_local$MLR_type == "lm") {
            i_lm_fit <- lm(as.formula(i_lm),
                           data = GLODAP_basin_era_slab)
          }
            
            # plot model diagnostics vs predictors
            
            p_model_predictors <- ggnostic(
              i_lm_fit,
              columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
              title = paste(
                "era:",
                i_era,
                "| eras:",
                i_eras,
                "| basin:",
                i_basin,
                "| gamma slab:",
                i_gamma_slab,
                "| predictors:",
                i_predictors
              )
            )
            
            ggsave(
              plot = p_model_predictors,
              path = paste(path_version_figures, "eMLR_diagnostics/", sep = ""),
              filename = paste(
                "MLR_residuals",
                i_era,
                i_eras,
                i_basin,
                i_gamma_slab,
                i_predictors,
                "predictors.png",
                sep = "_"
              ),
              width = 14,
              height = 8
            )

            rm(p_model_predictors)
            
            
            # plot model diagnostics vs location
            
            GLODAP_basin_era_slab <- GLODAP_basin_era_slab %>%
              mutate(fitted = i_lm_fit$fitted.values,
                     residuals = i_lm_fit$residuals)
            
            GLODAP_basin_era_slab_long <- GLODAP_basin_era_slab %>% 
              pivot_longer(cols = c(params_local$MLR_target , fitted, residuals),
                           names_to = "estimate",
                           values_to = "value"
              ) %>% 
              pivot_longer(cols = c(lat, lon, depth),
                           names_to = "coordinate_type",
                           values_to = "coordinate_value"
              )

             p_model_coordinate <- GLODAP_basin_era_slab_long %>%
              ggplot(aes(coordinate_value, value)) +
              geom_bin2d() +
              scale_fill_viridis_c() +
              labs(
                title = paste(
                  "era:",
                  i_era,
                  "| eras:",
                  i_eras,
                  "| basin:",
                  i_basin,
                  "| gamma slab:",
                  i_gamma_slab,
                  "| predictors:",
                  i_predictors
                )
              ) +
              facet_grid(estimate~coordinate_type,
                         scales = "free")

            ggsave(
              plot = p_model_coordinate,
              path = paste(path_version_figures, "eMLR_diagnostics", sep = ""),
              filename = paste(
                "Location_MLR_residuals",
                i_era,
                i_eras,
                i_basin,
                i_gamma_slab,
                i_predictors,
                "predictors.png",
                sep = "_"
              ),
              width = 14,
              height = 8
            )

            rm(p_model_coordinate)
            
          }
          
        }
        
      }
    }
  }
  
  rm(
    lm_best_plot,
    lm_best_basin_era_slab,
    i_rmse,
    GLODAP_basin_era,
    GLODAP_basin_era_slab,
    i_lm,
    lm_all_fitted,
    i_basin,
    i_era,
    i_gamma_slab,
    i_predictors,
    lm_all,
    i_aic,
    i_n_predictors,
    i_resid_max
  )
  
}

Individual residual plots of the MLR models for each basin, era, eras and neutral density (gamma) slab are available at:

/nfs/kryo/work/jenmueller/emlr_cant/model/v_XXX/figures/eMLR_diagnostics/

5.6 Cant coeffcients

A data frame of coefficient offsets is prepared to facilitate the direct mapping of Cant.

# pivot long format
lm_best_long <- lm_best_target %>%
  pivot_longer(cols = starts_with("coeff_"),
               names_to = "term",
               values_to = "estimate",
               names_prefix = "coeff_")

# subtract coefficients of adjacent era  
lm_best_long <- lm_best_long %>%
  arrange(era) %>%
  group_by(basin, gamma_slab, eras, model, term) %>%
  mutate(delta_coeff = estimate - lag(estimate)) %>%
  ungroup() %>%
  arrange(basin, gamma_slab, model, term, eras) %>%
  drop_na() %>%
  select(-c(era,estimate))

# pivot back to wide format
lm_best_cant <- lm_best_long %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

5.7 Write files

lm_best_target %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    era,
    starts_with("coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_target.csv",
                  sep = ""))

lm_best_cant %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    starts_with("delta_coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_cant.csv",
                  sep = ""))

6 Model diagnotics

6.1 Selection criterion vs predictors

The selection criterion (aic) was plotted against the number of predictors (limited to 3 - 9).

6.1.1 All models

lm_all_fitted_wide %>%
  ggplot(aes(as.factor(n_predictors),
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = 10) +
  geom_boxplot() +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1") +
  labs(x="Number of predictors")

Version Author Date
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
02b976d Donghe-Zhu 2021-02-24
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19

6.1.2 Best models

lm_best_target %>%
  ggplot(aes("",
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = 10) +
  geom_boxplot() +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1") +
  labs(x="Number of predictors pooled")

Version Author Date
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c407a50 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
e2ffc14 Donghe-Zhu 2021-02-05
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19

6.2 RMSE correlation between eras

RMSE was plotted to compare the agreement for one model applied to two adjacent eras (ie check whether the same predictor combination performs equal in both eras).

6.2.1 All models

# find max rmse to scale axis
max_rmse <-
  max(c(lm_all_fitted_wide_eras$rmse,
        lm_all_fitted_wide_eras$rmse_sum - lm_all_fitted_wide_eras$rmse))

lm_all_fitted_wide_eras %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0,max_rmse),
              ylim = c(0,max_rmse)) +
  facet_grid(eras ~ basin)

Version Author Date
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
02b976d Donghe-Zhu 2021-02-24
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
rm(max_rmse)

6.2.2 Best models

# find max rmse to scale axis
max_rmse <-
  max(c(lm_best$rmse,
        lm_best$rmse_sum - lm_best$rmse))

lm_best %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0,max_rmse),
              ylim = c(0,max_rmse)) +
  facet_grid(eras ~ basin)

Version Author Date
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c407a50 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
e2ffc14 Donghe-Zhu 2021-02-05
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
rm(max_rmse)

6.3 Predictor counts

The number of models where a particular predictor was included were counted for each basin, density slab and compared eras

# calculate cases of predictor used
lm_all_stats <- lm_best_long %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(basin, eras, gamma_slab) %>% 
  count(term) %>% 
  ungroup() %>% 
  pivot_wider(values_from = n,
              names_from = term,
              values_fill = 0)

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )
aou nitrate phosphate phosphate_star sal silicate temp
Atlantic - 1982-2000 --> 2001-2010
(-Inf,26] 5 1 4 5 3 2 2
(26,26.5] 5 3 2 4 1 4 4
(26.5,26.75] 5 1 4 4 2 5 2
(26.75,27] 5 1 4 4 1 5 3
(27,27.25] 5 2 3 4 3 5 2
(27.25,27.5] 5 4 1 3 3 5 2
(27.5,27.75] 5 1 4 3 4 3 1
(27.75,27.85] 5 2 3 3 5 4 0
(27.85,27.95] 5 0 5 5 2 3 2
(27.95,28.05] 5 2 3 5 2 3 3
(28.05,28.1] 5 0 5 5 2 3 2
(28.1,28.15] 5 1 4 5 3 4 1
(28.15,28.2] 5 5 0 4 2 3 3
(28.2, Inf] 5 5 0 3 4 3 1
total 70.00 28.00 42.00 57.00 37.00 52.00 28.00
Atlantic - 2001-2010 --> 2011-2019
(-Inf,26] 5 0 4 5 3 3 2
(26,26.5] 5 3 2 4 1 4 4
(26.5,26.75] 5 1 4 4 2 5 2
(26.75,27] 5 1 4 4 2 5 2
(27,27.25] 5 2 2 4 4 5 1
(27.25,27.5] 5 5 0 3 2 5 2
(27.5,27.75] 5 2 3 3 5 4 0
(27.75,27.85] 5 2 3 3 5 4 0
(27.85,27.95] 5 0 5 5 2 3 2
(27.95,28.05] 5 2 2 5 1 4 4
(28.05,28.1] 5 1 4 5 3 3 2
(28.1,28.15] 5 1 4 5 3 3 2
(28.15,28.2] 5 5 0 4 2 3 3
(28.2, Inf] 5 5 0 3 4 3 1
total 70.00 30.00 37.00 57.00 39.00 54.00 27.00
Indo-Pacific - 1982-2000 --> 2001-2010
(-Inf,26] 4 1 4 5 2 4 3
(26,26.5] 5 1 4 4 1 5 3
(26.5,26.75] 4 2 3 5 1 5 3
(26.75,27] 5 0 5 5 2 3 2
(27,27.25] 4 2 3 5 1 4 4
(27.25,27.5] 5 2 2 5 3 5 2
(27.5,27.75] 3 2 2 5 5 5 0
(27.75,27.85] 5 1 4 4 1 5 3
(27.85,27.95] 3 5 0 4 0 3 5
(27.95,28.05] 5 1 4 4 1 5 3
(28.05,28.1] 4 1 4 4 3 5 2
(28.1, Inf] 4 2 3 4 2 5 3
total 51.00 20.00 38.00 54.00 22.00 54.00 33.00
Indo-Pacific - 2001-2010 --> 2011-2019
(-Inf,26] 4 1 4 5 2 4 3
(26,26.5] 5 1 4 4 1 5 3
(26.5,26.75] 4 2 3 5 1 5 3
(26.75,27] 5 0 5 5 2 3 2
(27,27.25] 5 1 4 5 1 4 3
(27.25,27.5] 5 2 2 5 3 5 2
(27.5,27.75] 4 2 2 5 4 5 1
(27.75,27.85] 4 2 3 5 3 4 2
(27.85,27.95] 5 4 1 3 0 3 5
(27.95,28.05] 5 2 3 5 3 3 2
(28.05,28.1] 5 1 4 4 1 5 3
(28.1, Inf] 5 2 3 4 3 5 2
total 56.00 20.00 38.00 55.00 24.00 51.00 31.00

6.4 RMSE alternatives

AIC is an alternative criterion to RMSE to judge model quality, but not (yet) taken into account.

lm_all_fitted_wide_eras %>% 
  ggplot(aes(rmse, aic, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Version Author Date
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
02b976d Donghe-Zhu 2021-02-24
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
lm_best %>% 
  ggplot(aes(rmse, aic, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Version Author Date
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c407a50 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
e2ffc14 Donghe-Zhu 2021-02-05
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 

sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.2

Matrix products: default
BLAS:   /usr/local/R-4.0.3/lib64/R/lib/libRblas.so
LAPACK: /usr/local/R-4.0.3/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] gt_0.2.2         corrr_0.4.3      broom_0.7.5      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.3   
[21] tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] fs_1.5.0                 webshot_0.5.2            RColorBrewer_1.1-2      
 [4] httr_1.4.2               rprojroot_2.0.2          tools_4.0.3             
 [7] backports_1.1.10         R6_2.5.0                 nortest_1.0-4           
[10] DBI_1.1.0                colorspace_2.0-0         withr_2.3.0             
[13] gridExtra_2.3            tidyselect_1.1.0         curl_4.3                
[16] compiler_4.0.3           git2r_0.27.1             cli_2.2.0               
[19] rvest_0.3.6              xml2_1.3.2               sass_0.2.0              
[22] labeling_0.4.2           scales_1.1.1             checkmate_2.0.0         
[25] goftest_1.2-2            digest_0.6.27            foreign_0.8-80          
[28] rmarkdown_2.5            rio_0.5.16               pkgconfig_2.0.3         
[31] htmltools_0.5.0          highr_0.8                dbplyr_1.4.4            
[34] rlang_0.4.10             readxl_1.3.1             rstudioapi_0.13         
[37] farver_2.0.3             generics_0.1.0           jsonlite_1.7.2          
[40] zip_2.1.1                car_3.0-10               magrittr_2.0.1          
[43] Matrix_1.2-18            Rcpp_1.0.5               munsell_0.5.0           
[46] fansi_0.4.1              abind_1.4-5              lifecycle_0.2.0         
[49] stringi_1.5.3            whisker_0.4              yaml_2.2.1              
[52] carData_3.0-4            plyr_1.8.6               grid_4.0.3              
[55] blob_1.2.1               parallel_4.0.3           promises_1.1.1          
[58] crayon_1.3.4             lattice_0.20-41          haven_2.3.1             
[61] hms_0.5.3                pillar_1.4.7             reprex_0.3.0            
[64] glue_1.4.2               evaluate_0.14            RcppArmadillo_0.10.1.2.2
[67] data.table_1.13.6        modelr_0.1.8             vctrs_0.3.6             
[70] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[73] reshape_0.8.8            assertthat_0.2.1         xfun_0.20               
[76] openxlsx_4.2.3           RcppEigen_0.3.3.9.1      later_1.1.0.1           
[79] viridisLite_0.3.0        ellipsis_0.3.1           here_1.0.1