eMLR - model fitting

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Last updated: 2021-03-08

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Knit directory: emlr_mod_v_XXX/

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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, silicate, phosphate, phosphate_star

# the following code is a workaround to find all predictor combinations
# using the olsrr package and fit all models for one era, slab, and basin

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

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

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

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

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

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

# convert to tibble
lm_all <- as_tibble(lm_all)

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

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

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

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

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


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

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

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

# lm_full <- lm(paste(
#   params_local$MLR_target,
#   paste(params_local$MLR_predictors, collapse = " + "),
#   sep = " ~ "
# ),
# data = GLODAP_basin_era_slab)
# 
# lm_full <-
#   loess(
#     cstar_tref ~ sal + temp + aou + phosphate,
#     span = 0.1,
#     degree = 1,
#     data = GLODAP_basin_era_slab
#   )

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:

• 112

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 + temp + aou + phosphate + phosphate_star	52	0.7425615	130.61405	2.1602026	1982-1999 –> 2000-2012	2.2577295	335.39839
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou	52	0.7809678	133.85859	2.0772701	1982-1999 –> 2000-2012	2.4182795	344.70599
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	52	0.7425615	130.61405	2.1602026	1982-1999 –> 2000-2012	2.2577295	335.39839
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	52	0.7425615	130.61405	2.1602026	1982-1999 –> 2000-2012	2.2577295	335.39839
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + silicate	52	0.6812955	121.65866	1.8480163	1982-1999 –> 2000-2012	2.3184984	334.49915
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	52	0.7570324	130.62129	2.1365217	1982-1999 –> 2000-2012	2.4218012	343.19827
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	52	0.6801275	121.48021	1.9354268	1982-1999 –> 2000-2012	2.0465353	315.51708
Atlantic	(-Inf,26]	cstar_tref ~ temp + oxygen + aou + phosphate	52	0.7570324	130.62129	2.1365217	1982-1999 –> 2000-2012	2.4218012	343.19827
Atlantic	(-Inf,26]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	52	0.6801275	121.48021	1.9354268	1982-1999 –> 2000-2012	2.0465353	315.51708
Atlantic	(-Inf,26]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	52	0.6801275	121.48021	1.9354268	1982-1999 –> 2000-2012	2.0465353	315.51708
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	25	0.0440426	-71.18296	0.0902802	2000-2012 –> 2013-2019	0.7310401	51.34248
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	25	0.0439239	-71.31794	0.0921668	2000-2012 –> 2013-2019	0.7235239	50.08159
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	25	0.0438963	-71.34931	0.0930618	2000-2012 –> 2013-2019	0.7241262	50.14655
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + silicate	25	0.0481951	-66.67802	0.1236976	2000-2012 –> 2013-2019	0.7294906	54.98064
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	25	0.0439039	-71.34072	0.0953370	2000-2012 –> 2013-2019	0.7224621	49.89925
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	25	0.0439039	-71.34072	0.0953370	2000-2012 –> 2013-2019	0.7224621	49.89925
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	25	0.0439039	-71.34072	0.0953370	2000-2012 –> 2013-2019	0.7224621	49.89925
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	25	0.0438948	-71.35101	0.0947611	2000-2012 –> 2013-2019	0.7240223	50.12919
Atlantic	(-Inf,26]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	25	0.0438948	-71.35101	0.0947611	2000-2012 –> 2013-2019	0.7240223	50.12919
Atlantic	(-Inf,26]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	25	0.0438948	-71.35101	0.0947611	2000-2012 –> 2013-2019	0.7240223	50.12919
Atlantic	(26,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	966	4.2872855	5565.71235	13.5928278	1982-1999 –> 2000-2012	7.7444146	9396.57777
Atlantic	(26,26.75]	cstar_tref ~ oxygen + aou + silicate + phosphate	966	4.2872855	5565.71235	13.5928278	1982-1999 –> 2000-2012	7.7444146	9396.57777
Atlantic	(26,26.75]	cstar_tref ~ oxygen + aou + silicate + phosphate + phosphate_star	966	4.2872855	5565.71235	13.5928278	1982-1999 –> 2000-2012	7.7444146	9396.57777
Atlantic	(26,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	966	4.2046504	5530.11055	12.0567127	1982-1999 –> 2000-2012	7.3844182	9242.88282
Atlantic	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	966	4.2046504	5530.11055	12.0567127	1982-1999 –> 2000-2012	7.3844182	9242.88282
Atlantic	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	966	4.2046504	5530.11055	12.0567127	1982-1999 –> 2000-2012	7.3844182	9242.88282
Atlantic	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	966	4.3275035	5585.75150	12.3530427	1982-1999 –> 2000-2012	7.7071954	9386.08587
Atlantic	(26,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	966	4.2582748	5554.59468	14.2203472	1982-1999 –> 2000-2012	7.6989004	9380.58859
Atlantic	(26,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	966	4.2582748	5554.59468	14.2203472	1982-1999 –> 2000-2012	7.6989004	9380.58859
Atlantic	(26,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	966	4.2582748	5554.59468	14.2203472	1982-1999 –> 2000-2012	7.6989004	9380.58859
Atlantic	(26,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	287	3.0370306	1466.11600	10.8832286	2000-2012 –> 2013-2019	7.2416810	6996.22654
Atlantic	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	287	3.0370306	1466.11600	10.8832286	2000-2012 –> 2013-2019	7.2416810	6996.22654
Atlantic	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	287	3.0370306	1466.11600	10.8832286	2000-2012 –> 2013-2019	7.2416810	6996.22654
Atlantic	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	287	2.9950967	1458.13524	10.7980394	2000-2012 –> 2013-2019	7.3226002	7043.88674
Atlantic	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	287	2.9949380	1458.10482	10.7837269	2000-2012 –> 2013-2019	7.3662240	7063.30469
Atlantic	(26,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	287	2.9949664	1458.11027	10.7895022	2000-2012 –> 2013-2019	7.3779276	7068.46340
Atlantic	(26,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	287	2.9949664	1458.11027	10.7895022	2000-2012 –> 2013-2019	7.3779276	7068.46340
Atlantic	(26,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	287	2.9949664	1458.11027	10.7895022	2000-2012 –> 2013-2019	7.3779276	7068.46340
Atlantic	(26,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	287	3.8227039	1598.18061	13.3100505	2000-2012 –> 2013-2019	8.0809787	7152.77530
Atlantic	(26,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	287	3.8227039	1598.18061	13.3100505	2000-2012 –> 2013-2019	8.0809787	7152.77530
Atlantic	(26.75,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	2225	2.8510453	10988.47777	10.7656170	1982-1999 –> 2000-2012	5.3696491	19223.15560
Atlantic	(26.75,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2225	2.8336549	10963.25118	11.3675063	1982-1999 –> 2000-2012	4.9909461	18656.40072
Atlantic	(26.75,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2225	2.8336549	10963.25118	11.3675063	1982-1999 –> 2000-2012	4.9909461	18656.40072
Atlantic	(26.75,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2225	2.8336549	10963.25118	11.3675063	1982-1999 –> 2000-2012	4.9909461	18656.40072
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2225	2.8507802	10990.06407	10.8390345	1982-1999 –> 2000-2012	5.1496658	18906.34816
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2225	2.9358247	11120.87493	11.3392899	1982-1999 –> 2000-2012	5.3481700	19206.25317
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2225	2.9609982	11158.86918	11.6400291	1982-1999 –> 2000-2012	5.4106834	19298.16131
Atlantic	(26.75,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2225	2.8168654	10936.80643	13.8460932	1982-1999 –> 2000-2012	4.6994265	18151.82301
Atlantic	(26.75,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2225	2.8168654	10936.80643	13.8460932	1982-1999 –> 2000-2012	4.6994265	18151.82301
Atlantic	(26.75,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2225	2.8168654	10936.80643	13.8460932	1982-1999 –> 2000-2012	4.6994265	18151.82301
Atlantic	(26.75,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	626	2.6802924	3022.89024	10.7167808	2000-2012 –> 2013-2019	5.5313376	14011.36801
Atlantic	(26.75,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	626	2.5899124	2981.94436	9.5347250	2000-2012 –> 2013-2019	5.4235673	13945.19553
Atlantic	(26.75,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	626	2.5973770	2983.54765	9.2915686	2000-2012 –> 2013-2019	5.6727618	14309.08784
Atlantic	(26.75,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	626	2.5899124	2981.94436	9.5347250	2000-2012 –> 2013-2019	5.4235673	13945.19553
Atlantic	(26.75,27.25]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	626	2.5899124	2981.94436	9.5347250	2000-2012 –> 2013-2019	5.4235673	13945.19553
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	626	2.5624263	2968.58616	9.3731729	2000-2012 –> 2013-2019	5.4132065	13958.65023
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	626	2.5955783	2984.68035	9.4113477	2000-2012 –> 2013-2019	5.5314031	14105.55527
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	626	2.6014298	2987.49969	9.3966695	2000-2012 –> 2013-2019	5.5624280	14146.36887
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	626	2.6014298	2987.49969	9.3966695	2000-2012 –> 2013-2019	5.5624280	14146.36887
Atlantic	(26.75,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	626	2.6014298	2987.49969	9.3966695	2000-2012 –> 2013-2019	5.5624280	14146.36887
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	2298	3.3097080	12034.20996	19.2853994	1982-1999 –> 2000-2012	4.7971149	16909.38511
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2298	3.3097058	12036.20688	19.2757793	1982-1999 –> 2000-2012	4.6260814	16586.25872
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2298	3.3097058	12036.20688	19.2757793	1982-1999 –> 2000-2012	4.6260814	16586.25872
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2298	3.3097058	12036.20688	19.2757793	1982-1999 –> 2000-2012	4.6260814	16586.25872
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2298	3.2964181	12017.71780	18.7257268	1982-1999 –> 2000-2012	4.5415081	16418.67388
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2298	3.2252527	11917.40944	20.1109707	1982-1999 –> 2000-2012	4.5144786	16411.65128
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	2298	3.3988366	12158.34044	18.6106791	1982-1999 –> 2000-2012	5.1225724	17430.41251
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2298	3.2251848	11917.31269	20.0696031	1982-1999 –> 2000-2012	4.5302883	16444.33423
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2298	3.2251848	11917.31269	20.0696031	1982-1999 –> 2000-2012	4.5302883	16444.33423
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2298	3.2251848	11917.31269	20.0696031	1982-1999 –> 2000-2012	4.5302883	16444.33423
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	573	3.8687655	3188.56759	11.9597599	2000-2012 –> 2013-2019	7.1784735	15222.77755
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	573	3.7459411	3153.59467	10.2400948	2000-2012 –> 2013-2019	7.0556469	15189.80155
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	573	3.7459411	3153.59467	10.2400948	2000-2012 –> 2013-2019	7.0556469	15189.80155
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	573	3.7459411	3153.59467	10.2400948	2000-2012 –> 2013-2019	7.0556469	15189.80155
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	573	3.8596491	3187.86397	11.8244046	2000-2012 –> 2013-2019	7.1560672	15205.58177
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	573	3.7261089	3147.51126	9.2111956	2000-2012 –> 2013-2019	6.9513616	15064.92070
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	573	3.7231009	3146.58577	9.2453403	2000-2012 –> 2013-2019	6.9482857	15063.89845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	573	3.7231009	3146.58577	9.2453403	2000-2012 –> 2013-2019	6.9482857	15063.89845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	573	3.7231009	3146.58577	9.2453403	2000-2012 –> 2013-2019	6.9482857	15063.89845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	573	3.7301991	3146.76857	9.1869755	2000-2012 –> 2013-2019	6.9792901	15096.02271
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4108	2.4006938	18867.22503	19.3346654	1982-1999 –> 2000-2012	4.0408521	29395.26477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	4108	2.4006938	18867.22503	19.3346654	1982-1999 –> 2000-2012	4.0408521	29395.26477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	4108	2.4006938	18867.22503	19.3346654	1982-1999 –> 2000-2012	4.0408521	29395.26477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4108	2.3932563	18841.73164	19.5514846	1982-1999 –> 2000-2012	3.9172781	28966.29209
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4108	2.3595962	18725.35691	21.8075049	1982-1999 –> 2000-2012	3.7816419	28469.42314
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	4108	2.5343071	19312.22400	19.2526571	1982-1999 –> 2000-2012	4.1791520	29855.93995
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	4108	2.3602820	18727.74461	21.6593084	1982-1999 –> 2000-2012	3.7815198	28468.68874
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	4108	2.3602820	18727.74461	21.6593084	1982-1999 –> 2000-2012	3.7815198	28468.68874
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4108	2.3602820	18727.74461	21.6593084	1982-1999 –> 2000-2012	3.7815198	28468.68874
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	4108	2.4822913	19139.83859	24.4123097	1982-1999 –> 2000-2012	3.9137287	28918.07017
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	1190	2.1231849	5181.01682	10.9452919	2000-2012 –> 2013-2019	4.5271787	24057.52764
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1190	2.0796279	5133.68348	10.6683765	2000-2012 –> 2013-2019	4.4803217	24000.90851
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1190	2.0796279	5133.68348	10.6683765	2000-2012 –> 2013-2019	4.4803217	24000.90851
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1190	2.0796279	5133.68348	10.6683765	2000-2012 –> 2013-2019	4.4803217	24000.90851
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1190	2.1008012	5157.79241	10.8268946	2000-2012 –> 2013-2019	4.4940575	23999.52406
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1190	2.0544696	5104.71587	10.4705213	2000-2012 –> 2013-2019	4.4140658	23830.07278
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1190	2.0546389	5104.91193	10.4908237	2000-2012 –> 2013-2019	4.4149209	23832.65654
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1190	2.0546389	5104.91193	10.4908237	2000-2012 –> 2013-2019	4.4149209	23832.65654
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1190	2.0546389	5104.91193	10.4908237	2000-2012 –> 2013-2019	4.4149209	23832.65654
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	1190	2.0714609	5122.31846	10.3444180	2000-2012 –> 2013-2019	4.5537522	24262.15705
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1697	1.1913083	5424.00423	6.7089315	1982-1999 –> 2000-2012	1.8511426	7374.12625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1697	1.1913083	5424.00423	6.7089315	1982-1999 –> 2000-2012	1.8511426	7374.12625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1697	1.1913083	5424.00423	6.7089315	1982-1999 –> 2000-2012	1.8511426	7374.12625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1697	1.1707506	5364.92475	6.5856147	1982-1999 –> 2000-2012	1.8927577	7488.83602
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1697	1.2272623	5524.92083	6.8273131	1982-1999 –> 2000-2012	1.9110354	7543.82293
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	1697	1.1707506	5364.92475	6.5856147	1982-1999 –> 2000-2012	1.8927577	7488.83602
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	1697	1.1707506	5364.92475	6.5856147	1982-1999 –> 2000-2012	1.8927577	7488.83602
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1697	1.2873675	5687.19989	7.1263801	1982-1999 –> 2000-2012	2.0097888	7812.21797
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1697	1.2873675	5687.19989	7.1263801	1982-1999 –> 2000-2012	2.0097888	7812.21797
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1697	1.2873675	5687.19989	7.1263801	1982-1999 –> 2000-2012	2.0097888	7812.21797
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	379	1.0257425	1108.82129	3.8752299	2000-2012 –> 2013-2019	2.2170508	6532.82552
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	379	1.0257425	1108.82129	3.8752299	2000-2012 –> 2013-2019	2.2170508	6532.82552
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	379	1.0257425	1108.82129	3.8752299	2000-2012 –> 2013-2019	2.2170508	6532.82552
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	379	0.8362449	953.99945	5.2034351	2000-2012 –> 2013-2019	2.0069955	6318.92420
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	379	1.0502397	1126.71139	4.1044281	2000-2012 –> 2013-2019	2.2775020	6651.63222
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	379	0.8362449	953.99945	5.2034351	2000-2012 –> 2013-2019	2.0069955	6318.92420
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	379	0.8362449	953.99945	5.2034351	2000-2012 –> 2013-2019	2.0069955	6318.92420
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	379	1.0779195	1146.43030	4.3526831	2000-2012 –> 2013-2019	2.3652871	6833.63018
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	379	1.0779195	1146.43030	4.3526831	2000-2012 –> 2013-2019	2.3652871	6833.63018
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	379	1.0779195	1146.43030	4.3526831	2000-2012 –> 2013-2019	2.3652871	6833.63018
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1595	1.2840781	5338.04484	9.1027355	1982-1999 –> 2000-2012	2.2240530	8150.25392
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	1595	1.2840781	5338.04484	9.1027355	1982-1999 –> 2000-2012	2.2240530	8150.25392
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	1595	1.2840781	5338.04484	9.1027355	1982-1999 –> 2000-2012	2.2240530	8150.25392
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1595	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1595	1.5639527	5967.03418	8.5210370	1982-1999 –> 2000-2012	2.6097355	8999.19239
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate	1595	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	1595	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate_star	1595	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1595	1.5639527	5967.03418	8.5210370	1982-1999 –> 2000-2012	2.6097355	8999.19239
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1595	1.5639527	5967.03418	8.5210370	1982-1999 –> 2000-2012	2.6097355	8999.19239
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	328	0.7238751	732.84618	3.7436233	2000-2012 –> 2013-2019	2.0079532	6070.89102
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	328	0.7238751	732.84618	3.7436233	2000-2012 –> 2013-2019	2.0079532	6070.89102
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	328	0.7238751	732.84618	3.7436233	2000-2012 –> 2013-2019	2.0079532	6070.89102
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	328	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	328	0.9914174	939.16921	7.0181098	2000-2012 –> 2013-2019	2.5553701	6906.20339
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate	328	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	328	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate_star	328	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	328	0.9914174	939.16921	7.0181098	2000-2012 –> 2013-2019	2.5553701	6906.20339
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	328	0.9914174	939.16921	7.0181098	2000-2012 –> 2013-2019	2.5553701	6906.20339
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1941	4.3701951	11247.52274	18.6148284	1982-1999 –> 2000-2012	7.9966536	18208.18531
Atlantic	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1941	4.3701951	11247.52274	18.6148284	1982-1999 –> 2000-2012	7.9966536	18208.18531
Atlantic	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1941	4.3701951	11247.52274	18.6148284	1982-1999 –> 2000-2012	7.9966536	18208.18531
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1941	4.3749103	11251.70889	18.5325206	1982-1999 –> 2000-2012	7.9950015	18207.86217
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1941	4.3798004	11256.04564	18.4996250	1982-1999 –> 2000-2012	7.9992669	18211.75609
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	1941	4.3956104	11270.03344	18.8597477	1982-1999 –> 2000-2012	8.1481834	18318.41525
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	1941	4.3956104	11270.03344	18.8597477	1982-1999 –> 2000-2012	8.1481834	18318.41525
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1941	4.3801291	11256.33695	18.5032040	1982-1999 –> 2000-2012	7.9996326	18212.07359
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1941	4.3801291	11256.33695	18.5032040	1982-1999 –> 2000-2012	7.9996326	18212.07359
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1941	4.3801291	11256.33695	18.5032040	1982-1999 –> 2000-2012	7.9996326	18212.07359
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	411	0.4967798	605.28933	2.0457321	2000-2012 –> 2013-2019	4.8923902	11875.32277
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	411	0.4967798	605.28933	2.0457321	2000-2012 –> 2013-2019	4.8923902	11875.32277
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	411	0.4967798	605.28933	2.0457321	2000-2012 –> 2013-2019	4.8923902	11875.32277
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	411	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	411	0.6507941	827.26751	3.9028273	2000-2012 –> 2013-2019	5.1851958	12217.97970
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + phosphate	411	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	411	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + phosphate_star	411	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	411	0.6507941	827.26751	3.9028273	2000-2012 –> 2013-2019	5.1851958	12217.97970
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	411	0.6507941	827.26751	3.9028273	2000-2012 –> 2013-2019	5.1851958	12217.97970
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1119	1.1332606	3469.55601	8.5938983	1982-1999 –> 2000-2012	1.8480430	5060.63896
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	1119	1.1332606	3469.55601	8.5938983	1982-1999 –> 2000-2012	1.8480430	5060.63896
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	1119	1.1332606	3469.55601	8.5938983	1982-1999 –> 2000-2012	1.8480430	5060.63896
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1119	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1119	1.0289069	3253.36077	8.0287550	1982-1999 –> 2000-2012	1.6922335	4735.66502
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + phosphate	1119	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	1119	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + phosphate_star	1119	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1119	1.0289069	3253.36077	8.0287550	1982-1999 –> 2000-2012	1.6922335	4735.66502
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1119	1.0289069	3253.36077	8.0287550	1982-1999 –> 2000-2012	1.6922335	4735.66502
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	266	0.3756068	247.93433	1.8452256	2000-2012 –> 2013-2019	1.5088675	3717.49033
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	266	0.3756068	247.93433	1.8452256	2000-2012 –> 2013-2019	1.5088675	3717.49033
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	266	0.3756068	247.93433	1.8452256	2000-2012 –> 2013-2019	1.5088675	3717.49033
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	266	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	266	0.3036156	134.73516	2.4071938	2000-2012 –> 2013-2019	1.3325226	3388.09593
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + phosphate	266	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	266	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + phosphate_star	266	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	266	0.3036156	134.73516	2.4071938	2000-2012 –> 2013-2019	1.3325226	3388.09593
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	266	0.3036156	134.73516	2.4071938	2000-2012 –> 2013-2019	1.3325226	3388.09593
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1620	1.0456312	4755.93189	6.5487221	1982-1999 –> 2000-2012	1.6842745	6419.83177
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1620	1.0456312	4755.93189	6.5487221	1982-1999 –> 2000-2012	1.6842745	6419.83177
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1620	1.0456312	4755.93189	6.5487221	1982-1999 –> 2000-2012	1.6842745	6419.83177
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1620	0.9991957	4608.75378	6.6178803	1982-1999 –> 2000-2012	1.6824680	6387.48418
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	1620	0.9991957	4608.75378	6.6178803	1982-1999 –> 2000-2012	1.6824680	6387.48418
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	1620	0.9991957	4608.75378	6.6178803	1982-1999 –> 2000-2012	1.6824680	6387.48418
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1620	1.0112951	4645.75173	6.7220596	1982-1999 –> 2000-2012	1.6981345	6431.33415
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1620	0.8831303	4208.68546	7.3212528	1982-1999 –> 2000-2012	1.4033503	5523.92510
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1620	0.8831303	4208.68546	7.3212528	1982-1999 –> 2000-2012	1.4033503	5523.92510
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1620	0.8831303	4208.68546	7.3212528	1982-1999 –> 2000-2012	1.4033503	5523.92510
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	400	0.4128857	441.48317	1.5372758	2000-2012 –> 2013-2019	1.4585168	5197.41505
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	400	0.4128857	441.48317	1.5372758	2000-2012 –> 2013-2019	1.4585168	5197.41505
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	400	0.4128857	441.48317	1.5372758	2000-2012 –> 2013-2019	1.4585168	5197.41505
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	400	0.4564022	521.64615	1.8669196	2000-2012 –> 2013-2019	1.4555979	5130.39993
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	400	0.4564022	521.64615	1.8669196	2000-2012 –> 2013-2019	1.4555979	5130.39993
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	400	0.4564022	521.64615	1.8669196	2000-2012 –> 2013-2019	1.4555979	5130.39993
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	400	0.2797729	130.12915	1.2331882	2000-2012 –> 2013-2019	1.1629032	4338.81461
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + phosphate_star	400	0.4630860	531.27683	1.9104036	2000-2012 –> 2013-2019	1.4743811	5177.02856
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	400	0.2797729	130.12915	1.2331882	2000-2012 –> 2013-2019	1.1629032	4338.81461
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	400	0.2797729	130.12915	1.2331882	2000-2012 –> 2013-2019	1.1629032	4338.81461
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3033	0.8959016	7954.47796	11.9690641	1982-1999 –> 2000-2012	1.7475653	11758.70326
Atlantic	(28.15,28.2]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	3033	0.8959016	7954.47796	11.9690641	1982-1999 –> 2000-2012	1.7475653	11758.70326
Atlantic	(28.15,28.2]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	3033	0.8959016	7954.47796	11.9690641	1982-1999 –> 2000-2012	1.7475653	11758.70326
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3033	0.7236679	6659.39884	22.8046471	1982-1999 –> 2000-2012	1.5498097	10371.98357
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3033	0.9183865	8104.84010	11.8495950	1982-1999 –> 2000-2012	1.7830432	11954.66991
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	3033	0.7236679	6659.39884	22.8046471	1982-1999 –> 2000-2012	1.5498097	10371.98357
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	3033	0.7236679	6659.39884	22.8046471	1982-1999 –> 2000-2012	1.5498097	10371.98357
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3033	0.7863775	7163.51009	12.6015457	1982-1999 –> 2000-2012	1.6256286	10923.51391
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	3033	0.7863775	7163.51009	12.6015457	1982-1999 –> 2000-2012	1.6256286	10923.51391
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	3033	0.7863775	7163.51009	12.6015457	1982-1999 –> 2000-2012	1.6256286	10923.51391
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	872	0.6111236	1629.78548	2.4002237	2000-2012 –> 2013-2019	1.5070252	9584.26344
Atlantic	(28.15,28.2]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	872	0.6111236	1629.78548	2.4002237	2000-2012 –> 2013-2019	1.5070252	9584.26344
Atlantic	(28.15,28.2]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	872	0.6111236	1629.78548	2.4002237	2000-2012 –> 2013-2019	1.5070252	9584.26344
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	872	0.5480112	1439.68341	1.6829609	2000-2012 –> 2013-2019	1.2716791	8099.08224
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	872	0.6326753	1690.22922	2.5384461	2000-2012 –> 2013-2019	1.5510618	9795.06932
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	872	0.5480112	1439.68341	1.6829609	2000-2012 –> 2013-2019	1.2716791	8099.08224
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	872	0.5480112	1439.68341	1.6829609	2000-2012 –> 2013-2019	1.2716791	8099.08224
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	872	0.5876275	1561.41018	2.0095964	2000-2012 –> 2013-2019	1.3740050	8724.92028
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	872	0.5876275	1561.41018	2.0095964	2000-2012 –> 2013-2019	1.3740050	8724.92028
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	872	0.5876275	1561.41018	2.0095964	2000-2012 –> 2013-2019	1.3740050	8724.92028
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5729	0.8662496	14627.03325	4.5498357	1982-1999 –> 2000-2012	1.7234469	20891.92838
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	5729	0.8662496	14627.03325	4.5498357	1982-1999 –> 2000-2012	1.7234469	20891.92838
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	5729	0.8662496	14627.03325	4.5498357	1982-1999 –> 2000-2012	1.7234469	20891.92838
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5729	0.8671911	14639.48021	4.5268433	1982-1999 –> 2000-2012	1.7244049	20904.47039
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5729	0.8714105	14695.09389	4.6117260	1982-1999 –> 2000-2012	1.7292468	20963.67220
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	5729	0.8697380	14673.08243	4.5703170	1982-1999 –> 2000-2012	1.7272286	20939.66817
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	5729	0.8697380	14673.08243	4.5703170	1982-1999 –> 2000-2012	1.7272286	20939.66817
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5729	0.8697380	14673.08243	4.5703170	1982-1999 –> 2000-2012	1.7272286	20939.66817
Atlantic	(28.2, Inf]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	5729	0.8499989	14410.04126	6.2570512	1982-1999 –> 2000-2012	1.7301985	20805.80379
Atlantic	(28.2, Inf]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	5729	0.8499989	14410.04126	6.2570512	1982-1999 –> 2000-2012	1.7301985	20805.80379
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	948	0.5606895	1607.30470	2.2306790	2000-2012 –> 2013-2019	1.4269391	16234.33795
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	948	0.5606895	1607.30470	2.2306790	2000-2012 –> 2013-2019	1.4269391	16234.33795
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	948	0.5606895	1607.30470	2.2306790	2000-2012 –> 2013-2019	1.4269391	16234.33795
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	948	0.5217253	1470.74315	1.8633030	2000-2012 –> 2013-2019	1.4205311	16520.50612
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	948	0.5605984	1606.99660	2.2413317	2000-2012 –> 2013-2019	1.4277896	16246.47681
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	948	0.5217253	1470.74315	1.8633030	2000-2012 –> 2013-2019	1.4205311	16520.50612
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	948	0.5217253	1470.74315	1.8633030	2000-2012 –> 2013-2019	1.4205311	16520.50612
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	948	0.5607556	1607.52819	2.2624780	2000-2012 –> 2013-2019	1.4304937	16280.61061
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	948	0.5607556	1607.52819	2.2624780	2000-2012 –> 2013-2019	1.4304937	16280.61061
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	948	0.5607556	1607.52819	2.2624780	2000-2012 –> 2013-2019	1.4304937	16280.61061
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2616	5.9171365	16737.61137	24.5984660	1982-1999 –> 2000-2012	11.2468945	23867.95792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2616	5.6769089	16522.76715	22.3359678	1982-1999 –> 2000-2012	10.8818433	23600.55920
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + phosphate	2616	5.9171365	16737.61137	24.5984660	1982-1999 –> 2000-2012	11.2468945	23867.95792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + phosphate_star	2616	5.9171365	16737.61137	24.5984660	1982-1999 –> 2000-2012	11.2468945	23867.95792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2616	5.6769089	16522.76715	22.3359678	1982-1999 –> 2000-2012	10.8818433	23600.55920
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2616	5.6769089	16522.76715	22.3359678	1982-1999 –> 2000-2012	10.8818433	23600.55920
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2616	5.8480540	16678.16846	26.0845534	1982-1999 –> 2000-2012	10.9088253	23691.30149
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2616	6.0570773	16861.90814	20.7269795	1982-1999 –> 2000-2012	11.0381157	23838.48419
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	2616	5.8480540	16678.16846	26.0845534	1982-1999 –> 2000-2012	10.9088253	23691.30149
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	2616	5.8480540	16678.16846	26.0845534	1982-1999 –> 2000-2012	10.9088253	23691.30149
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2149	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2149	5.3293238	13304.11614	23.1544130	2000-2012 –> 2013-2019	11.0062327	29826.88329
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + phosphate	2149	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + phosphate + phosphate_star	2149	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + phosphate_star	2149	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2149	5.3293238	13304.11614	23.1544130	2000-2012 –> 2013-2019	11.0062327	29826.88329
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2149	5.3293238	13304.11614	23.1544130	2000-2012 –> 2013-2019	11.0062327	29826.88329
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2149	5.5249053	13459.02356	24.6947128	2000-2012 –> 2013-2019	11.3729593	30137.19202
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	2149	5.5249053	13459.02356	24.6947128	2000-2012 –> 2013-2019	11.3729593	30137.19202
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	2149	5.5249053	13459.02356	24.6947128	2000-2012 –> 2013-2019	11.3729593	30137.19202
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4972	4.7670355	29653.71434	31.9042723	1982-1999 –> 2000-2012	8.4364589	45910.85948
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	4972	4.7670355	29653.71434	31.9042723	1982-1999 –> 2000-2012	8.4364589	45910.85948
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	4972	4.7670355	29653.71434	31.9042723	1982-1999 –> 2000-2012	8.4364589	45910.85948
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4972	5.3490058	30799.12497	28.8875084	1982-1999 –> 2000-2012	9.4075247	47658.35102
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4972	4.9121341	29951.87392	34.9141988	1982-1999 –> 2000-2012	8.6909897	46384.57511
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4972	5.0242174	30176.22263	34.9787543	1982-1999 –> 2000-2012	8.9373840	46817.56989
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	4972	5.0353259	30198.18450	34.9153724	1982-1999 –> 2000-2012	8.9614889	46859.33971
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	4972	5.0353259	30198.18450	34.9153724	1982-1999 –> 2000-2012	8.9614889	46859.33971
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4972	5.0353259	30198.18450	34.9153724	1982-1999 –> 2000-2012	8.9614889	46859.33971
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	4972	5.1424704	30405.55882	32.2314701	1982-1999 –> 2000-2012	9.2683378	47361.10605
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2800	3.8355719	15488.23967	17.3812944	2000-2012 –> 2013-2019	8.6026074	45141.95401
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2800	3.8355719	15488.23967	17.3812944	2000-2012 –> 2013-2019	8.6026074	45141.95401
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2800	3.8355719	15488.23967	17.3812944	2000-2012 –> 2013-2019	8.6026074	45141.95401
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2800	3.9465213	15647.92908	17.5534022	2000-2012 –> 2013-2019	8.8586554	45599.80300
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2800	3.9941489	15715.10661	17.8285691	2000-2012 –> 2013-2019	9.0183662	45891.32924
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2800	4.0044072	15729.47087	17.8059480	2000-2012 –> 2013-2019	9.0397331	45927.65537
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2800	4.0044072	15729.47087	17.8059480	2000-2012 –> 2013-2019	9.0397331	45927.65537
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2800	4.0044072	15729.47087	17.8059480	2000-2012 –> 2013-2019	9.0397331	45927.65537
Indo-Pacific	(26,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	2800	4.2515093	16062.79052	16.7407058	2000-2012 –> 2013-2019	9.3939798	46468.34935
Indo-Pacific	(26,26.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2800	4.2379669	16046.92421	23.0762105	2000-2012 –> 2013-2019	10.0172864	47615.46834
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3376	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3376	4.3817574	19570.41455	15.2521912	1982-1999 –> 2000-2012	7.5408394	29660.89541
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + phosphate	3376	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + phosphate + phosphate_star	3376	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + phosphate_star	3376	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	3376	4.3817574	19570.41455	15.2521912	1982-1999 –> 2000-2012	7.5408394	29660.89541
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	3376	4.3817574	19570.41455	15.2521912	1982-1999 –> 2000-2012	7.5408394	29660.89541
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3376	4.2959923	19436.94559	21.1850201	1982-1999 –> 2000-2012	7.4358571	29503.49548
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	3376	4.2959923	19436.94559	21.1850201	1982-1999 –> 2000-2012	7.4358571	29503.49548
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	3376	4.2959923	19436.94559	21.1850201	1982-1999 –> 2000-2012	7.4358571	29503.49548
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1765	3.8037880	9738.92388	12.2952264	2000-2012 –> 2013-2019	8.1855454	29309.33842
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1765	3.8037880	9738.92388	12.2952264	2000-2012 –> 2013-2019	8.1855454	29309.33842
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1765	3.8037880	9738.92388	12.2952264	2000-2012 –> 2013-2019	8.1855454	29309.33842
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1765	3.8936510	9821.34889	15.8177101	2000-2012 –> 2013-2019	8.1896432	29258.29448
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	1765	3.8936510	9821.34889	15.8177101	2000-2012 –> 2013-2019	8.1896432	29258.29448
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	1765	3.8936510	9821.34889	15.8177101	2000-2012 –> 2013-2019	8.1896432	29258.29448
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1765	3.7693127	9706.78414	14.7360756	2000-2012 –> 2013-2019	8.1902712	29337.33644
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + phosphate_star	1765	3.9598723	9878.88056	16.8972842	2000-2012 –> 2013-2019	8.3822217	29509.55681
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1765	3.7693127	9706.78414	14.7360756	2000-2012 –> 2013-2019	8.1902712	29337.33644
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1765	3.7693127	9706.78414	14.7360756	2000-2012 –> 2013-2019	8.1902712	29337.33644
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4426	4.1321620	25133.66821	24.8385028	1982-1999 –> 2000-2012	7.0550807	36598.69969
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	4426	4.1321620	25133.66821	24.8385028	1982-1999 –> 2000-2012	7.0550807	36598.69969
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	4426	4.1321620	25133.66821	24.8385028	1982-1999 –> 2000-2012	7.0550807	36598.69969
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4426	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4426	3.5773624	23857.43128	16.0385121	1982-1999 –> 2000-2012	6.5289804	35367.36942
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + phosphate	4426	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	4426	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + phosphate_star	4426	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	4426	3.5773624	23857.43128	16.0385121	1982-1999 –> 2000-2012	6.5289804	35367.36942
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	4426	3.5773624	23857.43128	16.0385121	1982-1999 –> 2000-2012	6.5289804	35367.36942
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2578	4.2265824	14761.87306	19.4557796	2000-2012 –> 2013-2019	8.3587444	39895.54128
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	2578	4.2265824	14761.87306	19.4557796	2000-2012 –> 2013-2019	8.3587444	39895.54128
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	2578	4.2265824	14761.87306	19.4557796	2000-2012 –> 2013-2019	8.3587444	39895.54128
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2578	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2578	3.9209008	14374.80029	15.9055025	2000-2012 –> 2013-2019	7.4982632	38232.23158
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + phosphate	2578	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	2578	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + phosphate_star	2578	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2578	3.9209008	14374.80029	15.9055025	2000-2012 –> 2013-2019	7.4982632	38232.23158
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2578	3.9209008	14374.80029	15.9055025	2000-2012 –> 2013-2019	7.4982632	38232.23158
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5675	3.5890979	30623.12741	11.8601893	1982-1999 –> 2000-2012	6.2013888	45111.97410
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	5675	3.5890979	30623.12741	11.8601893	1982-1999 –> 2000-2012	6.2013888	45111.97410
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	5675	3.5890979	30623.12741	11.8601893	1982-1999 –> 2000-2012	6.2013888	45111.97410
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5675	3.5333545	30445.46369	11.3858029	1982-1999 –> 2000-2012	6.1456335	44934.28268
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + aou + silicate	5675	3.0844293	28903.21389	13.8988234	1982-1999 –> 2000-2012	6.0885567	44242.35773
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	5675	3.5521641	30505.72452	11.5994102	1982-1999 –> 2000-2012	6.2050185	45088.31716
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5675	3.1093132	28994.41341	18.0861691	1982-1999 –> 2000-2012	5.3556466	42565.01245
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate	5675	3.1933345	29295.04781	17.3970223	1982-1999 –> 2000-2012	6.2000755	44637.48242
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	5675	3.1093132	28994.41341	18.0861691	1982-1999 –> 2000-2012	5.3556466	42565.01245
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	5675	3.1093132	28994.41341	18.0861691	1982-1999 –> 2000-2012	5.3556466	42565.01245
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3422	3.4387736	18178.34160	13.7873631	2000-2012 –> 2013-2019	6.9721280	48623.80529
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3422	3.4626480	18225.69346	14.1337349	2000-2012 –> 2013-2019	7.0378726	48804.86347
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + aou + silicate	3422	2.9674206	17169.38673	11.9858738	2000-2012 –> 2013-2019	6.0518499	46072.60062
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3422	3.4424625	18185.67954	13.9244017	2000-2012 –> 2013-2019	6.9946266	48691.40406
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3422	3.4424625	18185.67954	13.9244017	2000-2012 –> 2013-2019	6.9946266	48691.40406
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3422	3.4424625	18185.67954	13.9244017	2000-2012 –> 2013-2019	6.9946266	48691.40406
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3422	3.3521746	18003.78126	14.9487549	2000-2012 –> 2013-2019	6.4614878	46998.19467
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate	3422	3.3739326	18046.06006	15.7011643	2000-2012 –> 2013-2019	6.5672671	47341.10787
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	3422	3.3521746	18003.78126	14.9487549	2000-2012 –> 2013-2019	6.4614878	46998.19467
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	3422	3.3521746	18003.78126	14.9487549	2000-2012 –> 2013-2019	6.4614878	46998.19467
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	6616	3.0324520	33468.59862	10.6583319	1982-1999 –> 2000-2012	5.3455127	48734.33749
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6616	2.9966623	33311.50296	10.1288040	1982-1999 –> 2000-2012	5.2982339	48543.60043
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6616	3.0054406	33350.20721	10.2540003	1982-1999 –> 2000-2012	5.3340552	48661.22392
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + silicate	6616	2.8595827	32691.93562	16.9783126	1982-1999 –> 2000-2012	5.1651164	47935.65360
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	6616	2.9972209	33313.96925	10.1530334	1982-1999 –> 2000-2012	5.3211866	48611.48443
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	6616	2.9972209	33313.96925	10.1530334	1982-1999 –> 2000-2012	5.3211866	48611.48443
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6616	2.9972209	33313.96925	10.1530334	1982-1999 –> 2000-2012	5.3211866	48611.48443
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	6616	3.0506844	33547.91724	20.5284776	1982-1999 –> 2000-2012	5.1485462	48153.91200
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	6616	3.0506844	33547.91724	20.5284776	1982-1999 –> 2000-2012	5.1485462	48153.91200
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	6616	3.0506844	33547.91724	20.5284776	1982-1999 –> 2000-2012	5.1485462	48153.91200
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3904	2.7574902	19012.88985	12.6480309	2000-2012 –> 2013-2019	5.7899422	52481.48847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	3904	2.7574902	19012.88985	12.6480309	2000-2012 –> 2013-2019	5.7899422	52481.48847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	3904	2.7574902	19012.88985	12.6480309	2000-2012 –> 2013-2019	5.7899422	52481.48847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3904	2.7447079	18976.61186	12.1505620	2000-2012 –> 2013-2019	5.7413703	52288.11481
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3904	2.7455471	18978.99873	12.2093988	2000-2012 –> 2013-2019	5.7509877	52329.20594
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + aou + silicate	3904	2.7499572	18991.53044	11.4294859	2000-2012 –> 2013-2019	5.6095399	51683.46607
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3904	2.7432404	18972.43604	12.0931425	2000-2012 –> 2013-2019	5.7404613	52286.40530
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3904	2.7432404	18972.43604	12.0931425	2000-2012 –> 2013-2019	5.7404613	52286.40530
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate	3904	2.9944894	19654.68141	8.4412807	2000-2012 –> 2013-2019	5.9931860	52973.16393
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3904	2.7432404	18972.43604	12.0931425	2000-2012 –> 2013-2019	5.7404613	52286.40530
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2605	3.1679730	13414.27883	9.0214032	1982-1999 –> 2000-2012	4.7844113	18624.39065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	2605	3.1679730	13414.27883	9.0214032	1982-1999 –> 2000-2012	4.7844113	18624.39065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	2605	3.1679730	13414.27883	9.0214032	1982-1999 –> 2000-2012	4.7844113	18624.39065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + aou + silicate	2605	3.1166679	13329.21260	9.8754952	1982-1999 –> 2000-2012	4.8010415	18651.96162
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2605	3.2261932	13507.15762	8.4447285	1982-1999 –> 2000-2012	4.8439305	18717.46738
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2605	2.9949800	13121.71449	7.6320448	1982-1999 –> 2000-2012	4.5310097	18192.22406
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + phosphate	2605	3.2261932	13507.15762	8.4447285	1982-1999 –> 2000-2012	4.8439305	18717.46738
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate	2605	3.1403948	13366.72560	9.8600442	1982-1999 –> 2000-2012	4.8314447	18698.29785
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2605	2.9949800	13121.71449	7.6320448	1982-1999 –> 2000-2012	4.5310097	18192.22406
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2605	2.9949800	13121.71449	7.6320448	1982-1999 –> 2000-2012	4.5310097	18192.22406
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1520	2.4782579	7086.54298	9.5043297	2000-2012 –> 2013-2019	5.4128162	20102.07446
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1520	2.4782579	7086.54298	9.5043297	2000-2012 –> 2013-2019	5.4128162	20102.07446
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1520	2.4782579	7086.54298	9.5043297	2000-2012 –> 2013-2019	5.4128162	20102.07446
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1520	2.4923267	7103.75193	8.9701919	2000-2012 –> 2013-2019	5.4253579	20116.57147
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1520	2.4967804	7109.17935	8.8090180	2000-2012 –> 2013-2019	5.4296020	20121.62661
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1520	2.4996524	7112.67420	8.7188128	2000-2012 –> 2013-2019	5.4324523	20125.08297
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1520	2.4996524	7112.67420	8.7188128	2000-2012 –> 2013-2019	5.4324523	20125.08297
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1520	2.4996524	7112.67420	8.7188128	2000-2012 –> 2013-2019	5.4324523	20125.08297
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1520	2.8722373	7535.05058	8.9679710	2000-2012 –> 2013-2019	5.8672173	20656.76507
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1520	2.8722373	7535.05058	8.9679710	2000-2012 –> 2013-2019	5.8672173	20656.76507
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3162	3.2949562	16528.05985	17.9094571	1982-1999 –> 2000-2012	4.7655574	21876.48639
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	3162	3.2949562	16528.05985	17.9094571	1982-1999 –> 2000-2012	4.7655574	21876.48639
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	3162	3.2949562	16528.05985	17.9094571	1982-1999 –> 2000-2012	4.7655574	21876.48639
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3162	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3162	3.1574651	16258.50971	17.2112577	1982-1999 –> 2000-2012	4.5916452	21532.80599
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate	3162	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	3162	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + phosphate_star	3162	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	3162	3.1574651	16258.50971	17.2112577	1982-1999 –> 2000-2012	4.5916452	21532.80599
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	3162	3.1574651	16258.50971	17.2112577	1982-1999 –> 2000-2012	4.5916452	21532.80599
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1823	3.3105153	9552.09060	9.3111647	2000-2012 –> 2013-2019	6.4646724	25803.97121
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1823	3.3105153	9552.09060	9.3111647	2000-2012 –> 2013-2019	6.4646724	25803.97121
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1823	3.3105153	9552.09060	9.3111647	2000-2012 –> 2013-2019	6.4646724	25803.97121
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1823	3.3444727	9589.29868	9.4041251	2000-2012 –> 2013-2019	6.5013077	25846.54623
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1823	3.3596636	9605.82162	9.4523390	2000-2012 –> 2013-2019	6.5193746	25868.82796
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1823	3.3664542	9613.18354	9.4679657	2000-2012 –> 2013-2019	6.5273716	25878.60401
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1823	3.3664542	9613.18354	9.4679657	2000-2012 –> 2013-2019	6.5273716	25878.60401
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1823	3.3664542	9613.18354	9.4679657	2000-2012 –> 2013-2019	6.5273716	25878.60401
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1823	3.4615597	9714.75830	9.8097748	2000-2012 –> 2013-2019	6.6190247	25973.26800
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1823	3.4615597	9714.75830	9.8097748	2000-2012 –> 2013-2019	6.6190247	25973.26800
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3864	1.6905568	15037.20482	8.5730976	1982-1999 –> 2000-2012	3.3434758	21960.85175
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + aou + phosphate	3864	1.6905568	15037.20482	8.5730976	1982-1999 –> 2000-2012	3.3434758	21960.85175
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + aou + phosphate_star	3864	1.6905568	15037.20482	8.5730976	1982-1999 –> 2000-2012	3.3434758	21960.85175
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3864	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3864	1.6609148	14900.50096	9.0532945	1982-1999 –> 2000-2012	3.1884612	21540.49536
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + phosphate	3864	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + phosphate + phosphate_star	3864	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + phosphate_star	3864	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	3864	1.6609148	14900.50096	9.0532945	1982-1999 –> 2000-2012	3.1884612	21540.49536
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	3864	1.6609148	14900.50096	9.0532945	1982-1999 –> 2000-2012	3.1884612	21540.49536
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2207	1.5684161	8263.78728	9.1231543	2000-2012 –> 2013-2019	3.2553057	23284.20999
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2207	1.5684161	8263.78728	9.1231543	2000-2012 –> 2013-2019	3.2553057	23284.20999
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2207	1.5684161	8263.78728	9.1231543	2000-2012 –> 2013-2019	3.2553057	23284.20999
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2207	1.5711791	8271.55624	9.0746907	2000-2012 –> 2013-2019	3.2716587	23353.98826
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2207	1.5719412	8273.69666	9.0469574	2000-2012 –> 2013-2019	3.2769267	23376.57902
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2207	1.5719951	8273.84817	9.0399522	2000-2012 –> 2013-2019	3.2783238	23382.81616
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2207	1.5719951	8273.84817	9.0399522	2000-2012 –> 2013-2019	3.2783238	23382.81616
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2207	1.5719951	8273.84817	9.0399522	2000-2012 –> 2013-2019	3.2783238	23382.81616
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2207	1.6205132	8408.02173	9.7347045	2000-2012 –> 2013-2019	3.2814280	23308.52268
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2207	1.6205132	8408.02173	9.7347045	2000-2012 –> 2013-2019	3.2814280	23308.52268
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2202	1.5548808	8206.92595	7.3193185	1982-1999 –> 2000-2012	3.0992837	12361.81446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	2202	1.5548808	8206.92595	7.3193185	1982-1999 –> 2000-2012	3.0992837	12361.81446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	2202	1.5548808	8206.92595	7.3193185	1982-1999 –> 2000-2012	3.0992837	12361.81446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2202	1.5610214	8224.28432	7.3829130	1982-1999 –> 2000-2012	3.1157460	12394.05355
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2202	1.5627952	8229.28564	7.4071916	1982-1999 –> 2000-2012	3.1210987	12404.19167
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2202	1.5627952	8229.28564	7.4071916	1982-1999 –> 2000-2012	3.1210987	12404.19167
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2202	1.5627952	8229.28564	7.4071916	1982-1999 –> 2000-2012	3.1210987	12404.19167
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2202	1.5307379	8138.00775	6.1987387	1982-1999 –> 2000-2012	2.9717656	12138.12294
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	2202	1.5307379	8138.00775	6.1987387	1982-1999 –> 2000-2012	2.9717656	12138.12294
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	2202	1.5307379	8138.00775	6.1987387	1982-1999 –> 2000-2012	2.9717656	12138.12294
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1247	1.2902622	4188.41727	5.8262405	2000-2012 –> 2013-2019	2.8451430	12395.34322
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	1247	1.2902622	4188.41727	5.8262405	2000-2012 –> 2013-2019	2.8451430	12395.34322
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	1247	1.2902622	4188.41727	5.8262405	2000-2012 –> 2013-2019	2.8451430	12395.34322
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1247	1.2934477	4194.56700	5.7870805	2000-2012 –> 2013-2019	2.8544691	12418.85132
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1247	1.2941037	4195.83169	5.7686036	2000-2012 –> 2013-2019	2.8568989	12425.11733
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1247	1.2941037	4195.83169	5.7686036	2000-2012 –> 2013-2019	2.8568989	12425.11733
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1247	1.2941037	4195.83169	5.7686036	2000-2012 –> 2013-2019	2.8568989	12425.11733
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1247	1.2940968	4195.81825	6.4737894	2000-2012 –> 2013-2019	2.8248346	12333.82600
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate	1247	1.2940968	4195.81825	6.4737894	2000-2012 –> 2013-2019	2.8248346	12333.82600
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + aou + silicate + phosphate_star	1247	1.2940968	4195.81825	6.4737894	2000-2012 –> 2013-2019	2.8248346	12333.82600
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	24009	1.5862780	90301.63353	10.1419768	1982-1999 –> 2000-2012	3.0021288	135289.49705
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	24009	1.5457119	89059.68970	9.6225706	1982-1999 –> 2000-2012	2.8533113	132024.68257
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	24009	1.5457119	89059.68970	9.6225706	1982-1999 –> 2000-2012	2.8533113	132024.68257
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	24009	1.5457119	89059.68970	9.6225706	1982-1999 –> 2000-2012	2.8533113	132024.68257
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	24009	1.5458590	89064.25855	9.6237779	1982-1999 –> 2000-2012	2.8526421	132013.35434
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	24009	1.5460122	89069.01719	9.6248630	1982-1999 –> 2000-2012	2.8517894	131998.50803
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	24009	1.5460006	89068.65692	9.6251167	1982-1999 –> 2000-2012	2.8518187	131998.94619
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	24009	1.5460006	89068.65692	9.6251167	1982-1999 –> 2000-2012	2.8518187	131998.94619
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	24009	1.5460006	89068.65692	9.6251167	1982-1999 –> 2000-2012	2.8518187	131998.94619
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate_star	24009	1.5530253	89284.34511	9.2818343	1982-1999 –> 2000-2012	2.8718943	132465.81043
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	14824	1.2904044	49641.61538	9.2901765	2000-2012 –> 2013-2019	2.8361163	138701.30508
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate	14824	1.2904044	49641.61538	9.2901765	2000-2012 –> 2013-2019	2.8361163	138701.30508
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + aou + silicate + phosphate_star	14824	1.2904044	49641.61538	9.2901765	2000-2012 –> 2013-2019	2.8361163	138701.30508
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	14824	1.2907334	49649.17197	9.2905994	2000-2012 –> 2013-2019	2.8365924	138713.43051
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14824	1.2911776	49659.37507	9.2937847	2000-2012 –> 2013-2019	2.8371898	138728.39227
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	14824	1.2911324	49658.33768	9.2927061	2000-2012 –> 2013-2019	2.8371331	138726.99460
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	14824	1.2911324	49658.33768	9.2927061	2000-2012 –> 2013-2019	2.8371331	138726.99460
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	14824	1.2911324	49658.33768	9.2927061	2000-2012 –> 2013-2019	2.8371331	138726.99460
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate_star	14824	1.3186734	50282.10445	10.1511497	2000-2012 –> 2013-2019	2.8716987	139566.44956
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	14824	1.3443327	50855.46644	9.7413986	2000-2012 –> 2013-2019	2.9266322	141038.51664

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	2.2493175	331.83481
Atlantic	(-Inf,26]	2000-2012 –> 2013-2019	0.7247634	50.66366
Atlantic	(26,26.75]	1982-1999 –> 2000-2012	7.6190395	9344.62334
Atlantic	(26,26.75]	2000-2012 –> 2013-2019	7.4709608	7060.68118
Atlantic	(26.75,27.25]	1982-1999 –> 2000-2012	5.0349286	18705.85894
Atlantic	(26.75,27.25]	2000-2012 –> 2013-2019	5.5106695	14065.93546
Atlantic	(27.25,27.5]	1982-1999 –> 2000-2012	4.6444783	16626.19016
Atlantic	(27.25,27.5]	2000-2012 –> 2013-2019	7.0276990	15135.04028
Atlantic	(27.5,27.75]	1982-1999 –> 2000-2012	3.9258917	28980.15859
Atlantic	(27.5,27.75]	2000-2012 –> 2013-2019	4.4674782	23964.99767
Atlantic	(27.75,27.85]	1982-1999 –> 2000-2012	1.9172103	7556.93637
Atlantic	(27.75,27.85]	2000-2012 –> 2013-2019	2.2045502	6570.77719
Atlantic	(27.85,27.95]	1982-1999 –> 2000-2012	2.4961967	8747.30619
Atlantic	(27.85,27.95]	2000-2012 –> 2013-2019	2.3959675	6659.84026
Atlantic	(27.95,28.05]	1982-1999 –> 2000-2012	8.0279494	18231.72255
Atlantic	(27.95,28.05]	2000-2012 –> 2013-2019	5.1023703	12119.83838
Atlantic	(28.05,28.1]	1982-1999 –> 2000-2012	1.8059909	4971.01703
Atlantic	(28.05,28.1]	2000-2012 –> 2013-2019	1.4896801	3660.34453
Atlantic	(28.1,28.15]	1982-1999 –> 2000-2012	1.6008413	6142.50573
Atlantic	(28.1,28.15]	2000-2012 –> 2013-2019	1.3705435	4917.69173
Atlantic	(28.15,28.2]	1982-1999 –> 2000-2012	1.6552054	11111.72721
Atlantic	(28.15,28.2]	2000-2012 –> 2013-2019	1.4009190	8901.98672
Atlantic	(28.2, Inf]	1982-1999 –> 2000-2012	1.7266075	20897.45398
Atlantic	(28.2, Inf]	2000-2012 –> 2013-2019	1.4261681	16335.28409
Indo-Pacific	(-Inf,26]	1982-1999 –> 2000-2012	11.0150805	23731.79400
Indo-Pacific	(-Inf,26]	2000-2012 –> 2013-2019	11.3566063	30117.69247
Indo-Pacific	(26,26.75]	1982-1999 –> 2000-2012	8.8498079	46653.21996
Indo-Pacific	(26,26.75]	2000-2012 –> 2013-2019	9.0215309	45878.37780
Indo-Pacific	(26.75,27]	1982-1999 –> 2000-2012	7.5276394	29634.76392
Indo-Pacific	(26.75,27]	2000-2012 –> 2013-2019	8.2078601	29322.44649
Indo-Pacific	(27,27.25]	1982-1999 –> 2000-2012	6.9315030	36288.39091
Indo-Pacific	(27,27.25]	2000-2012 –> 2013-2019	8.1519589	39468.69168
Indo-Pacific	(27.25,27.5]	1982-1999 –> 2000-2012	5.9310391	44193.33996
Indo-Pacific	(27.25,27.5]	2000-2012 –> 2013-2019	6.6997461	47791.11734
Indo-Pacific	(27.5,27.75]	1982-1999 –> 2000-2012	5.2552117	48417.10048
Indo-Pacific	(27.5,27.75]	2000-2012 –> 2013-2019	5.7686294	52357.76321
Indo-Pacific	(27.75,27.85]	1982-1999 –> 2000-2012	4.7266610	18523.50384
Indo-Pacific	(27.75,27.85]	2000-2012 –> 2013-2019	5.5125200	20223.32005
Indo-Pacific	(27.85,27.95]	1982-1999 –> 2000-2012	4.7197185	21783.99386
Indo-Pacific	(27.85,27.95]	2000-2012 –> 2013-2019	6.5234864	25870.96358
Indo-Pacific	(27.95,28.05]	1982-1999 –> 2000-2012	3.3186672	21928.38655
Indo-Pacific	(27.95,28.05]	2000-2012 –> 2013-2019	3.2712330	23334.86911
Indo-Pacific	(28.05,28.1]	1982-1999 –> 2000-2012	3.0692190	12310.64408
Indo-Pacific	(28.05,28.1]	2000-2012 –> 2013-2019	2.8435099	12388.17110
Indo-Pacific	(28.1, Inf]	1982-1999 –> 2000-2012	2.8693845	132383.80561
Indo-Pacific	(28.1, Inf]	2000-2012 –> 2013-2019	2.8491861	139033.16880

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
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
02b976d	Donghe-Zhu	2021-02-24
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

6.1.2 Best models

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

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c407a50	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
e2ffc14	Donghe-Zhu	2021-02-05
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

6.2 RMSE correlation between eras

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

6.2.1 All models

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

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

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
02b976d	Donghe-Zhu	2021-02-24
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

rm(max_rmse)

6.2.2 Best models

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

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

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c407a50	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
e2ffc14	Donghe-Zhu	2021-02-05
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

rm(max_rmse)

6.3 Predictor counts

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

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

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )

	aou	oxygen	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	10	7	6	5	5	4	10
(26,26.75]	10	6	8	5	4	10	4
(26.75,27.25]	9	4	7	6	7	10	6
(27.25,27.5]	7	5	6	6	10	9	6
(27.5,27.75]	6	5	6	6	10	9	7
(27.75,27.85]	7	6	7	6	10	7	7
(27.85,27.95]	10	7	7	6	3	3	10
(27.95,28.05]	7	6	6	6	10	8	7
(28.05,28.1]	10	7	7	6	3	3	10
(28.1,28.15]	10	6	7	7	6	6	7
(28.15,28.2]	10	6	7	6	7	7	7
(28.2, Inf]	7	6	6	6	8	10	7
total	103.00	71.00	80.00	71.00	83.00	86.00	88.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	7	6	5	6	7	10	9
(26,26.75]	7	5	7	6	8	10	7
(26.75,27.25]	7	4	6	6	10	10	5
(27.25,27.5]	6	4	6	6	10	10	6
(27.5,27.75]	6	4	6	6	10	10	6
(27.75,27.85]	7	6	7	6	10	7	7
(27.85,27.95]	10	7	7	6	3	3	10
(27.95,28.05]	10	7	7	6	3	3	10
(28.05,28.1]	10	7	7	6	3	3	10
(28.1,28.15]	10	7	6	7	6	6	7
(28.15,28.2]	10	6	7	6	7	7	7
(28.2, Inf]	7	6	7	6	10	7	7
total	97.00	69.00	78.00	73.00	87.00	86.00	91.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	10	6	7	6	10	4	4
(26,26.75]	6	4	6	7	10	9	7
(26.75,27]	10	7	7	6	10	3	3
(27,27.25]	10	7	7	6	3	3	10
(27.25,27.5]	9	7	5	5	6	10	7
(27.5,27.75]	7	6	6	5	7	10	9
(27.75,27.85]	10	7	6	5	4	5	10
(27.85,27.95]	10	7	7	6	3	3	10
(27.95,28.05]	10	7	7	6	3	3	10
(28.05,28.1]	7	6	7	6	7	10	7
(28.1, Inf]	6	4	6	6	10	10	6
total	95.00	68.00	71.00	64.00	73.00	70.00	83.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	10	7	7	6	10	3	3
(26,26.75]	6	5	6	6	9	10	7
(26.75,27]	10	7	6	7	6	6	7
(27,27.25]	10	7	7	6	3	3	10
(27.25,27.5]	7	6	5	5	6	10	10
(27.5,27.75]	6	5	6	5	10	10	7
(27.75,27.85]	7	6	6	6	8	10	7
(27.85,27.95]	7	6	6	6	8	10	7
(27.95,28.05]	7	5	7	6	8	10	7
(28.05,28.1]	7	6	7	6	7	10	7
(28.1, Inf]	6	4	6	7	9	10	7
total	83.00	64.00	69.00	66.00	84.00	92.00	79.00

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
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
02b976d	Donghe-Zhu	2021-02-24
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

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

Past versions of aic_vs_rmse_selected_models-1.png

Version	Author	Date
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c407a50	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
e2ffc14	Donghe-Zhu	2021-02-05
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

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_0.7.5      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.3   
[21] tidyverse_1.3.0  workflowr_1.6.2 

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