eMLR - model fitting

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Last updated: 2021-02-15

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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, oxygen, aou, nitrate, silicate, silicate_star, 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, "nitrate") &
      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, "nitrate") &
      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_si, lm_rm_o2) %>%
  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: 2
  
• Maximum: 5

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:

• 313

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:

• 10

The criterion used to select the best models was:

• rmse

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 + silicate_star + phosphate + phosphate_star	158	1.0475856	477.0748	4.332795	1982-1999 –> 2000-2012	2.3832111	1201.7435
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	158	1.0382074	474.2332	3.944222	1982-1999 –> 2000-2012	2.3741051	1198.9867
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	158	1.0382074	474.2332	3.944222	1982-1999 –> 2000-2012	2.3741051	1198.9867
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate	158	1.0475856	477.0748	4.332795	1982-1999 –> 2000-2012	2.3832111	1201.7435
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	158	1.0475856	477.0748	4.332795	1982-1999 –> 2000-2012	2.3832111	1201.7435
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	158	1.0440638	476.0107	4.148260	1982-1999 –> 2000-2012	2.3813170	1201.1861
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	158	1.0458289	476.5445	4.199297	1982-1999 –> 2000-2012	2.3833703	1201.8095
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	158	1.0447877	476.2297	3.991338	1982-1999 –> 2000-2012	2.3809752	1201.0734
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	158	1.0447877	476.2297	3.991338	1982-1999 –> 2000-2012	2.3809752	1201.0734
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	158	1.0447877	476.2297	3.991338	1982-1999 –> 2000-2012	2.3809752	1201.0734
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	72	1.1936365	243.8158	3.237974	2000-2012 –> 2013-2019	2.2417197	721.0407
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	72	1.1326926	236.2692	2.855476	2000-2012 –> 2013-2019	2.1709001	710.5024
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	72	1.1326926	236.2692	2.855476	2000-2012 –> 2013-2019	2.1709001	710.5024
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	72	1.1936365	243.8158	3.237974	2000-2012 –> 2013-2019	2.2417197	721.0407
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	72	1.1936365	243.8158	3.237974	2000-2012 –> 2013-2019	2.2417197	721.0407
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	72	1.1361477	236.7078	2.802670	2000-2012 –> 2013-2019	2.1802115	712.7185
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	72	1.1377961	236.9166	2.786570	2000-2012 –> 2013-2019	2.1836250	713.4610
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	72	1.1990801	244.4710	3.379652	2000-2012 –> 2013-2019	2.2529029	723.4217
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	72	1.1396017	237.1449	2.772460	2000-2012 –> 2013-2019	2.1874195	714.2898
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	72	1.1396017	237.1449	2.772460	2000-2012 –> 2013-2019	2.1874195	714.2898
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	1046	3.3042550	5482.8009	13.811611	1982-1999 –> 2000-2012	6.5688725	13433.1484
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	1046	3.3042550	5482.8009	13.811611	1982-1999 –> 2000-2012	6.5688725	13433.1484
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate	1046	3.2403045	5441.9154	14.502344	1982-1999 –> 2000-2012	6.4880149	13376.4262
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate_star	1046	3.2403045	5441.9154	14.502344	1982-1999 –> 2000-2012	6.4880149	13376.4262
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + silicate + silicate_star	1046	3.2403045	5441.9154	14.502344	1982-1999 –> 2000-2012	6.4880149	13376.4262
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate	1046	3.3139957	5488.9589	14.956164	1982-1999 –> 2000-2012	6.6524475	13507.5183
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate_star	1046	3.3139957	5488.9589	14.956164	1982-1999 –> 2000-2012	6.6524475	13507.5183
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + silicate_star	1046	3.3139957	5488.9589	14.956164	1982-1999 –> 2000-2012	6.6524475	13507.5183
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + nitrate + silicate_star	1046	3.3407849	5505.8019	15.174084	1982-1999 –> 2000-2012	6.7113159	13553.5288
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + silicate_star	1046	3.3407849	5505.8019	15.174084	1982-1999 –> 2000-2012	6.7113159	13553.5288
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	567	3.2403908	2956.3132	10.534106	2000-2012 –> 2013-2019	6.5446458	8439.1141
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate	567	3.0857248	2900.8523	9.468161	2000-2012 –> 2013-2019	6.3260293	8342.7677
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate_star	567	3.0857248	2900.8523	9.468161	2000-2012 –> 2013-2019	6.3260293	8342.7677
Atlantic	(26,26.5]	cstar_tref ~ sal + oxygen + aou + silicate + silicate_star	567	3.0857248	2900.8523	9.468161	2000-2012 –> 2013-2019	6.3260293	8342.7677
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate	567	3.1723161	2932.2362	9.432214	2000-2012 –> 2013-2019	6.4863118	8421.1950
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate_star	567	3.1723161	2932.2362	9.432214	2000-2012 –> 2013-2019	6.4863118	8421.1950
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + silicate_star	567	3.1723161	2932.2362	9.432214	2000-2012 –> 2013-2019	6.4863118	8421.1950
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + nitrate + silicate	567	3.1999712	2942.0791	9.522004	2000-2012 –> 2013-2019	6.5407562	8447.8810
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + nitrate + silicate_star	567	3.1999712	2942.0791	9.522004	2000-2012 –> 2013-2019	6.5407562	8447.8810
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + silicate_star	567	3.1999712	2942.0791	9.522004	2000-2012 –> 2013-2019	6.5407562	8447.8810
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	1397	3.2423787	7265.1167	9.560288	1982-1999 –> 2000-2012	6.2982027	16900.6544
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1397	3.2249399	7250.0489	10.037456	1982-1999 –> 2000-2012	6.2079736	16794.1190
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1397	3.2249399	7250.0489	10.037456	1982-1999 –> 2000-2012	6.2079736	16794.1190
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1397	3.2249399	7250.0489	10.037456	1982-1999 –> 2000-2012	6.2079736	16794.1190
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	656	3.3433340	3459.1900	9.454244	2000-2012 –> 2013-2019	6.5857127	10724.3067
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	656	3.3238240	3451.5114	11.113656	2000-2012 –> 2013-2019	6.5487639	10701.5603
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	656	3.3238240	3451.5114	11.113656	2000-2012 –> 2013-2019	6.5487639	10701.5603
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	656	3.3238240	3451.5114	11.113656	2000-2012 –> 2013-2019	6.5487639	10701.5603
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	2398	2.0422179	10243.7478	13.072427	1982-1999 –> 2000-2012	3.6820169	22274.6044
Atlantic	(26.75,27]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	2398	2.0422179	10243.7478	13.072427	1982-1999 –> 2000-2012	3.6820169	22274.6044
Atlantic	(26.75,27]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	2398	2.0422179	10243.7478	13.072427	1982-1999 –> 2000-2012	3.6820169	22274.6044
Atlantic	(26.75,27]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	2398	2.0422179	10243.7478	13.072427	1982-1999 –> 2000-2012	3.6820169	22274.6044
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2398	2.0001820	10143.9994	14.081577	1982-1999 –> 2000-2012	3.6531709	22225.1681
Atlantic	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2398	2.0001820	10143.9994	14.081577	1982-1999 –> 2000-2012	3.6531709	22225.1681
Atlantic	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2398	2.0001820	10143.9994	14.081577	1982-1999 –> 2000-2012	3.6531709	22225.1681
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2398	2.0860637	10345.6268	19.975942	1982-1999 –> 2000-2012	3.5995129	21872.9381
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2398	2.0860637	10345.6268	19.975942	1982-1999 –> 2000-2012	3.5995129	21872.9381
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2398	2.0860637	10345.6268	19.975942	1982-1999 –> 2000-2012	3.5995129	21872.9381
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	1263	2.5145378	5927.4356	22.300060	2000-2012 –> 2013-2019	4.5567556	16171.1833
Atlantic	(26.75,27]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	1263	2.5145378	5927.4356	22.300060	2000-2012 –> 2013-2019	4.5567556	16171.1833
Atlantic	(26.75,27]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	1263	2.5145378	5927.4356	22.300060	2000-2012 –> 2013-2019	4.5567556	16171.1833
Atlantic	(26.75,27]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	1263	2.5145378	5927.4356	22.300060	2000-2012 –> 2013-2019	4.5567556	16171.1833
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1263	2.5330762	5945.9902	25.891764	2000-2012 –> 2013-2019	4.5332582	16089.9896
Atlantic	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1263	2.5330762	5945.9902	25.891764	2000-2012 –> 2013-2019	4.5332582	16089.9896
Atlantic	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1263	2.5330762	5945.9902	25.891764	2000-2012 –> 2013-2019	4.5332582	16089.9896
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1263	2.2552518	5652.5376	22.583567	2000-2012 –> 2013-2019	4.3413155	15998.1644
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1263	2.2552518	5652.5376	22.583567	2000-2012 –> 2013-2019	4.3413155	15998.1644
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1263	2.2552518	5652.5376	22.583567	2000-2012 –> 2013-2019	4.3413155	15998.1644
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	2031	1.8626152	8304.2173	11.021443	1982-1999 –> 2000-2012	3.5644105	18504.3667
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	2031	1.8626152	8304.2173	11.021443	1982-1999 –> 2000-2012	3.5644105	18504.3667
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2031	1.8904789	8364.5325	9.689213	1982-1999 –> 2000-2012	3.4604645	18143.6984
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2031	1.8904789	8364.5325	9.689213	1982-1999 –> 2000-2012	3.4604645	18143.6984
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2031	1.8904789	8364.5325	9.689213	1982-1999 –> 2000-2012	3.4604645	18143.6984
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2031	1.8979717	8380.6003	9.355072	1982-1999 –> 2000-2012	3.4547428	18115.6267
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2031	1.9187787	8424.8886	8.642107	1982-1999 –> 2000-2012	3.5002075	18241.9782
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2031	1.9234272	8434.7175	8.493771	1982-1999 –> 2000-2012	3.5167839	18291.0461
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2031	1.9234272	8434.7175	8.493771	1982-1999 –> 2000-2012	3.5167839	18291.0461
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2031	1.9234272	8434.7175	8.493771	1982-1999 –> 2000-2012	3.5167839	18291.0461
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	1142	2.1593133	5013.0566	10.465472	2000-2012 –> 2013-2019	4.0219286	13317.2739
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	1142	2.1593133	5013.0566	10.465472	2000-2012 –> 2013-2019	4.0219286	13317.2739
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1142	2.3003827	5155.6000	13.777336	2000-2012 –> 2013-2019	4.2152027	13570.0995
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1142	2.2946948	5151.9457	14.080782	2000-2012 –> 2013-2019	4.1851737	13516.4782
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate	1142	2.1593133	5013.0566	10.465472	2000-2012 –> 2013-2019	4.0219286	13317.2739
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1142	2.2946948	5151.9457	14.080782	2000-2012 –> 2013-2019	4.1851737	13516.4782
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1142	2.2946948	5151.9457	14.080782	2000-2012 –> 2013-2019	4.1851737	13516.4782
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1142	2.2882847	5145.5566	14.231726	2000-2012 –> 2013-2019	4.1862565	13526.1569
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1142	2.3093184	5166.4549	14.219293	2000-2012 –> 2013-2019	4.2280971	13591.3435
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1142	2.3127467	5169.8432	14.213647	2000-2012 –> 2013-2019	4.2361739	13604.5606
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	2025	2.2571186	9057.7617	21.333316	1982-1999 –> 2000-2012	3.9135961	20144.1869
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	2025	2.2571186	9057.7617	21.333316	1982-1999 –> 2000-2012	3.9135961	20144.1869
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	2025	2.2571186	9057.7617	21.333316	1982-1999 –> 2000-2012	3.9135961	20144.1869
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	2025	2.2571186	9057.7617	21.333316	1982-1999 –> 2000-2012	3.9135961	20144.1869
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate	2025	2.1403141	8842.5591	17.909272	1982-1999 –> 2000-2012	3.7787585	19865.9783
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate_star	2025	2.1403141	8842.5591	17.909272	1982-1999 –> 2000-2012	3.7787585	19865.9783
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + silicate_star	2025	2.1403141	8842.5591	17.909272	1982-1999 –> 2000-2012	3.7787585	19865.9783
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate	2025	2.1625100	8884.3428	12.574713	1982-1999 –> 2000-2012	3.8613513	20116.1247
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate_star	2025	2.1625100	8884.3428	12.574713	1982-1999 –> 2000-2012	3.8613513	20116.1247
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + silicate_star	2025	2.1625100	8884.3428	12.574713	1982-1999 –> 2000-2012	3.8613513	20116.1247
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	1109	2.7884162	5435.7065	20.513112	2000-2012 –> 2013-2019	5.0455349	14493.4682
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	1109	2.7884162	5435.7065	20.513112	2000-2012 –> 2013-2019	5.0455349	14493.4682
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	1109	2.7884162	5435.7065	20.513112	2000-2012 –> 2013-2019	5.0455349	14493.4682
Atlantic	(27.25,27.5]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	1109	2.7884162	5435.7065	20.513112	2000-2012 –> 2013-2019	5.0455349	14493.4682
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate	1109	2.7818295	5430.4610	17.251552	2000-2012 –> 2013-2019	4.9221436	14273.0201
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate_star	1109	2.7818295	5430.4610	17.251552	2000-2012 –> 2013-2019	4.9221436	14273.0201
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + silicate_star	1109	2.7818295	5430.4610	17.251552	2000-2012 –> 2013-2019	4.9221436	14273.0201
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate	1109	2.8205406	5461.1132	14.090309	2000-2012 –> 2013-2019	4.9830506	14345.4560
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate_star	1109	2.8205406	5461.1132	14.090309	2000-2012 –> 2013-2019	4.9830506	14345.4560
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + silicate_star	1109	2.8205406	5461.1132	14.090309	2000-2012 –> 2013-2019	4.9830506	14345.4560
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2804	2.3920617	12862.4560	14.587684	1982-1999 –> 2000-2012	4.4588552	28894.8448
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2804	2.4132697	12911.9574	14.216479	1982-1999 –> 2000-2012	4.4797512	28943.2189
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate	2804	2.3839660	12843.4441	14.796406	1982-1999 –> 2000-2012	4.4516637	28879.0996
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate_star	2804	2.4092938	12902.7105	14.400897	1982-1999 –> 2000-2012	4.4794481	28947.2331
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2804	2.4122515	12909.5908	14.214259	1982-1999 –> 2000-2012	4.4796273	28944.0833
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2804	2.4122515	12909.5908	14.214259	1982-1999 –> 2000-2012	4.4796273	28944.0833
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate	2804	2.4048587	12892.3776	14.428218	1982-1999 –> 2000-2012	4.4743063	28934.3505
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate_star	2804	2.4048587	12892.3776	14.428218	1982-1999 –> 2000-2012	4.4743063	28934.3505
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2804	2.4122515	12909.5908	14.214259	1982-1999 –> 2000-2012	4.4796273	28944.0833
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate_star + phosphate + phosphate_star	2804	2.4048587	12892.3776	14.428218	1982-1999 –> 2000-2012	4.4743063	28934.3505
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	1515	2.7078202	7331.6999	19.383046	2000-2012 –> 2013-2019	5.0921815	20176.0738
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	1515	2.7078202	7331.6999	19.383046	2000-2012 –> 2013-2019	5.0921815	20176.0738
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate	1515	2.7078202	7331.6999	19.383046	2000-2012 –> 2013-2019	5.0921815	20176.0738
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate_star + phosphate + phosphate_star	1515	2.8440453	7480.4229	15.889857	2000-2012 –> 2013-2019	5.2298715	20328.2412
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate	1515	2.8440453	7480.4229	15.889857	2000-2012 –> 2013-2019	5.2298715	20328.2412
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	1515	2.8440453	7480.4229	15.889857	2000-2012 –> 2013-2019	5.2298715	20328.2412
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate	1515	2.8424715	7478.7457	15.993945	2000-2012 –> 2013-2019	5.2264375	20322.1898
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate	1515	2.8404338	7476.5728	17.250180	2000-2012 –> 2013-2019	5.2452924	20368.9504
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate_star	1515	2.8404338	7476.5728	17.250180	2000-2012 –> 2013-2019	5.2452924	20368.9504
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate_star + phosphate + phosphate_star	1515	2.8404338	7476.5728	17.250180	2000-2012 –> 2013-2019	5.2452924	20368.9504
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1036	1.5641536	3880.9392	12.798383	1982-1999 –> 2000-2012	3.1611985	8876.8661
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate_star + phosphate + phosphate_star	1036	1.5578540	3872.5773	12.740813	1982-1999 –> 2000-2012	3.1520469	8863.7855
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	1036	1.5100084	3807.9434	14.539112	1982-1999 –> 2000-2012	3.0360994	8683.8943
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	1036	1.5100084	3807.9434	14.539112	1982-1999 –> 2000-2012	3.0360994	8683.8943
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1036	1.5641536	3880.9392	12.798383	1982-1999 –> 2000-2012	3.1611985	8876.8661
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate	1036	1.5578540	3872.5773	12.740813	1982-1999 –> 2000-2012	3.1520469	8863.7855
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	1036	1.5578540	3872.5773	12.740813	1982-1999 –> 2000-2012	3.1520469	8863.7855
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	1036	1.5197119	3821.2156	14.808950	1982-1999 –> 2000-2012	3.0586861	8719.3599
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	1036	1.5430795	3852.8330	15.324821	1982-1999 –> 2000-2012	3.1087399	8796.3632
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	1036	1.5430795	3852.8330	15.324821	1982-1999 –> 2000-2012	3.1087399	8796.3632
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate_star + phosphate + phosphate_star	513	1.7382180	2037.0658	11.972402	2000-2012 –> 2013-2019	3.2960719	5909.6431
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	513	1.7094323	2019.9324	13.736344	2000-2012 –> 2013-2019	3.2194407	5827.8758
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	513	1.7094323	2019.9324	13.736344	2000-2012 –> 2013-2019	3.2194407	5827.8758
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	513	1.7475521	2042.5606	12.039326	2000-2012 –> 2013-2019	3.3117057	5923.4997
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	513	1.7475521	2042.5606	12.039326	2000-2012 –> 2013-2019	3.3117057	5923.4997
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate	513	1.7382180	2037.0658	11.972402	2000-2012 –> 2013-2019	3.2960719	5909.6431
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	513	1.7382180	2037.0658	11.972402	2000-2012 –> 2013-2019	3.2960719	5909.6431
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	513	1.7242945	2028.8142	13.967079	2000-2012 –> 2013-2019	3.2440064	5850.0298
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	513	1.7556052	2047.2777	14.468303	2000-2012 –> 2013-2019	3.2986847	5900.1107
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	513	1.7556052	2047.2777	14.468303	2000-2012 –> 2013-2019	3.2986847	5900.1107
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	983	2.9304503	4917.3900	22.456892	1982-1999 –> 2000-2012	5.6593028	11405.1644
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	983	3.0630171	5004.3744	26.240993	1982-1999 –> 2000-2012	5.9542902	11646.6323
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	983	2.9304503	4917.3900	22.456892	1982-1999 –> 2000-2012	5.6593028	11405.1644
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	983	2.9304503	4917.3900	22.456892	1982-1999 –> 2000-2012	5.6593028	11405.1644
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	983	3.0757549	5012.5332	23.130965	1982-1999 –> 2000-2012	5.9400103	11629.7050
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	983	3.0758688	5012.6060	23.140031	1982-1999 –> 2000-2012	5.9407219	11630.3353
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	983	3.0757549	5012.5332	23.130965	1982-1999 –> 2000-2012	5.9400103	11629.7050
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	983	3.0757549	5012.5332	23.130965	1982-1999 –> 2000-2012	5.9400103	11629.7050
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	983	3.0758688	5012.6060	23.140031	1982-1999 –> 2000-2012	5.9407219	11630.3353
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	983	3.0758688	5012.6060	23.140031	1982-1999 –> 2000-2012	5.9407219	11630.3353
Atlantic	(27.85,27.95]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	569	3.2198068	2959.4398	28.682477	2000-2012 –> 2013-2019	6.6553718	8189.4735
Atlantic	(27.85,27.95]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	569	3.2198068	2959.4398	28.682477	2000-2012 –> 2013-2019	6.6553718	8189.4735
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	569	3.3261262	2996.4099	29.121490	2000-2012 –> 2013-2019	6.2565764	7913.7999
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	569	3.5578347	3073.0472	28.721108	2000-2012 –> 2013-2019	6.6208518	8077.4216
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	569	3.3261262	2996.4099	29.121490	2000-2012 –> 2013-2019	6.2565764	7913.7999
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	569	3.3261262	2996.4099	29.121490	2000-2012 –> 2013-2019	6.2565764	7913.7999
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	569	3.6600265	3105.2733	23.151675	2000-2012 –> 2013-2019	6.7357814	8117.8065
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	569	3.6603862	3105.3852	23.147178	2000-2012 –> 2013-2019	6.7362550	8117.9912
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	569	3.6600265	3105.2733	23.151675	2000-2012 –> 2013-2019	6.7357814	8117.8065
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	569	3.6600265	3105.2733	23.151675	2000-2012 –> 2013-2019	6.7357814	8117.8065
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1204	3.8590720	6682.6316	25.099675	1982-1999 –> 2000-2012	7.3908813	15682.5017
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate_star + phosphate_star	1204	3.8590720	6682.6316	25.099675	1982-1999 –> 2000-2012	7.3908813	15682.5017
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + silicate_star + phosphate_star	1204	3.8590720	6682.6316	25.099675	1982-1999 –> 2000-2012	7.3908813	15682.5017
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate_star + phosphate	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate_star + phosphate_star	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + silicate + silicate_star + phosphate	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + silicate + silicate_star + phosphate_star	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ temp + silicate + silicate_star + phosphate + phosphate_star	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	666	3.5357472	3586.2418	25.590197	2000-2012 –> 2013-2019	7.4915867	10328.5101
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	666	3.5060655	3575.0128	26.986021	2000-2012 –> 2013-2019	7.3651375	10257.6443
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate_star + phosphate_star	666	3.5060655	3575.0128	26.986021	2000-2012 –> 2013-2019	7.3651375	10257.6443
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + silicate_star + phosphate_star	666	3.5060655	3575.0128	26.986021	2000-2012 –> 2013-2019	7.3651375	10257.6443
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate_star + phosphate	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate_star + phosphate_star	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + silicate + silicate_star + phosphate	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + silicate + silicate_star + phosphate_star	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	804	0.9934328	2285.0583	8.087713	1982-1999 –> 2000-2012	1.8641000	5054.5716
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	804	1.0115481	2314.1161	9.678931	1982-1999 –> 2000-2012	1.8601691	5028.4371
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	804	0.9934328	2285.0583	8.087713	1982-1999 –> 2000-2012	1.8641000	5054.5716
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	804	0.9934328	2285.0583	8.087713	1982-1999 –> 2000-2012	1.8641000	5054.5716
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	804	1.0436142	2364.2985	12.188672	1982-1999 –> 2000-2012	1.8828911	5054.7923
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	804	1.0427660	2362.9910	12.172235	1982-1999 –> 2000-2012	1.8811182	5051.1125
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	804	1.0436142	2364.2985	12.188672	1982-1999 –> 2000-2012	1.8828911	5054.7923
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	804	1.0436142	2364.2985	12.188672	1982-1999 –> 2000-2012	1.8828911	5054.7923
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	804	1.0427660	2362.9910	12.172235	1982-1999 –> 2000-2012	1.8811182	5051.1125
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	804	1.0427660	2362.9910	12.172235	1982-1999 –> 2000-2012	1.8811182	5051.1125
Atlantic	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	434	1.0460351	1284.7046	7.627744	2000-2012 –> 2013-2019	2.0692031	3617.1869
Atlantic	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	434	1.0460351	1284.7046	7.627744	2000-2012 –> 2013-2019	2.0692031	3617.1869
Atlantic	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	434	1.0577152	1294.3431	7.425265	2000-2012 –> 2013-2019	2.0896374	3640.5250
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	434	1.0500656	1288.0427	7.506976	2000-2012 –> 2013-2019	2.0773265	3626.9446
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	434	1.0174317	1260.6390	9.169936	2000-2012 –> 2013-2019	2.0108645	3545.6973
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	434	1.0478798	1286.2340	10.830251	2000-2012 –> 2013-2019	2.0594278	3600.3501
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	434	1.0174317	1260.6390	9.169936	2000-2012 –> 2013-2019	2.0108645	3545.6973
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	434	1.0174317	1260.6390	9.169936	2000-2012 –> 2013-2019	2.0108645	3545.6973
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	434	1.0517810	1289.4595	7.474466	2000-2012 –> 2013-2019	2.0814698	3632.1573
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	434	1.0517810	1289.4595	7.474466	2000-2012 –> 2013-2019	2.0814698	3632.1573
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	936	0.7505637	2133.1187	7.864208	1982-1999 –> 2000-2012	1.3349866	4431.0017
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	936	0.7856962	2218.7544	10.025704	1982-1999 –> 2000-2012	1.3744859	4535.9182
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	936	0.7848370	2216.7061	10.063082	1982-1999 –> 2000-2012	1.3705842	4520.4516
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate	936	0.7987682	2249.6435	10.877044	1982-1999 –> 2000-2012	1.3708704	4492.3408
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate_star	936	0.7987682	2249.6435	10.877044	1982-1999 –> 2000-2012	1.3708704	4492.3408
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	936	0.7856962	2218.7544	10.025704	1982-1999 –> 2000-2012	1.3744859	4535.9182
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	936	0.7856962	2218.7544	10.025704	1982-1999 –> 2000-2012	1.3744859	4535.9182
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + silicate_star	936	0.7987682	2249.6435	10.877044	1982-1999 –> 2000-2012	1.3708704	4492.3408
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	936	0.7848370	2216.7061	10.063082	1982-1999 –> 2000-2012	1.3705842	4520.4516
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	936	0.7848370	2216.7061	10.063082	1982-1999 –> 2000-2012	1.3705842	4520.4516
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	497	0.8712585	1287.4353	6.182326	2000-2012 –> 2013-2019	1.6311195	3443.5998
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate_star + phosphate + phosphate_star	497	0.8712841	1287.4645	6.182969	2000-2012 –> 2013-2019	1.6311181	3443.5627
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	497	0.8712585	1287.4353	6.182326	2000-2012 –> 2013-2019	1.6311195	3443.5998
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	497	0.8712585	1287.4353	6.182326	2000-2012 –> 2013-2019	1.6311195	3443.5998
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate	497	0.8712841	1287.4645	6.182969	2000-2012 –> 2013-2019	1.6311181	3443.5627
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	497	0.8712841	1287.4645	6.182969	2000-2012 –> 2013-2019	1.6311181	3443.5627
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	497	0.8492568	1262.0116	6.971050	2000-2012 –> 2013-2019	1.6225461	3450.9696
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	497	0.8286782	1237.6291	9.047780	2000-2012 –> 2013-2019	1.5792420	3370.7478
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	497	0.8492568	1262.0116	6.971050	2000-2012 –> 2013-2019	1.6225461	3450.9696
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	497	0.8492568	1262.0116	6.971050	2000-2012 –> 2013-2019	1.6225461	3450.9696
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1540	0.5471615	2527.0561	2.040783	1982-1999 –> 2000-2012	1.0648603	5924.1022
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate_star	1540	0.5471615	2527.0561	2.040783	1982-1999 –> 2000-2012	1.0648603	5924.1022
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate_star	1540	0.5471615	2527.0561	2.040783	1982-1999 –> 2000-2012	1.0648603	5924.1022
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	1540	0.3811816	1413.7338	1.800271	1982-1999 –> 2000-2012	0.8158366	4033.0874
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate	1540	0.4269578	1761.0344	1.632599	1982-1999 –> 2000-2012	0.8645347	4408.1894
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate	1540	0.3447362	1104.2051	1.681506	1982-1999 –> 2000-2012	0.7503579	3416.0603
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate_star	1540	0.3447362	1104.2051	1.681506	1982-1999 –> 2000-2012	0.7503579	3416.0603
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate	1540	0.3632927	1265.6880	1.840394	1982-1999 –> 2000-2012	0.7552045	3424.6025
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate_star	1540	0.3632927	1265.6880	1.840394	1982-1999 –> 2000-2012	0.7552045	3424.6025
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + silicate + silicate_star	1540	0.3632927	1265.6880	1.840394	1982-1999 –> 2000-2012	0.7552045	3424.6025
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	819	0.7372762	1838.9708	4.731734	2000-2012 –> 2013-2019	1.2844377	4366.0269
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate_star	819	0.7372762	1838.9708	4.731734	2000-2012 –> 2013-2019	1.2844377	4366.0269
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate_star	819	0.7372762	1838.9708	4.731734	2000-2012 –> 2013-2019	1.2844377	4366.0269
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	819	0.6963213	1745.3570	6.846739	2000-2012 –> 2013-2019	1.0775029	3159.0908
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate	819	0.7030888	1759.1996	7.602305	2000-2012 –> 2013-2019	1.1300465	3520.2341
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate	819	0.6693303	1680.6011	8.052277	2000-2012 –> 2013-2019	1.0140665	2784.8062
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate_star	819	0.6693303	1680.6011	8.052277	2000-2012 –> 2013-2019	1.0140665	2784.8062
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate	819	0.6403755	1608.1638	7.320694	2000-2012 –> 2013-2019	1.0036682	2873.8518
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate_star	819	0.6403755	1608.1638	7.320694	2000-2012 –> 2013-2019	1.0036682	2873.8518
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + silicate + silicate_star	819	0.6403755	1608.1638	7.320694	2000-2012 –> 2013-2019	1.0036682	2873.8518
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	2693	0.3242828	1591.0173	2.115462	1982-1999 –> 2000-2012	0.6239944	3193.3546
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2693	0.3463114	1944.9979	1.900529	1982-1999 –> 2000-2012	0.6453988	3531.8596
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	2693	0.3242828	1591.0173	2.115462	1982-1999 –> 2000-2012	0.6239944	3193.3546
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate_star	2693	0.3463114	1944.9979	1.900529	1982-1999 –> 2000-2012	0.6453988	3531.8596
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate	2693	0.3242828	1591.0173	2.115462	1982-1999 –> 2000-2012	0.6239944	3193.3546
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate_star	2693	0.3463114	1944.9979	1.900529	1982-1999 –> 2000-2012	0.6453988	3531.8596
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	2693	0.3469830	1955.4330	2.125336	1982-1999 –> 2000-2012	0.6488837	3611.7830
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	2693	0.3469830	1955.4330	2.125336	1982-1999 –> 2000-2012	0.6488837	3611.7830
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	2693	0.3457583	1936.3893	2.124533	1982-1999 –> 2000-2012	0.6437290	3495.4877
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	2693	0.3457583	1936.3893	2.124533	1982-1999 –> 2000-2012	0.6437290	3495.4877
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate	1557	0.3868691	1473.3053	2.525540	2000-2012 –> 2013-2019	0.7361466	3462.2365
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	1557	0.3502557	1165.7023	2.704232	2000-2012 –> 2013-2019	0.6745385	2756.7196
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	1557	0.3502557	1165.7023	2.704232	2000-2012 –> 2013-2019	0.6745385	2756.7196
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate	1557	0.3502557	1165.7023	2.704232	2000-2012 –> 2013-2019	0.6745385	2756.7196
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	1557	0.3797467	1417.4419	2.705317	2000-2012 –> 2013-2019	0.7267298	3372.8749
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	1557	0.3797467	1417.4419	2.705317	2000-2012 –> 2013-2019	0.7267298	3372.8749
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	1557	0.3800118	1419.6148	2.702494	2000-2012 –> 2013-2019	0.7271406	3377.3089
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	1557	0.3803071	1422.0335	2.702200	2000-2012 –> 2013-2019	0.7276306	3382.7492
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	1557	0.3788592	1410.1550	2.700717	2000-2012 –> 2013-2019	0.7246175	3346.5443
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	1557	0.3788592	1410.1550	2.700717	2000-2012 –> 2013-2019	0.7246175	3346.5443
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5288	6.1928478	34304.9200	29.527354	1982-1999 –> 2000-2012	12.6716991	81612.6324
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	5288	5.9081446	33807.1795	33.261331	1982-1999 –> 2000-2012	12.1256599	80522.5792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	5288	5.9081446	33807.1795	33.261331	1982-1999 –> 2000-2012	12.1256599	80522.5792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	5288	6.1928478	34304.9200	29.527354	1982-1999 –> 2000-2012	12.6716991	81612.6324
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	5288	6.1928478	34304.9200	29.527354	1982-1999 –> 2000-2012	12.6716991	81612.6324
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	5288	6.0145280	33995.9192	33.811166	1982-1999 –> 2000-2012	12.3312392	80939.0253
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	5288	6.0656694	34085.4664	34.021650	1982-1999 –> 2000-2012	12.4290401	81134.4469
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	5288	6.2323348	34372.1408	29.869481	1982-1999 –> 2000-2012	12.7604050	81788.7288
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	5288	6.0863610	34121.4827	34.020695	1982-1999 –> 2000-2012	12.4717454	81220.1444
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	5288	6.0863610	34121.4827	34.020695	1982-1999 –> 2000-2012	12.4717454	81220.1444
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2816	5.8778725	17980.8313	24.128023	2000-2012 –> 2013-2019	12.0707203	52285.7513
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	2816	5.6382388	17746.4099	27.667683	2000-2012 –> 2013-2019	11.5463834	51553.5894
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	2816	5.6382388	17746.4099	27.667683	2000-2012 –> 2013-2019	11.5463834	51553.5894
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2816	5.8778725	17980.8313	24.128023	2000-2012 –> 2013-2019	12.0707203	52285.7513
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2816	5.8778725	17980.8313	24.128023	2000-2012 –> 2013-2019	12.0707203	52285.7513
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	2816	5.7297950	17837.1302	28.456699	2000-2012 –> 2013-2019	11.7443230	51833.0493
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	2816	5.7800044	17886.2676	29.028201	2000-2012 –> 2013-2019	11.8456737	51971.7340
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2816	5.9502121	18049.7219	24.771202	2000-2012 –> 2013-2019	12.1825468	52421.8627
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	2816	5.7921918	17898.1305	28.600115	2000-2012 –> 2013-2019	11.8785528	52019.6131
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	2816	5.7921918	17898.1305	28.600115	2000-2012 –> 2013-2019	11.8785528	52019.6131
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5525	4.5360650	32401.5327	43.772780	1982-1999 –> 2000-2012	8.7824377	76605.3494
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	5525	4.5360650	32401.5327	43.772780	1982-1999 –> 2000-2012	8.7824377	76605.3494
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	5525	4.5360650	32401.5327	43.772780	1982-1999 –> 2000-2012	8.7824377	76605.3494
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5525	4.5877220	32526.6595	39.934460	1982-1999 –> 2000-2012	8.8818706	76903.0425
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5525	4.6579284	32694.4781	38.557719	1982-1999 –> 2000-2012	9.0054183	77261.2754
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	5525	4.6658266	32713.1992	39.207721	1982-1999 –> 2000-2012	9.0244249	77319.3567
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	5525	4.6658266	32713.1992	39.207721	1982-1999 –> 2000-2012	9.0244249	77319.3567
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5525	4.6658266	32713.1992	39.207721	1982-1999 –> 2000-2012	9.0244249	77319.3567
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	5525	4.7292783	32862.4581	47.412368	1982-1999 –> 2000-2012	9.1428442	77661.9159
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + silicate_star + phosphate	5525	4.7292783	32862.4581	47.412368	1982-1999 –> 2000-2012	9.1428442	77661.9159
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2918	4.4724496	17036.8813	46.310491	2000-2012 –> 2013-2019	9.0085146	49438.4140
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2918	4.4724496	17036.8813	46.310491	2000-2012 –> 2013-2019	9.0085146	49438.4140
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2918	4.4724496	17036.8813	46.310491	2000-2012 –> 2013-2019	9.0085146	49438.4140
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2918	4.5594237	17149.2824	39.840874	2000-2012 –> 2013-2019	9.1471456	49675.9420
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2918	4.6381187	17249.1516	36.657339	2000-2012 –> 2013-2019	9.2960471	49943.6297
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2918	4.6426236	17254.8173	36.476302	2000-2012 –> 2013-2019	9.3084502	49968.0165
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2918	4.6426236	17254.8173	36.476302	2000-2012 –> 2013-2019	9.3084502	49968.0165
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	2918	4.5489045	17135.8025	48.107779	2000-2012 –> 2013-2019	9.2781828	49998.2607
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate_star + phosphate	2918	4.5489045	17135.8025	48.107779	2000-2012 –> 2013-2019	9.2781828	49998.2607
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + silicate_star + phosphate	2918	4.5489045	17135.8025	48.107779	2000-2012 –> 2013-2019	9.2781828	49998.2607
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	4544	3.8913517	25257.6932	27.853242	1982-1999 –> 2000-2012	7.7641398	60143.8499
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	4544	3.8913517	25257.6932	27.853242	1982-1999 –> 2000-2012	7.7641398	60143.8499
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	4544	3.8913517	25257.6932	27.853242	1982-1999 –> 2000-2012	7.7641398	60143.8499
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	4544	3.8913517	25257.6932	27.853242	1982-1999 –> 2000-2012	7.7641398	60143.8499
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	4544	3.8913517	25257.6932	27.853242	1982-1999 –> 2000-2012	7.7641398	60143.8499
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4544	3.9265162	25339.4488	20.226531	1982-1999 –> 2000-2012	7.6839109	59845.1956
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	4544	3.9266514	25339.7617	26.472095	1982-1999 –> 2000-2012	7.7219783	59971.8309
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	4544	3.9266514	25339.7617	26.472095	1982-1999 –> 2000-2012	7.7219783	59971.8309
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	4544	3.9265162	25339.4488	20.226531	1982-1999 –> 2000-2012	7.6839109	59845.1956
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	4544	3.9265162	25339.4488	20.226531	1982-1999 –> 2000-2012	7.6839109	59845.1956
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	2447	4.2048977	13987.2925	31.207461	2000-2012 –> 2013-2019	8.0962494	39244.9857
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	2447	4.2585434	14049.3348	30.985390	2000-2012 –> 2013-2019	8.1851948	39389.0965
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	2447	4.2585434	14049.3348	30.985390	2000-2012 –> 2013-2019	8.1851948	39389.0965
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate_star + phosphate_star	2447	4.2783866	14072.0860	34.710261	2000-2012 –> 2013-2019	8.2080586	39418.8360
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5354	4.1643941	30483.7138	22.734855	1982-1999 –> 2000-2012	7.7513405	71108.4774
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	5354	4.1643941	30483.7138	22.734855	1982-1999 –> 2000-2012	7.7513405	71108.4774
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	5354	4.1643941	30483.7138	22.734855	1982-1999 –> 2000-2012	7.7513405	71108.4774
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5354	4.1702723	30498.8181	21.453131	1982-1999 –> 2000-2012	7.8227361	71396.2141
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	5354	4.1165993	30360.1074	20.285252	1982-1999 –> 2000-2012	7.7366826	71123.3780
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate_star	5354	4.1734420	30506.9538	22.914051	1982-1999 –> 2000-2012	7.8375806	71452.4177
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	5354	4.1702723	30498.8181	21.453131	1982-1999 –> 2000-2012	7.8227361	71396.2141
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	5354	4.1702723	30498.8181	21.453131	1982-1999 –> 2000-2012	7.8227361	71396.2141
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	5354	4.1165993	30360.1074	20.285252	1982-1999 –> 2000-2012	7.7366826	71123.3780
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	5354	4.1165993	30360.1074	20.285252	1982-1999 –> 2000-2012	7.7366826	71123.3780
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2868	4.5360260	16826.1577	17.606576	2000-2012 –> 2013-2019	8.7004201	47309.8716
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	2868	4.5360260	16826.1577	17.606576	2000-2012 –> 2013-2019	8.7004201	47309.8716
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	2868	4.5360260	16826.1577	17.606576	2000-2012 –> 2013-2019	8.7004201	47309.8716
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2868	4.5537010	16848.4650	17.066955	2000-2012 –> 2013-2019	8.7239733	47347.2831
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	2868	4.5010869	16781.8046	18.240062	2000-2012 –> 2013-2019	8.6176862	47141.9121
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate	2868	4.5371637	16827.5961	18.186152	2000-2012 –> 2013-2019	8.7106057	47334.5499
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate_star	2868	4.5371637	16827.5961	18.186152	2000-2012 –> 2013-2019	8.7106057	47334.5499
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2868	4.5537010	16848.4650	17.066955	2000-2012 –> 2013-2019	8.7239733	47347.2831
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	2868	4.5010869	16781.8046	18.240062	2000-2012 –> 2013-2019	8.6176862	47141.9121
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	2868	4.5010869	16781.8046	18.240062	2000-2012 –> 2013-2019	8.6176862	47141.9121
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	6466	3.9057692	35982.9778	48.713871	1982-1999 –> 2000-2012	7.0697021	81432.4909
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	6466	3.7382856	35416.1990	36.297381	1982-1999 –> 2000-2012	6.8506238	80575.1233
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	6466	3.7382856	35416.1990	36.297381	1982-1999 –> 2000-2012	6.8506238	80575.1233
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	6466	3.7382856	35416.1990	36.297381	1982-1999 –> 2000-2012	6.8506238	80575.1233
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	3470	4.7284767	20643.4390	37.054814	2000-2012 –> 2013-2019	8.6342459	56626.4168
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	3470	4.7284767	20643.4390	37.054814	2000-2012 –> 2013-2019	8.6342459	56626.4168
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	3470	4.7284767	20643.4390	37.054814	2000-2012 –> 2013-2019	8.6342459	56626.4168
Indo-Pacific	(27,27.25]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	3470	4.7284767	20643.4390	37.054814	2000-2012 –> 2013-2019	8.6342459	56626.4168
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3470	4.4723380	20256.9380	25.616236	2000-2012 –> 2013-2019	8.4223646	56385.6280
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	3470	4.3257326	20025.6292	30.341767	2000-2012 –> 2013-2019	8.0640183	55441.8282
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	3470	4.4723380	20256.9380	25.616236	2000-2012 –> 2013-2019	8.4223646	56385.6280
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	3470	4.4723380	20256.9380	25.616236	2000-2012 –> 2013-2019	8.4223646	56385.6280
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	3470	4.3257326	20025.6292	30.341767	2000-2012 –> 2013-2019	8.0640183	55441.8282
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	3470	4.3257326	20025.6292	30.341767	2000-2012 –> 2013-2019	8.0640183	55441.8282
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + nitrate + silicate_star + phosphate_star	5847	3.4222130	30994.0484	31.732058	1982-1999 –> 2000-2012	6.3354476	70281.8372
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + silicate + silicate_star + phosphate_star	5847	3.4222130	30994.0484	31.732058	1982-1999 –> 2000-2012	6.3354476	70281.8372
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + silicate_star + phosphate + phosphate_star	5847	3.4222130	30994.0484	31.732058	1982-1999 –> 2000-2012	6.3354476	70281.8372
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate	5847	3.4154823	30971.0264	32.897684	1982-1999 –> 2000-2012	6.3144388	70181.2655
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5847	3.3461863	30731.3292	33.390589	1982-1999 –> 2000-2012	6.2704796	70078.9213
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	5847	3.2436714	30367.4652	32.825325	1982-1999 –> 2000-2012	6.1083715	69390.0778
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	5847	3.3461863	30731.3292	33.390589	1982-1999 –> 2000-2012	6.2704796	70078.9213
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	5847	3.3461863	30731.3292	33.390589	1982-1999 –> 2000-2012	6.2704796	70078.9213
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	5847	3.2436714	30367.4652	32.825325	1982-1999 –> 2000-2012	6.1083715	69390.0778
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	5847	3.2436714	30367.4652	32.825325	1982-1999 –> 2000-2012	6.1083715	69390.0778
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + aou + silicate	3127	3.8005574	17238.0556	34.420220	2000-2012 –> 2013-2019	7.2184615	48217.3705
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3127	3.8437243	17308.6883	33.232474	2000-2012 –> 2013-2019	7.1899105	48040.0175
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	3127	3.7456570	17147.0555	32.042107	2000-2012 –> 2013-2019	6.9893284	47514.5206
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate	3127	3.8712880	17353.3764	34.429027	2000-2012 –> 2013-2019	7.3474353	48530.2857
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate_star	3127	3.8712880	17353.3764	34.429027	2000-2012 –> 2013-2019	7.3474353	48530.2857
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	3127	3.8437243	17308.6883	33.232474	2000-2012 –> 2013-2019	7.1899105	48040.0175
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	3127	3.8437243	17308.6883	33.232474	2000-2012 –> 2013-2019	7.1899105	48040.0175
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + silicate_star	3127	3.8712880	17353.3764	34.429027	2000-2012 –> 2013-2019	7.3474353	48530.2857
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	3127	3.7456570	17147.0555	32.042107	2000-2012 –> 2013-2019	6.9893284	47514.5206
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	3127	3.7456570	17147.0555	32.042107	2000-2012 –> 2013-2019	6.9893284	47514.5206
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5836	3.1735450	30055.2512	8.689085	1982-1999 –> 2000-2012	5.4890819	66680.8347
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate	5836	3.1344878	29910.7112	10.233030	1982-1999 –> 2000-2012	5.4222114	66340.4081
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate_star	5836	3.1418231	29937.9938	9.677288	1982-1999 –> 2000-2012	5.4431377	66463.7071
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + silicate	5836	3.0304211	29516.6154	12.981932	1982-1999 –> 2000-2012	5.4431860	66808.9455
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + silicate_star	5836	3.0146454	29455.6947	12.492589	1982-1999 –> 2000-2012	5.4351087	66799.6634
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	5836	3.1698959	30041.8225	8.686571	1982-1999 –> 2000-2012	5.4929254	66719.7736
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate	5836	3.1324239	29903.0232	9.658767	1982-1999 –> 2000-2012	5.4289174	66394.7415
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate_star	5836	3.1324239	29903.0232	9.658767	1982-1999 –> 2000-2012	5.4289174	66394.7415
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5836	3.1698959	30041.8225	8.686571	1982-1999 –> 2000-2012	5.4929254	66719.7736
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate_star + phosphate + phosphate_star	5836	3.1324239	29903.0232	9.658767	1982-1999 –> 2000-2012	5.4289174	66394.7415
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate	3104	3.6583719	16874.6595	10.327691	2000-2012 –> 2013-2019	6.7928597	46785.3707
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate_star + phosphate_star	3104	3.6626957	16881.9924	10.327653	2000-2012 –> 2013-2019	6.8045188	46819.9862
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	3104	3.7023122	16948.7788	17.138991	2000-2012 –> 2013-2019	6.8317603	46840.7084
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate_star + phosphate	3104	3.7023122	16948.7788	17.138991	2000-2012 –> 2013-2019	6.8317603	46840.7084
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + silicate	3104	3.4945155	16590.1873	14.687842	2000-2012 –> 2013-2019	6.5249366	46106.8027
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + silicate_star	3104	3.4641763	16536.0544	14.191842	2000-2012 –> 2013-2019	6.4788216	45991.7492
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate	3104	3.6489118	16858.5855	10.306258	2000-2012 –> 2013-2019	6.7813357	46761.6087
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate_star + phosphate_star	3104	3.6489118	16858.5855	10.306258	2000-2012 –> 2013-2019	6.7813357	46761.6087
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + silicate_star + phosphate	3104	3.7023122	16948.7788	17.138991	2000-2012 –> 2013-2019	6.8317603	46840.7084
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate_star + phosphate + phosphate_star	3104	3.6489118	16858.5855	10.306258	2000-2012 –> 2013-2019	6.7813357	46761.6087
Indo-Pacific	(27.75,27.85]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	2317	2.7212475	11228.4142	21.917997	1982-1999 –> 2000-2012	4.6418941	24214.7759
Indo-Pacific	(27.75,27.85]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	2317	2.7212475	11228.4142	21.917997	1982-1999 –> 2000-2012	4.6418941	24214.7759
Indo-Pacific	(27.75,27.85]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	2317	2.7212475	11228.4142	21.917997	1982-1999 –> 2000-2012	4.6418941	24214.7759
Indo-Pacific	(27.75,27.85]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	2317	2.7212475	11228.4142	21.917997	1982-1999 –> 2000-2012	4.6418941	24214.7759
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2317	2.6406178	11089.0349	20.968772	1982-1999 –> 2000-2012	4.5482001	24032.6569
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	2317	2.6387258	11085.7135	21.377698	1982-1999 –> 2000-2012	4.5432730	24019.3645
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2317	2.6406178	11089.0349	20.968772	1982-1999 –> 2000-2012	4.5482001	24032.6569
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2317	2.6406178	11089.0349	20.968772	1982-1999 –> 2000-2012	4.5482001	24032.6569
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	2317	2.6387258	11085.7135	21.377698	1982-1999 –> 2000-2012	4.5432730	24019.3645
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	2317	2.6387258	11085.7135	21.377698	1982-1999 –> 2000-2012	4.5432730	24019.3645
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + silicate	1264	2.9877934	6368.0614	34.251747	2000-2012 –> 2013-2019	5.6399206	17477.2502
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + silicate_star	1264	2.9835090	6364.4337	34.942250	2000-2012 –> 2013-2019	5.6451919	17490.2890
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1264	3.0665742	6433.8549	28.861392	2000-2012 –> 2013-2019	5.7071919	17522.8898
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	1264	3.0580694	6426.8341	29.049935	2000-2012 –> 2013-2019	5.6967952	17512.5476
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate	1264	3.0654818	6432.9542	34.187580	2000-2012 –> 2013-2019	5.7289961	17561.9969
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1264	3.0665742	6433.8549	28.861392	2000-2012 –> 2013-2019	5.7071919	17522.8898
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1264	3.0665742	6433.8549	28.861392	2000-2012 –> 2013-2019	5.7071919	17522.8898
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + silicate_star	1264	3.0654818	6432.9542	34.187580	2000-2012 –> 2013-2019	5.7289961	17561.9969
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	1264	3.0580694	6426.8341	29.049935	2000-2012 –> 2013-2019	5.6967952	17512.5476
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	1264	3.0580694	6426.8341	29.049935	2000-2012 –> 2013-2019	5.6967952	17512.5476
Indo-Pacific	(27.85,27.95]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	2907	2.7369084	14117.4123	28.359649	1982-1999 –> 2000-2012	4.8476476	31502.5456
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	2907	2.7387015	14121.2200	28.728209	1982-1999 –> 2000-2012	4.8508407	31511.6713
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate	2907	2.7026569	14044.1928	28.417644	1982-1999 –> 2000-2012	4.8043308	31394.8076
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate_star	2907	2.7026569	14044.1928	28.417644	1982-1999 –> 2000-2012	4.8043308	31394.8076
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	1542	3.2823201	8055.4962	31.823285	2000-2012 –> 2013-2019	6.0192285	22172.9085
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	1542	3.2823201	8055.4962	31.823285	2000-2012 –> 2013-2019	6.0192285	22172.9085
Indo-Pacific	(27.85,27.95]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	1542	3.2823201	8055.4962	31.823285	2000-2012 –> 2013-2019	6.0192285	22172.9085
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + nitrate	1542	3.1822377	7959.9974	32.017867	2000-2012 –> 2013-2019	5.9064125	22050.2967
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate	1542	3.1823803	7958.1357	31.944102	2000-2012 –> 2013-2019	5.9067160	22046.7781
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate	1542	3.1767686	7954.6926	31.850384	2000-2012 –> 2013-2019	5.8794254	21998.8853
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate + phosphate_star	1542	3.1767686	7954.6926	31.850384	2000-2012 –> 2013-2019	5.8794254	21998.8853
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate	1542	3.1822510	7960.0104	31.986959	2000-2012 –> 2013-2019	5.9062344	22049.9010
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + nitrate + silicate_star	1542	3.1822510	7960.0104	31.986959	2000-2012 –> 2013-2019	5.9062344	22049.9010
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + silicate_star	1542	3.1822510	7960.0104	31.986959	2000-2012 –> 2013-2019	5.9062344	22049.9010
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate	2467	2.1792907	10858.6260	8.502155	1982-1999 –> 2000-2012	4.0658897	25425.2456
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + nitrate + silicate_star	2467	2.1792907	10858.6260	8.502155	1982-1999 –> 2000-2012	4.0658897	25425.2456
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + silicate + silicate_star	2467	2.1792907	10858.6260	8.502155	1982-1999 –> 2000-2012	4.0658897	25425.2456
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + silicate_star	2467	2.1868435	10875.6962	8.583791	1982-1999 –> 2000-2012	4.0752629	25449.1497
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2467	2.1886299	10879.7253	7.878228	1982-1999 –> 2000-2012	4.0642895	25405.1370
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	2467	2.1895879	10881.8845	7.849347	1982-1999 –> 2000-2012	4.0701805	25425.9079
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2467	2.1886299	10879.7253	7.878228	1982-1999 –> 2000-2012	4.0642895	25405.1370
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2467	2.1886299	10879.7253	7.878228	1982-1999 –> 2000-2012	4.0642895	25405.1370
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	2467	2.1895879	10881.8845	7.849347	1982-1999 –> 2000-2012	4.0701805	25425.9079
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	2467	2.1895879	10881.8845	7.849347	1982-1999 –> 2000-2012	4.0701805	25425.9079
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate_star	1354	2.4007452	6228.0956	8.259744	2000-2012 –> 2013-2019	4.5943605	17119.0470
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate	1354	2.3937485	6220.1919	8.306747	2000-2012 –> 2013-2019	4.5799110	17094.3514
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + nitrate + phosphate_star	1354	2.3937485	6220.1919	8.306747	2000-2012 –> 2013-2019	4.5799110	17094.3514
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	1354	2.3949270	6221.5248	8.259385	2000-2012 –> 2013-2019	4.5805806	17094.5357
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	1354	2.3941382	6220.6327	8.284045	2000-2012 –> 2013-2019	4.5799766	17094.0607
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	1354	2.3891259	6214.9574	8.045546	2000-2012 –> 2013-2019	4.5812165	17102.4783
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate_star + phosphate	1354	2.3891259	6214.9574	8.045546	2000-2012 –> 2013-2019	4.5812165	17102.4783
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate	1354	2.3949943	6221.6009	8.251733	2000-2012 –> 2013-2019	4.5805940	17094.4901
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + nitrate + phosphate_star	1354	2.3949943	6221.6009	8.251733	2000-2012 –> 2013-2019	4.5805940	17094.4901
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + silicate_star + phosphate	1354	2.3891259	6214.9574	8.045546	2000-2012 –> 2013-2019	4.5812165	17102.4783
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	1718	1.8463208	6996.4105	10.225349	1982-1999 –> 2000-2012	3.4405196	16640.5731
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1718	1.8032691	6915.3424	9.697645	1982-1999 –> 2000-2012	3.4298781	16662.3098
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1718	1.8032691	6915.3424	9.697645	1982-1999 –> 2000-2012	3.4298781	16662.3098
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1718	1.8032691	6915.3424	9.697645	1982-1999 –> 2000-2012	3.4298781	16662.3098
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	966	2.0390556	4131.9137	9.747515	2000-2012 –> 2013-2019	3.8840888	11125.9270
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	966	2.0390556	4131.9137	9.747515	2000-2012 –> 2013-2019	3.8840888	11125.9270
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	966	2.0390556	4131.9137	9.747515	2000-2012 –> 2013-2019	3.8840888	11125.9270
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate_star + phosphate_star	966	2.0395415	4132.3740	9.670797	2000-2012 –> 2013-2019	3.8877643	11132.3223
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	966	2.0001288	4094.6740	9.111786	2000-2012 –> 2013-2019	3.8033978	11010.0164
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate_star + phosphate + phosphate_star	966	2.0180718	4111.9285	9.104081	2000-2012 –> 2013-2019	3.8390788	11060.9042
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	966	2.0001288	4094.6740	9.111786	2000-2012 –> 2013-2019	3.8033978	11010.0164
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	966	2.0001288	4094.6740	9.111786	2000-2012 –> 2013-2019	3.8033978	11010.0164
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate	966	2.0180718	4111.9285	9.104081	2000-2012 –> 2013-2019	3.8390788	11060.9042
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate_star + phosphate_star	966	2.0180718	4111.9285	9.104081	2000-2012 –> 2013-2019	3.8390788	11060.9042
Indo-Pacific	(28.1, Inf]	cstar_tref ~ aou + silicate + silicate_star + phosphate + phosphate_star	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + aou + nitrate + silicate + phosphate_star	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + aou + nitrate + silicate_star + phosphate_star	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + aou + silicate + silicate_star + phosphate_star	14627	1.3445893	50185.4032	13.266137	1982-1999 –> 2000-2012	2.4490842	111949.7485
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	14627	1.2494600	48038.8292	11.951281	1982-1999 –> 2000-2012	2.3095030	108132.5045
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	14627	1.2494600	48038.8292	11.951281	1982-1999 –> 2000-2012	2.3095030	108132.5045
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate	14627	1.2494600	48038.8292	11.951281	1982-1999 –> 2000-2012	2.3095030	108132.5045
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	7804	1.4123708	27549.7620	9.529089	2000-2012 –> 2013-2019	2.6618308	75588.5913
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate_star + phosphate	7804	1.4123708	27549.7620	9.529089	2000-2012 –> 2013-2019	2.6618308	75588.5913
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + silicate_star + phosphate	7804	1.4123708	27549.7620	9.529089	2000-2012 –> 2013-2019	2.6618308	75588.5913
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate_star + phosphate	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate_star + phosphate_star	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + silicate + silicate_star + phosphate	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + silicate + silicate_star + phosphate_star	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + silicate + silicate_star + phosphate + phosphate_star	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816

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]	1982-1999 –> 2000-2012	2.3805456	1200.9420
Atlantic	(-Inf,26]	2000-2012 –> 2013-2019	2.2058537	716.2307
Atlantic	(26,26.5]	1982-1999 –> 2000-2012	6.5981764	13462.5188
Atlantic	(26,26.5]	2000-2012 –> 2013-2019	6.4603938	8407.4645
Atlantic	(26.5,26.75]	1982-1999 –> 2000-2012	6.2711340	16868.6938
Atlantic	(26.5,26.75]	2000-2012 –> 2013-2019	6.5746280	10717.4828
Atlantic	(26.75,27]	1982-1999 –> 2000-2012	3.6486119	22139.2736
Atlantic	(26.75,27]	2000-2012 –> 2013-2019	4.4850744	16094.9195
Atlantic	(27,27.25]	1982-1999 –> 2000-2012	3.5015516	18267.0572
Atlantic	(27,27.25]	2000-2012 –> 2013-2019	4.1487037	13479.3417
Atlantic	(27.25,27.5]	1982-1999 –> 2000-2012	3.8574714	20052.3057
Atlantic	(27.25,27.5]	2000-2012 –> 2013-2019	4.9897722	14382.9301
Atlantic	(27.5,27.75]	1982-1999 –> 2000-2012	4.4731519	28929.9698
Atlantic	(27.5,27.75]	2000-2012 –> 2013-2019	5.1928474	20294.1986
Atlantic	(27.75,27.85]	1982-1999 –> 2000-2012	3.1126903	8802.4964
Atlantic	(27.75,27.85]	2000-2012 –> 2013-2019	3.2791884	5888.1932
Atlantic	(27.85,27.95]	1982-1999 –> 2000-2012	5.8574395	11564.2247
Atlantic	(27.85,27.95]	2000-2012 –> 2013-2019	6.5644924	8066.9179
Atlantic	(27.95,28.05]	1982-1999 –> 2000-2012	7.5343927	15794.3689
Atlantic	(27.95,28.05]	2000-2012 –> 2013-2019	7.4578198	10309.2740
Atlantic	(28.05,28.1]	1982-1999 –> 2000-2012	1.8744497	5050.9867
Atlantic	(28.05,28.1]	2000-2012 –> 2013-2019	2.0560331	3600.3600
Atlantic	(28.1,28.15]	1982-1999 –> 2000-2012	1.3682808	4507.7133
Atlantic	(28.1,28.15]	2000-2012 –> 2013-2019	1.6233593	3438.5144
Atlantic	(28.15,28.2]	1982-1999 –> 2000-2012	0.8641282	4331.9512
Atlantic	(28.15,28.2]	2000-2012 –> 2013-2019	1.1100000	3396.8573
Atlantic	(28.2, Inf]	1982-1999 –> 2000-2012	0.6393405	3439.0184
Atlantic	(28.2, Inf]	2000-2012 –> 2013-2019	0.7117228	3193.1292
Indo-Pacific	(-Inf,26]	1982-1999 –> 2000-2012	12.4730592	81218.5546
Indo-Pacific	(-Inf,26]	2000-2012 –> 2013-2019	11.8834577	52023.0305
Indo-Pacific	(26,26.5]	1982-1999 –> 2000-2012	8.9593565	77126.2268
Indo-Pacific	(26,26.5]	2000-2012 –> 2013-2019	9.1920185	49786.5629
Indo-Pacific	(26.5,26.75]	1982-1999 –> 2000-2012	7.7316388	60019.8498
Indo-Pacific	(26.5,26.75]	2000-2012 –> 2013-2019	8.1252194	39291.1929
Indo-Pacific	(26.75,27]	1982-1999 –> 2000-2012	7.7769858	71233.6626
Indo-Pacific	(26.75,27]	2000-2012 –> 2013-2019	8.6823477	47271.9017
Indo-Pacific	(27,27.25]	1982-1999 –> 2000-2012	7.0039786	81175.2806
Indo-Pacific	(27,27.25]	2000-2012 –> 2013-2019	8.3996132	56198.8036
Indo-Pacific	(27.25,27.5]	1982-1999 –> 2000-2012	6.2457335	69943.3774
Indo-Pacific	(27.25,27.5]	2000-2012 –> 2013-2019	7.1798484	48047.1842
Indo-Pacific	(27.5,27.75]	1982-1999 –> 2000-2012	5.4505329	66571.7330
Indo-Pacific	(27.5,27.75]	2000-2012 –> 2013-2019	6.7440425	46651.0860
Indo-Pacific	(27.75,27.85]	1982-1999 –> 2000-2012	4.5841996	24101.5168
Indo-Pacific	(27.75,27.85]	2000-2012 –> 2013-2019	5.6955066	17519.7845
Indo-Pacific	(27.85,27.95]	1982-1999 –> 2000-2012	4.8393035	31481.9106
Indo-Pacific	(27.85,27.95]	2000-2012 –> 2013-2019	5.9348368	22076.3274
Indo-Pacific	(27.95,28.05]	1982-1999 –> 2000-2012	4.0676342	25421.8021
Indo-Pacific	(27.95,28.05]	2000-2012 –> 2013-2019	4.5819577	17099.2761
Indo-Pacific	(28.05,28.1]	1982-1999 –> 2000-2012	3.4373272	16647.0941
Indo-Pacific	(28.05,28.1]	2000-2012 –> 2013-2019	3.8467460	11072.2865
Indo-Pacific	(28.1, Inf]	1982-1999 –> 2000-2012	2.4072098	110804.5753
Indo-Pacific	(28.1, Inf]	2000-2012 –> 2013-2019	2.7377567	76949.4545

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 (rmse) was plotted against the number of predictors (limited to 2 - 5).

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")

Past versions of eMLR_predictor_model_quality_all-1.png

Version	Author	Date
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")

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
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)

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
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)

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
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	oxygen	phosphate	phosphate_star	sal	silicate_star	temp	silicate
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	10	4	6	6	6	10	3	5	0
(26,26.5]	8	7	7	1	1	10	6	5	5
(26.5,26.75]	10	4	8	6	6	0	5	3	8
(26.75,27]	10	2	7	8	5	3	3	3	9
(27,27.25]	7	2	4	7	5	10	1	5	9
(27.25,27.5]	10	8	7	2	2	6	6	3	6
(27.5,27.75]	4	0	4	6	6	10	5	10	5
(27.75,27.85]	8	5	7	7	5	10	3	3	2
(27.85,27.95]	10	1	7	6	6	4	3	10	3
(27.95,28.05]	3	6	6	4	7	0	7	10	7
(28.05,28.1]	10	1	7	6	6	4	3	10	3
(28.1,28.15]	10	3	8	4	4	1	5	10	5
(28.15,28.2]	10	8	7	1	4	4	4	7	4
(28.2, Inf]	8	8	4	5	5	10	4	2	4
total	118.00	59.00	89.00	69.00	68.00	82.00	58.00	86.00	70.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	8	6	6	6	5	10	0	5	4
(26,26.5]	7	7	7	1	0	10	6	6	6
(26.5,26.75]	10	4	8	6	6	0	5	3	8
(26.75,27]	10	2	7	8	5	3	3	3	9
(27,27.25]	9	2	3	7	4	10	2	3	9
(27.25,27.5]	10	8	7	2	2	6	6	3	6
(27.5,27.75]	7	2	4	8	4	10	9	4	2
(27.75,27.85]	8	5	8	6	5	10	3	3	2
(27.85,27.95]	10	3	7	6	6	6	1	8	3
(27.95,28.05]	4	7	6	3	7	1	6	10	6
(28.05,28.1]	8	6	8	5	5	10	1	7	0
(28.1,28.15]	10	1	7	6	6	10	3	4	3
(28.15,28.2]	10	8	7	1	4	4	4	7	4
(28.2, Inf]	8	9	4	7	3	10	2	4	2
total	119.00	70.00	89.00	72.00	62.00	100.00	51.00	70.00	64.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	8	6	7	5	6	10	0	5	3
(26,26.5]	7	1	4	7	5	8	1	7	10
(26.5,26.75]	10	6	9	5	6	5	3	0	6
(26.75,27]	10	1	7	6	7	3	3	10	3
(27,27.25]	10	4	8	6	6	0	8	3	5
(27.25,27.5]	7	1	6	6	7	4	7	7	5
(27.5,27.75]	5	0	5	6	4	10	6	10	4
(27.75,27.85]	10	2	8	6	6	0	7	6	5
(27.85,27.95]	10	7	9	6	5	1	5	2	5
(27.95,28.05]	10	2	7	4	4	4	6	7	6
(28.05,28.1]	10	4	8	6	6	0	5	3	8
(28.1, Inf]	10	6	6	7	4	3	7	0	7
total	107.00	40.00	84.00	70.00	66.00	48.00	58.00	60.00	67.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	8	6	6	6	6	10	0	5	3
(26,26.5]	8	2	3	7	5	7	2	7	9
(26.5,26.75]	9	7	8	5	6	3	6	1	5
(26.75,27]	10	2	7	7	6	3	3	10	2
(27,27.25]	10	3	8	5	7	0	5	6	6
(27.25,27.5]	10	2	8	4	4	1	5	10	6
(27.5,27.75]	4	2	4	6	3	10	8	10	3
(27.75,27.85]	10	1	8	4	4	2	5	10	6
(27.85,27.95]	10	9	10	2	3	1	3	7	4
(27.95,28.05]	5	8	4	6	4	10	3	7	3
(28.05,28.1]	10	0	7	6	7	4	4	6	6
(28.1, Inf]	3	6	6	7	4	10	7	0	7
total	97.00	48.00	79.00	65.00	59.00	61.00	51.00	79.00	60.00

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)

Past versions of aic_vs_rmse_all_models-1.png

Version	Author	Date
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)

Past versions of aic_vs_rmse_selected_models-1.png

Version	Author	Date
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

Session information

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_0.7.3      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