eMLR - model fitting

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Last updated: 2021-03-03

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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, aou, nitrate, silicate, phosphate, phosphate_star

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

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

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

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

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

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

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

# convert to tibble
lm_all <- as_tibble(lm_all)

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

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

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

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

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


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

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

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

3 Apply predictor threshold

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

• Minimum: 3
  
• Maximum: 9

lm_all <- lm_all %>% 
  filter(n >= params_local$MLR_predictors_min,
         n <= params_local$MLR_predictors_max)

This results in a total number of MLR models of:

• 45

4 Fit all models

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

• cstar_tref

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

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

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

5 Prepare coeffcients

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

5.1 Formatting

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

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

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

5.2 Predictor selection

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

• 5

The criterion used to select the best models was:

• aic

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

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

# remove models with predictors fitted as NA

lm_all_fitted_wide <- lm_all_fitted_wide %>%
  filter(na_predictor == FALSE)

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

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

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

5.3 RMSE tables

5.3.1 per model

lm_best %>%
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	gamma_slab	model	nr_obs	rmse	aic	resid_max	eras	rmse_sum	aic_sum
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate_star	146	1.5497398	554.2515	6.779875	1982-1996 –> 1997-2008	3.2465650	1236.2594
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	146	1.0520163	441.1370	4.374551	1982-1996 –> 1997-2008	2.4166632	1048.1999
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	146	1.0518302	443.0853	4.400153	1982-1996 –> 1997-2008	2.4151224	1051.8066
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	146	1.4666454	538.1596	7.367948	1982-1996 –> 1997-2008	3.1957722	1226.6545
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	146	1.4638268	539.5978	7.187528	1982-1996 –> 1997-2008	3.1924621	1229.9950
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	120	1.1639689	388.9858	3.443761	1997-2008 –> 2009-2019	2.2159852	830.1228
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	120	1.1032974	378.1381	3.121374	1997-2008 –> 2009-2019	2.1551277	821.2234
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate_star	120	1.6504991	472.8039	4.220872	1997-2008 –> 2009-2019	3.1951574	1026.0964
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	120	1.5135931	452.0220	6.318368	1997-2008 –> 2009-2019	2.9802386	990.1815
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	120	1.4696627	446.9532	5.722394	1997-2008 –> 2009-2019	2.9334895	986.5510
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	969	3.5045654	5194.2838	13.212095	1982-1996 –> 1997-2008	6.9766541	12037.9975
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	969	4.1719459	5530.1083	10.383853	1982-1996 –> 1997-2008	8.3677529	12857.2624
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	969	4.0102833	5453.5172	11.933724	1982-1996 –> 1997-2008	8.1283216	12732.7020
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	969	4.0011567	5451.1017	12.464976	1982-1996 –> 1997-2008	8.1155697	12730.0283
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	969	4.2435626	5565.0942	13.044934	1982-1996 –> 1997-2008	8.5287394	12948.2875
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	887	3.5766351	4792.0224	11.509131	1997-2008 –> 2009-2019	7.0812005	9986.3061
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	887	4.1181347	5040.1171	12.061754	1997-2008 –> 2009-2019	8.2900807	10570.2255
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	887	3.9565691	4969.1162	16.433540	1997-2008 –> 2009-2019	7.9668524	10422.6334
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	887	3.9408963	4964.0751	18.038103	1997-2008 –> 2009-2019	7.9420530	10415.1768
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	887	4.2298592	5089.6042	11.623373	1997-2008 –> 2009-2019	8.4734218	10654.6984
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1282	3.1608290	6600.8976	10.318355	1982-1996 –> 1997-2008	6.2543364	14665.3489
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	1282	3.1961002	6629.3505	10.049965	1982-1996 –> 1997-2008	6.3543361	14759.2392
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1282	3.1030255	6555.5746	10.376132	1982-1996 –> 1997-2008	6.1650156	14589.6660
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1282	3.1858367	6623.1036	10.059773	1982-1996 –> 1997-2008	6.3254869	14736.3413
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1282	3.0469927	6508.8521	9.480321	1982-1996 –> 1997-2008	6.0292890	14459.6095
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1088	3.6028024	5888.6155	11.507716	1997-2008 –> 2009-2019	6.7636314	12489.5131
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	1088	3.5167576	5836.0161	11.179635	1997-2008 –> 2009-2019	6.7128578	12465.3665
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1088	3.4970317	5825.7763	11.382695	1997-2008 –> 2009-2019	6.6000572	12381.3509
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1088	3.5173399	5838.3763	9.303961	1997-2008 –> 2009-2019	6.7031766	12461.4799
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1088	3.4808595	5815.6899	10.801616	1997-2008 –> 2009-2019	6.5278523	12324.5420
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2190	1.9895745	9240.0438	14.066373	1982-1996 –> 1997-2008	3.6463628	19282.8388
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2190	1.9034540	9048.2259	13.441245	1982-1996 –> 1997-2008	3.5437509	19040.8615
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2190	2.1022469	9483.3203	15.899876	1982-1996 –> 1997-2008	3.8820103	19901.4347
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	2190	2.0909073	9457.6305	14.567048	1982-1996 –> 1997-2008	3.8638648	19853.7680
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2190	1.9869981	9236.3682	17.584990	1982-1996 –> 1997-2008	3.4834060	18750.3079
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2004	2.4497762	9290.2603	27.463653	1997-2008 –> 2009-2019	4.4393507	18530.3042
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	2004	2.4126150	9228.9963	24.703523	1997-2008 –> 2009-2019	4.5306803	18743.1504
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2004	2.3482362	9122.5930	25.940225	1997-2008 –> 2009-2019	4.2516902	18170.8189
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2004	2.5042136	9380.3485	23.426544	1997-2008 –> 2009-2019	4.6064605	18863.6687
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2004	2.1044039	8683.1870	22.765287	1997-2008 –> 2009-2019	4.0914020	17919.5552
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1894	2.0854736	8173.1038	10.811524	1982-1996 –> 1997-2008	4.3470262	17663.4620
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1894	1.8615505	7740.8392	10.568580	1982-1996 –> 1997-2008	3.5664220	16031.1351
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1894	1.8207833	7658.9619	10.353334	1982-1996 –> 1997-2008	3.3668982	15536.8211
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1894	1.9989140	8012.5232	13.218031	1982-1996 –> 1997-2008	3.6404184	16144.2223
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1894	2.2543701	8468.0930	21.306001	1982-1996 –> 1997-2008	4.2867238	17505.3773
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1770	2.1957025	7821.2597	11.870716	1997-2008 –> 2009-2019	4.2811761	15994.3635
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1770	2.1848856	7801.7771	13.569860	1997-2008 –> 2009-2019	4.0464361	15542.6163
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1770	2.1848757	7803.7610	13.557213	1997-2008 –> 2009-2019	4.0056590	15462.7228
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	1770	2.2804983	7953.3970	14.908620	1997-2008 –> 2009-2019	4.4090721	16201.9892
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1770	2.3928360	8125.6190	19.363213	1997-2008 –> 2009-2019	4.3917499	16138.1422
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1904	2.4727827	8862.8683	12.792903	1982-1996 –> 1997-2008	5.1237765	20394.1857
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1904	2.3787934	8717.3056	12.935771	1982-1996 –> 1997-2008	4.9537934	20110.6657
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1904	2.5027529	8910.7439	20.150364	1982-1996 –> 1997-2008	4.6549157	19440.9456
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1904	2.1576638	8343.7692	11.413683	1982-1996 –> 1997-2008	3.8586083	17739.7572
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1904	2.0464298	8144.2143	14.786810	1982-1996 –> 1997-2008	3.7467610	17540.4670
Atlantic	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	1702	2.9549498	8530.2384	21.650262	1997-2008 –> 2009-2019	5.5905647	17635.9520
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1702	2.8677604	8428.2875	16.040376	1997-2008 –> 2009-2019	5.3405431	17291.1558
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1702	2.7136930	8242.3155	17.246937	1997-2008 –> 2009-2019	5.0924864	16959.6211
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1702	3.0012510	8583.1622	11.700791	1997-2008 –> 2009-2019	5.1589148	16926.9314
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1702	2.7021751	8227.8369	17.252150	1997-2008 –> 2009-2019	4.7486049	16372.0512
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	2619	2.7198667	12683.4530	13.245897	1982-1996 –> 1997-2008	5.1778031	27038.8503
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2619	2.6994928	12646.0688	13.726300	1982-1996 –> 1997-2008	4.8882562	26285.7482
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	2619	2.4559246	12150.7605	13.466377	1982-1996 –> 1997-2008	4.8153784	26255.1177
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2619	2.3958748	12023.0944	14.280411	1982-1996 –> 1997-2008	4.4261967	25199.7926
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2619	3.0129659	13223.5209	15.600728	1982-1996 –> 1997-2008	5.2886409	27106.1609
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2340	3.1208758	11981.0043	15.244357	1997-2008 –> 2009-2019	5.8942753	24770.5511
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	2340	3.2193610	12122.4083	13.884231	1997-2008 –> 2009-2019	5.9392277	24805.8614
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2340	3.2193457	12124.3861	13.894909	1997-2008 –> 2009-2019	5.9188385	24770.4549
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	2340	2.7289817	11351.0180	14.950042	1997-2008 –> 2009-2019	5.1849064	23501.7784
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2340	2.7164500	11331.4775	14.798604	1997-2008 –> 2009-2019	5.1123248	23354.5718
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	900	1.9111538	3731.9623	13.337451	1982-1996 –> 1997-2008	3.9036933	8416.0625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	900	1.8506803	3676.0853	14.205377	1982-1996 –> 1997-2008	3.7915191	8303.9276
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	900	1.8293894	3653.2574	12.560489	1982-1996 –> 1997-2008	3.5060474	7954.8596
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	900	1.7150314	3537.0658	12.330292	1982-1996 –> 1997-2008	3.5181722	7999.8322
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	900	1.5104975	3310.4797	12.896290	1982-1996 –> 1997-2008	3.1107426	7510.7149
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	861	2.0091785	3656.8962	12.547977	1997-2008 –> 2009-2019	3.9203323	7388.8584
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	861	1.9932243	3645.1678	12.962072	1997-2008 –> 2009-2019	3.8439046	7321.2531
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	861	2.3474123	3924.8181	11.404366	1997-2008 –> 2009-2019	4.1768017	7578.0755
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	861	1.8364097	3502.0651	11.597744	1997-2008 –> 2009-2019	3.5514410	7039.1309
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	861	1.7164355	3387.7222	11.994150	1997-2008 –> 2009-2019	3.2269330	6698.2019
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	903	2.9972679	4557.0513	32.447722	1982-1996 –> 1997-2008	6.0329251	10093.1877
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	903	2.9997106	4558.5226	30.014544	1982-1996 –> 1997-2008	5.9054075	9999.0987
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	903	2.9876304	4553.2349	27.632975	1982-1996 –> 1997-2008	5.8926069	9995.2695
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	903	2.7117956	4376.2884	21.731416	1982-1996 –> 1997-2008	5.7854493	9939.5917
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	903	2.6989057	4369.6836	21.521888	1982-1996 –> 1997-2008	5.7193921	9896.8780
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	893	3.6388755	4853.1553	24.564776	1997-2008 –> 2009-2019	6.6361435	9410.2066
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	893	3.2764028	4665.7528	31.808520	1997-2008 –> 2009-2019	6.2761134	9224.2753
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	893	3.2010827	4626.2158	30.563544	1997-2008 –> 2009-2019	6.1887131	9179.4507
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	893	3.5763422	4822.1964	23.280568	1997-2008 –> 2009-2019	6.2881378	9198.4849
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	893	3.5520614	4812.0294	24.376118	1997-2008 –> 2009-2019	6.2509671	9181.7130
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1098	4.8642380	6601.8635	25.792846	1982-1996 –> 1997-2008	9.6052740	14920.6058
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1098	4.7748519	6563.1341	24.911954	1982-1996 –> 1997-2008	9.4330465	14834.6597
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1098	4.2153808	6287.4619	22.348711	1982-1996 –> 1997-2008	8.2330503	14143.9783
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1098	3.9443873	6143.5458	26.307254	1982-1996 –> 1997-2008	7.5172695	13674.4786
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1098	4.7747944	6563.1076	21.520605	1982-1996 –> 1997-2008	9.5363197	14895.8900
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1052	4.3783749	6104.3764	24.778686	1997-2008 –> 2009-2019	9.2426129	12706.2399
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1052	4.3189470	6077.6231	24.715518	1997-2008 –> 2009-2019	9.0937988	12640.7572
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1052	3.8344411	5825.2725	22.665961	1997-2008 –> 2009-2019	8.0498219	12112.7344
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1052	3.4529907	5606.8092	27.139851	1997-2008 –> 2009-2019	7.3973780	11750.3550
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1052	4.4232551	6127.8335	23.229057	1997-2008 –> 2009-2019	9.1980495	12690.9412
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	743	1.1729477	2357.5893	10.038524	1982-1996 –> 1997-2008	2.0942163	4770.7245
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	743	1.0406554	2179.7607	6.731081	1982-1996 –> 1997-2008	1.9087851	4486.1947
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	743	1.0156908	2145.6782	5.795841	1982-1996 –> 1997-2008	1.8831344	4452.6919
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	743	1.1252912	2295.9529	10.212504	1982-1996 –> 1997-2008	2.0347955	4686.0058
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	743	1.0468957	2190.6450	11.352439	1982-1996 –> 1997-2008	1.8733036	4410.6209
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	673	1.1480158	2109.6865	8.049134	1997-2008 –> 2009-2019	2.2645459	4396.0246
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	673	1.0731011	2016.8552	9.691677	1997-2008 –> 2009-2019	2.1137565	4196.6159
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	673	1.0390706	1975.4790	8.643193	1997-2008 –> 2009-2019	2.0547614	4121.1571
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	673	1.0632974	2004.5018	13.201907	1997-2008 –> 2009-2019	2.1885886	4300.4547
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	673	1.0029755	1927.8904	13.995196	1997-2008 –> 2009-2019	2.0498712	4118.5354
Atlantic	(28.1,28.15]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	867	0.8382734	2166.5429	9.188588	1982-1996 –> 1997-2008	1.5154137	4423.9556
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	867	0.8178349	2125.7410	5.793449	1982-1996 –> 1997-2008	1.5088889	4429.5345
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	867	0.7446359	1961.1524	5.319070	1982-1996 –> 1997-2008	1.4077145	4172.7760
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	867	0.7236954	1913.6904	5.240222	1982-1996 –> 1997-2008	1.3447242	3984.3579
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	867	0.7559212	1989.2348	9.303963	1982-1996 –> 1997-2008	1.3432304	3938.0897
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	770	0.8961317	2030.2768	7.973080	1997-2008 –> 2009-2019	1.7139666	4156.0178
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	770	0.8166830	1885.3088	7.028213	1997-2008 –> 2009-2019	1.5613190	3846.4613
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	770	0.8154600	1885.0009	7.017951	1997-2008 –> 2009-2019	1.5391554	3798.6912
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	770	0.8766659	1994.4562	11.848627	1997-2008 –> 2009-2019	1.7185636	4168.4799
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	770	0.7933963	1842.7593	12.250467	1997-2008 –> 2009-2019	1.5493175	3831.9942
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1407	0.5841786	2492.2314	1.980710	1982-1996 –> 1997-2008	1.1040213	5376.4806
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1407	0.5391101	2268.3040	1.963077	1982-1996 –> 1997-2008	1.0448435	5051.2003
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1407	0.5882267	2511.6642	2.095192	1982-1996 –> 1997-2008	1.1391407	5613.9582
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1407	0.5601250	2373.9120	2.108705	1982-1996 –> 1997-2008	1.0988386	5392.0914
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1407	0.5482794	2315.7626	2.225938	1982-1996 –> 1997-2008	1.0867809	5334.4632
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1298	0.7148302	2824.0606	5.571969	1997-2008 –> 2009-2019	1.2990088	5316.2921
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1298	0.7054925	2791.9262	6.356481	1997-2008 –> 2009-2019	1.2446026	5060.2302
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1298	0.8189368	3177.0178	9.752451	1997-2008 –> 2009-2019	1.4071636	5688.6820
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1298	0.8075260	3140.5916	10.459046	1997-2008 –> 2009-2019	1.3676511	5514.5036
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1298	0.8075158	3142.5587	10.484177	1997-2008 –> 2009-2019	1.3557952	5458.3212
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	2510	0.3533001	1910.0753	3.547623	1982-1996 –> 1997-2008	0.6466399	3111.7423
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2510	0.3453344	1797.5970	2.232031	1982-1996 –> 1997-2008	0.6362008	2948.8481
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	2510	0.3509029	1877.8972	2.649311	1982-1996 –> 1997-2008	0.6439100	3074.5405
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2510	0.3408894	1734.5610	2.978453	1982-1996 –> 1997-2008	0.6271391	2788.7779
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2510	0.5649587	4270.6385	11.792191	1982-1996 –> 1997-2008	0.9856043	7707.5468
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	2356	0.4048932	2435.7681	2.383068	1997-2008 –> 2009-2019	0.7581932	4345.8435
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2356	0.3912592	2276.3681	2.329236	1997-2008 –> 2009-2019	0.7365936	4073.9651
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	2356	0.4002060	2382.9022	2.376657	1997-2008 –> 2009-2019	0.7511088	4260.7994
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2356	0.3839474	2189.4776	2.545602	1997-2008 –> 2009-2019	0.7248368	3924.0386
Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	2356	0.6313333	4530.8893	4.749645	1997-2008 –> 2009-2019	1.2229465	9030.9511
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4824	6.3385719	31518.4319	30.385002	1982-1996 –> 1997-2008	12.8627112	71156.0472
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4824	6.2932572	31451.2102	29.922107	1982-1996 –> 1997-2008	12.7665016	70996.6271
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4824	7.3048692	32889.3639	31.801896	1982-1996 –> 1997-2008	14.8115373	74216.2993
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4824	7.3875765	32997.9868	29.636700	1982-1996 –> 1997-2008	14.9511779	74415.8026
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	4824	7.5000916	33141.8211	28.899363	1982-1996 –> 1997-2008	15.1894006	74755.9001
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4459	6.0310286	28691.0048	24.778598	1997-2008 –> 2009-2019	12.3696005	60209.4367
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4459	5.9692539	28601.1884	24.098032	1997-2008 –> 2009-2019	12.2625112	60052.3986
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4459	7.0467156	30081.0385	25.923585	1997-2008 –> 2009-2019	14.3515848	62970.4024
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4459	7.1134116	30165.0489	25.398300	1997-2008 –> 2009-2019	14.5009881	63163.0357
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	4459	7.2315127	30309.8953	24.429455	1997-2008 –> 2009-2019	14.7316043	63451.7164
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5084	4.7301243	30240.3457	41.005350	1982-1996 –> 1997-2008	9.4013419	68482.4127
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5084	4.3880526	29479.0751	43.823154	1982-1996 –> 1997-2008	8.6484228	66534.2313
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5084	4.5942393	29945.9658	48.673491	1982-1996 –> 1997-2008	9.0172947	67485.0701
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	5084	4.7363470	30253.7134	39.273930	1982-1996 –> 1997-2008	9.3794473	68417.8128
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5084	4.7228399	30226.6748	40.410257	1982-1996 –> 1997-2008	9.3658890	68392.6319
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4614	4.9091889	27788.7162	41.959096	1997-2008 –> 2009-2019	9.6393132	58029.0619
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4614	4.5485519	27086.6215	45.085074	1997-2008 –> 2009-2019	8.9366045	56565.6965
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4614	4.7038052	27396.3397	47.887037	1997-2008 –> 2009-2019	9.2980445	57342.3056
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	4614	4.8959995	27763.8901	40.766362	1997-2008 –> 2009-2019	9.6323465	58017.6035
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4614	4.8929016	27760.0494	41.227023	1997-2008 –> 2009-2019	9.6157415	57986.7242
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4197	3.9975331	23553.9466	21.220619	1982-1996 –> 1997-2008	7.9285007	52815.7974
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4197	4.1713234	23911.1607	17.248494	1982-1996 –> 1997-2008	8.0563088	53049.5587
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4197	3.9090256	23368.0107	19.168907	1982-1996 –> 1997-2008	7.6163424	52017.2691
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4197	4.0055015	23572.6619	31.979471	1982-1996 –> 1997-2008	7.9789008	52949.1587
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4197	3.9282075	23409.0999	19.456795	1982-1996 –> 1997-2008	7.7789454	52456.5973
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3836	4.3185308	22121.5823	25.159708	1997-2008 –> 2009-2019	8.3160640	45675.5289
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3836	4.1788159	21871.2707	25.715301	1997-2008 –> 2009-2019	8.0878415	45239.2815
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3836	4.2292460	21963.3024	33.372085	1997-2008 –> 2009-2019	8.2347475	45535.9643
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3836	4.1844077	21881.5300	23.557925	1997-2008 –> 2009-2019	8.1126152	45290.6300
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	3836	4.2320442	21966.3768	34.676735	1997-2008 –> 2009-2019	8.2384042	45538.8375
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4851	4.3904399	28131.9660	18.713225	1982-1996 –> 1997-2008	8.3449386	63245.1733
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4851	4.1417105	27566.1399	21.820850	1982-1996 –> 1997-2008	7.7895020	61665.0314
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4851	4.1277332	27535.3425	20.917441	1982-1996 –> 1997-2008	7.7607256	61585.1581
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4851	4.0577816	27367.5163	19.648084	1982-1996 –> 1997-2008	7.7044680	61462.6008
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4851	4.0252512	27291.4238	18.015644	1982-1996 –> 1997-2008	7.6447605	61294.5241
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4620	4.8346391	27683.4439	18.928175	1997-2008 –> 2009-2019	9.2250790	55815.4100
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4620	4.6186014	27261.0415	21.294506	1997-2008 –> 2009-2019	8.7603119	54827.1815
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4620	4.6042741	27234.3336	20.417790	1997-2008 –> 2009-2019	8.7320072	54769.6761
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4620	4.5195678	27060.7592	22.587891	1997-2008 –> 2009-2019	8.5773494	54428.2755
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4620	4.4910489	27004.2693	21.096126	1997-2008 –> 2009-2019	8.5163001	54295.6930
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6051	4.2305928	34641.2186	38.987956	1982-1996 –> 1997-2008	7.6898959	73778.5820
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	6051	4.0079275	33986.8895	48.292564	1982-1996 –> 1997-2008	7.2653220	72239.7211
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	6051	4.2520624	34700.4788	43.293651	1982-1996 –> 1997-2008	7.7371725	73945.1595
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	6051	3.8421055	33475.5346	28.263619	1982-1996 –> 1997-2008	7.0506832	71506.2768
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	6051	4.4688453	35302.2621	70.598421	1982-1996 –> 1997-2008	7.8137708	73943.1026
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5368	4.9996749	32523.9515	33.137375	1997-2008 –> 2009-2019	9.2875410	67325.9063
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5368	4.9630411	32446.9967	35.215683	1997-2008 –> 2009-2019	9.1936339	67088.2152
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5368	4.8065903	32103.1149	38.756934	1997-2008 –> 2009-2019	8.8145179	66090.0044
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5368	4.9677680	32455.2170	41.181662	1997-2008 –> 2009-2019	9.2198304	67155.6958
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5368	4.3759429	31095.3701	26.859631	1997-2008 –> 2009-2019	8.2180484	64570.9047
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5356	3.3508041	28166.6235	31.725692	1982-1996 –> 1997-2008	6.2193149	60697.0434
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5356	3.5855384	28891.9148	31.557514	1982-1996 –> 1997-2008	6.5918168	62039.1998
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	5356	3.6026641	28940.9572	31.009468	1982-1996 –> 1997-2008	6.6089873	62086.4381
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5356	3.5425511	28762.7118	32.702786	1982-1996 –> 1997-2008	6.5699892	62002.2289
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5356	3.2822506	27945.1958	32.907034	1982-1996 –> 1997-2008	6.1446823	60447.7179
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4935	3.7984566	27191.3742	30.763268	1997-2008 –> 2009-2019	7.1492606	55357.9977
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4935	4.1106150	27970.8855	32.033024	1997-2008 –> 2009-2019	7.6961534	56862.8003
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	4935	4.1456000	28052.5325	30.395240	1997-2008 –> 2009-2019	7.7482641	56993.4897
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4935	4.0646343	27859.8589	30.502849	1997-2008 –> 2009-2019	7.6071854	56622.5708
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4935	3.6825512	26885.5122	32.539426	1997-2008 –> 2009-2019	6.9648017	54830.7080
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5404	3.0139376	27273.7857	30.484892	1982-1996 –> 1997-2008	5.2553883	57406.4016
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5404	3.0005119	27225.5333	32.159061	1982-1996 –> 1997-2008	5.2675720	57511.8586
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	5404	3.1022166	27583.8070	29.657836	1982-1996 –> 1997-2008	5.3877529	57977.9528
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	5404	3.1540479	27762.8931	29.786246	1982-1996 –> 1997-2008	5.4655826	58310.0770
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5404	3.1465773	27737.2632	29.021158	1982-1996 –> 1997-2008	5.4483392	58227.1230
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4876	3.8360163	26962.4128	26.671827	1997-2008 –> 2009-2019	6.8499539	54236.1985
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4876	3.7213482	26666.4554	10.513159	1997-2008 –> 2009-2019	6.7218601	53891.9887
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	4876	3.9928783	27351.2531	24.983842	1997-2008 –> 2009-2019	7.0950949	54935.0601
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	4876	3.9962227	27359.4179	32.475641	1997-2008 –> 2009-2019	7.1502706	55122.3110
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4876	3.9296820	27197.6711	19.536419	1997-2008 –> 2009-2019	7.0690291	54912.0714
Indo-Pacific	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2094	2.6281235	10001.2537	20.315850	1982-1996 –> 1997-2008	4.4758882	20551.8859
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2094	2.6280726	10003.1726	20.269819	1982-1996 –> 1997-2008	4.4588982	20508.0622
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2094	2.6308738	10007.6341	20.381031	1982-1996 –> 1997-2008	4.4838926	20574.9863
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate	2094	2.6381137	10017.1432	19.942730	1982-1996 –> 1997-2008	4.4989867	20604.4218
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2094	2.5477803	9873.2264	20.283242	1982-1996 –> 1997-2008	4.3766509	20372.5776
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2026	2.9681471	10171.8633	31.686491	1997-2008 –> 2009-2019	5.6042834	20187.8663
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2026	3.0026006	10218.6269	30.980275	1997-2008 –> 2009-2019	5.6306731	20221.7995
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	2026	2.9867207	10195.1402	28.760017	1997-2008 –> 2009-2019	5.6233457	20209.9195
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2026	2.9577599	10155.6582	31.706119	1997-2008 –> 2009-2019	5.6098592	20194.9449
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2026	2.9108359	10092.8590	29.031327	1997-2008 –> 2009-2019	5.4586162	19966.0854
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2613	2.6666131	12553.0814	27.978031	1982-1996 –> 1997-2008	4.8253084	27275.7924
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	2613	2.6730626	12565.7058	28.004716	1982-1996 –> 1997-2008	4.8934547	27477.8411
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2613	2.6631932	12548.3748	27.690692	1982-1996 –> 1997-2008	4.8210526	27270.4824
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + phosphate_star	2613	2.6858774	12588.6997	31.246516	1982-1996 –> 1997-2008	4.8531973	27336.2134
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2613	2.6801210	12579.4874	30.642253	1982-1996 –> 1997-2008	4.8469152	27327.3701
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2485	2.9891703	12506.2540	34.512839	1997-2008 –> 2009-2019	5.6557834	25059.3354
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	2485	2.9841143	12497.8404	33.884360	1997-2008 –> 2009-2019	5.6571769	25063.5462
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2485	2.9784354	12490.3733	34.058594	1997-2008 –> 2009-2019	5.6416286	25038.7481
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2485	2.9350011	12417.3624	38.832321	1997-2008 –> 2009-2019	5.6494671	25065.3939
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2485	2.9786599	12488.7479	33.688880	1997-2008 –> 2009-2019	5.6587810	25068.2352
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2262	2.1747367	9946.0079	8.214049	1982-1996 –> 1997-2008	4.0766303	22250.3913
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2262	2.1336211	9861.6582	8.412054	1982-1996 –> 1997-2008	4.0059512	22074.6391
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2262	2.1809880	9960.9936	8.079286	1982-1996 –> 1997-2008	4.0956826	22307.3706
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	2262	2.1885477	9974.6474	8.264438	1982-1996 –> 1997-2008	4.1009138	22311.7697
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2262	2.1155350	9823.1462	7.887572	1982-1996 –> 1997-2008	3.9723739	21986.5934
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2121	2.3344559	9627.4152	8.114849	1997-2008 –> 2009-2019	4.5069068	19568.6656
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2121	2.3295082	9620.4150	8.254005	1997-2008 –> 2009-2019	4.4750922	19507.3677
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2121	2.4048197	9755.3859	8.396749	1997-2008 –> 2009-2019	4.5384407	19617.0440
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2121	2.3980224	9741.3788	8.922395	1997-2008 –> 2009-2019	4.5895159	19722.1114
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2121	2.3597710	9675.1682	8.699549	1997-2008 –> 2009-2019	4.4753061	19498.3145
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	1614	1.9019794	6667.5990	8.587643	1982-1996 –> 1997-2008	3.5004886	14775.3859
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1614	1.8253304	6536.8182	9.104401	1982-1996 –> 1997-2008	3.4031448	14590.7286
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1614	1.9091530	6679.7511	8.729869	1982-1996 –> 1997-2008	3.5282651	14842.4521
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1614	1.8471680	6575.2076	9.930455	1982-1996 –> 1997-2008	3.4318712	14647.7989
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1614	1.7919389	6477.2202	9.116922	1982-1996 –> 1997-2008	3.4075173	14632.5524
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1480	2.0189887	6291.7443	9.987210	1997-2008 –> 2009-2019	3.8973463	12919.0020
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1480	1.9639299	6211.9027	9.739216	1997-2008 –> 2009-2019	3.7892603	12748.7209
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1480	1.9976364	6262.2735	10.515985	1997-2008 –> 2009-2019	3.8448044	12837.4810
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	1480	2.0305789	6308.6880	10.033303	1997-2008 –> 2009-2019	3.9190479	12953.2757
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1480	1.9240869	6151.2346	9.194710	1997-2008 –> 2009-2019	3.7160258	12628.4548
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	13531	1.3930357	47381.9699	13.340246	1982-1996 –> 1997-2008	2.6526001	103206.7729
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	13531	1.2999037	45511.4122	15.704489	1982-1996 –> 1997-2008	2.4519905	98320.7023
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	13531	1.3138971	45801.1765	12.674226	1982-1996 –> 1997-2008	2.4157006	97100.6627
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	13531	1.3573410	46681.5043	16.484019	1982-1996 –> 1997-2008	2.5801569	101506.5527
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	13531	1.5119803	49599.2934	16.999926	1982-1996 –> 1997-2008	2.8159892	106597.2985
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	12319	1.6225597	46898.7219	9.024654	1997-2008 –> 2009-2019	3.1034885	95938.4580
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	12319	1.5499918	45769.4022	10.853455	1997-2008 –> 2009-2019	2.9430275	93151.3721
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	12319	1.4654909	44390.2118	13.078916	1997-2008 –> 2009-2019	2.7653947	89901.6241
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	12319	1.5412287	45631.7127	12.618266	1997-2008 –> 2009-2019	2.8551258	91432.8892
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	12319	1.5232127	45342.0128	14.186735	1997-2008 –> 2009-2019	2.8805537	92023.5171

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]	1982-1996 –> 1997-2008	2.8933170	1158.583
Atlantic	(-Inf,26]	1997-2008 –> 2009-2019	2.6959997	930.835
Atlantic	(26,26.5]	1982-1996 –> 1997-2008	8.0234076	12661.256
Atlantic	(26,26.5]	1997-2008 –> 2009-2019	7.9507217	10409.808
Atlantic	(26.5,26.75]	1982-1996 –> 1997-2008	6.2256928	14642.041
Atlantic	(26.5,26.75]	1997-2008 –> 2009-2019	6.6615151	12424.450
Atlantic	(26.75,27]	1982-1996 –> 1997-2008	3.6838790	19365.842
Atlantic	(26.75,27]	1997-2008 –> 2009-2019	4.3839167	18445.499
Atlantic	(27,27.25]	1982-1996 –> 1997-2008	3.8414977	16576.204
Atlantic	(27,27.25]	1997-2008 –> 2009-2019	4.2268186	15867.967
Atlantic	(27.25,27.5]	1982-1996 –> 1997-2008	4.4675710	19045.204
Atlantic	(27.25,27.5]	1997-2008 –> 2009-2019	5.1862228	17037.142
Atlantic	(27.5,27.75]	1982-1996 –> 1997-2008	4.9192551	26377.134
Atlantic	(27.5,27.75]	1997-2008 –> 2009-2019	5.6099146	24240.644
Atlantic	(27.75,27.85]	1982-1996 –> 1997-2008	3.5660349	8037.079
Atlantic	(27.75,27.85]	1997-2008 –> 2009-2019	3.7438825	7205.104
Atlantic	(27.85,27.95]	1982-1996 –> 1997-2008	5.8671562	9984.805
Atlantic	(27.85,27.95]	1997-2008 –> 2009-2019	6.3280150	9238.826
Atlantic	(27.95,28.05]	1982-1996 –> 1997-2008	8.8649920	14493.922
Atlantic	(27.95,28.05]	1997-2008 –> 2009-2019	8.5963322	12380.206
Atlantic	(28.05,28.1]	1982-1996 –> 1997-2008	1.9588470	4561.248
Atlantic	(28.05,28.1]	1997-2008 –> 2009-2019	2.1343047	4226.558
Atlantic	(28.1,28.15]	1982-1996 –> 1997-2008	1.4239944	4189.743
Atlantic	(28.1,28.15]	1997-2008 –> 2009-2019	1.6164644	3960.329
Atlantic	(28.15,28.2]	1982-1996 –> 1997-2008	1.0947250	5353.639
Atlantic	(28.15,28.2]	1997-2008 –> 2009-2019	1.3348442	5407.606
Atlantic	(28.2, Inf]	1982-1996 –> 1997-2008	0.7078988	3926.291
Atlantic	(28.2, Inf]	1997-2008 –> 2009-2019	0.8387358	5127.120
Indo-Pacific	(-Inf,26]	1982-1996 –> 1997-2008	14.1162657	73108.135
Indo-Pacific	(-Inf,26]	1997-2008 –> 2009-2019	13.6432578	61969.398
Indo-Pacific	(26,26.5]	1982-1996 –> 1997-2008	9.1624791	67862.432
Indo-Pacific	(26,26.5]	1997-2008 –> 2009-2019	9.4244100	57588.278
Indo-Pacific	(26.5,26.75]	1982-1996 –> 1997-2008	7.8717996	52657.676
Indo-Pacific	(26.5,26.75]	1997-2008 –> 2009-2019	8.1979345	45456.048
Indo-Pacific	(26.75,27]	1982-1996 –> 1997-2008	7.8488789	61850.498
Indo-Pacific	(26.75,27]	1997-2008 –> 2009-2019	8.7622095	54827.247
Indo-Pacific	(27,27.25]	1982-1996 –> 1997-2008	7.5113689	73082.568
Indo-Pacific	(27,27.25]	1997-2008 –> 2009-2019	8.9467143	66446.145
Indo-Pacific	(27.25,27.5]	1982-1996 –> 1997-2008	6.4269581	61454.526
Indo-Pacific	(27.25,27.5]	1997-2008 –> 2009-2019	7.4331331	56133.513
Indo-Pacific	(27.5,27.75]	1982-1996 –> 1997-2008	5.3649270	57886.683
Indo-Pacific	(27.5,27.75]	1997-2008 –> 2009-2019	6.9772417	54619.526
Indo-Pacific	(27.75,27.85]	1982-1996 –> 1997-2008	4.4588633	20522.387
Indo-Pacific	(27.75,27.85]	1997-2008 –> 2009-2019	5.5853555	20156.123
Indo-Pacific	(27.85,27.95]	1982-1996 –> 1997-2008	4.8479856	27337.540
Indo-Pacific	(27.85,27.95]	1997-2008 –> 2009-2019	5.6525674	25059.052
Indo-Pacific	(27.95,28.05]	1982-1996 –> 1997-2008	4.0503104	22186.153
Indo-Pacific	(27.95,28.05]	1997-2008 –> 2009-2019	4.5170523	19582.701
Indo-Pacific	(28.05,28.1]	1982-1996 –> 1997-2008	3.4542574	14697.784
Indo-Pacific	(28.05,28.1]	1997-2008 –> 2009-2019	3.8332969	12817.387
Indo-Pacific	(28.1, Inf]	1982-1996 –> 1997-2008	2.5832875	101346.398
Indo-Pacific	(28.1, Inf]	1997-2008 –> 2009-2019	2.9095180	92489.572

5.4 Target variable coefficients

A data frame to map the target variable is prepared.

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

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

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

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

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.5 Plot selected model residuals

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

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

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

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

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

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

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

5.6 Cant coeffcients

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

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

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

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

5.7 Write files

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

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

6 Model diagnotics

6.1 Selection criterion vs predictors

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

6.1.1 All models

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

Past versions of eMLR_predictor_model_quality_all-1.png

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

rm(max_rmse)

6.3 Predictor counts

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

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

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

	aou	nitrate	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1996 --> 1997-2008
(-Inf,26]	5	1	4	5	3	2	2
(26,26.5]	5	3	2	4	1	4	4
(26.5,26.75]	5	1	4	4	2	5	2
(26.75,27]	5	1	4	4	1	5	3
(27,27.25]	5	2	3	4	3	5	2
(27.25,27.5]	5	4	1	3	3	5	2
(27.5,27.75]	5	1	4	3	4	3	1
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	3	5	2	3	3
(28.05,28.1]	5	0	5	5	2	3	2
(28.1,28.15]	5	1	4	5	3	4	1
(28.15,28.2]	5	5	0	4	2	3	3
(28.2, Inf]	5	5	0	3	4	3	1
total	70.00	28.00	42.00	57.00	37.00	52.00	28.00
Atlantic - 1997-2008 --> 2009-2019
(-Inf,26]	5	0	4	5	3	3	2
(26,26.5]	5	3	2	4	1	4	4
(26.5,26.75]	5	1	4	4	2	5	2
(26.75,27]	5	1	4	4	2	5	2
(27,27.25]	5	2	2	4	4	5	1
(27.25,27.5]	5	5	0	3	2	5	2
(27.5,27.75]	5	1	4	3	5	3	0
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	3	5	2	3	3
(28.05,28.1]	5	1	4	5	3	3	2
(28.1,28.15]	5	1	4	5	3	3	2
(28.15,28.2]	5	5	0	4	2	3	3
(28.2, Inf]	4	5	0	3	5	3	0
total	69.00	29.00	39.00	57.00	41.00	52.00	25.00
Indo-Pacific - 1982-1996 --> 1997-2008
(-Inf,26]	4	1	4	5	2	4	3
(26,26.5]	5	1	4	4	1	5	3
(26.5,26.75]	5	1	4	5	2	4	2
(26.75,27]	5	0	5	5	2	3	2
(27,27.25]	4	2	3	5	1	4	4
(27.25,27.5]	5	2	2	5	3	5	2
(27.5,27.75]	3	2	2	5	5	5	0
(27.75,27.85]	5	1	4	4	1	5	3
(27.85,27.95]	3	5	0	4	0	3	5
(27.95,28.05]	5	1	4	4	1	5	3
(28.05,28.1]	4	1	4	4	3	5	2
(28.1, Inf]	4	2	3	4	2	5	3
total	52.00	19.00	39.00	54.00	23.00	53.00	32.00
Indo-Pacific - 1997-2008 --> 2009-2019
(-Inf,26]	4	1	4	5	2	4	3
(26,26.5]	5	1	4	4	1	5	3
(26.5,26.75]	4	2	3	5	1	5	3
(26.75,27]	5	0	5	5	2	3	2
(27,27.25]	5	1	4	5	1	4	3
(27.25,27.5]	5	2	2	5	3	5	2
(27.5,27.75]	4	2	2	5	4	5	1
(27.75,27.85]	4	2	3	5	3	4	2
(27.85,27.95]	4	4	1	4	0	4	5
(27.95,28.05]	5	2	3	5	3	3	2
(28.05,28.1]	5	1	4	4	1	5	3
(28.1, Inf]	5	2	3	4	3	5	2
total	55.00	20.00	38.00	56.00	24.00	52.00	31.00

6.4 RMSE alternatives

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

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

Past versions of aic_vs_rmse_all_models-1.png

Version	Author	Date
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
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