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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:

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:

The criterion used to select the best models was:

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	110	1.5828856	425.2014	6.118695	1982-1999 –> 2000-2008	3.2725872	1245.6934
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	110	1.0603826	337.0650	3.928445	1982-1999 –> 2000-2008	2.3967310	1059.9588
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	110	1.0603443	339.0571	3.915891	1982-1999 –> 2000-2008	2.3960368	1063.7467
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	110	1.4642866	408.0675	6.241851	1982-1999 –> 2000-2008	3.1265567	1221.7505
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	110	1.4500076	407.9116	5.857137	1982-1999 –> 2000-2008	3.1114961	1223.3990
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	120	1.1639689	388.9858	3.443761	2000-2008 –> 2009-2019	2.2243515	726.0508
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	120	1.1032974	378.1381	3.121374	2000-2008 –> 2009-2019	2.1636418	717.1951
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate_star	120	1.6504991	472.8039	4.220872	2000-2008 –> 2009-2019	3.2269102	897.1036
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	120	1.5135931	452.0220	6.318368	2000-2008 –> 2009-2019	2.9778797	860.0894
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	120	1.4696627	446.9532	5.722394	2000-2008 –> 2009-2019	2.9196703	854.8648
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	726	3.5639121	3919.5858	13.498559	1982-1999 –> 2000-2008	7.0106570	12035.5107
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	726	4.2320872	4167.0923	10.513592	1982-1999 –> 2000-2008	8.3905003	12853.5121
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	726	4.0421862	4100.4316	12.239560	1982-1999 –> 2000-2008	8.1265625	12732.0596
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	726	4.0305485	4098.2451	12.838926	1982-1999 –> 2000-2008	8.1122044	12729.8411
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	726	4.3194413	4198.7578	13.094755	1982-1999 –> 2000-2008	8.5545406	12942.9110
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	887	3.5766351	4792.0224	11.509131	2000-2008 –> 2009-2019	7.1405472	8711.6082
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	887	4.1181347	5040.1171	12.061754	2000-2008 –> 2009-2019	8.3502219	9207.2095
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	887	3.9565691	4969.1162	16.433540	2000-2008 –> 2009-2019	7.9987553	9069.5478
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	887	3.9408963	4964.0751	18.038103	2000-2008 –> 2009-2019	7.9714448	9062.3202
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	887	4.2298592	5089.6042	11.623373	2000-2008 –> 2009-2019	8.5493005	9288.3620
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	965	3.1511176	4965.7227	10.227600	1982-1999 –> 2000-2008	6.2497311	14652.0178
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	965	3.2075368	4999.9727	9.941595	1982-1999 –> 2000-2008	6.3544848	14744.9927
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	965	3.1000501	4936.1886	10.294776	1982-1999 –> 2000-2008	6.1592002	14575.8537
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	965	3.1717239	4980.3026	9.984350	1982-1999 –> 2000-2008	6.3164669	14724.6632
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	965	3.0448187	4901.4932	9.419208	1982-1999 –> 2000-2008	6.0278524	14445.5633
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1088	3.6028024	5888.6155	11.507716	2000-2008 –> 2009-2019	6.7539200	10854.3382
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	1088	3.5167576	5836.0161	11.179635	2000-2008 –> 2009-2019	6.7242944	10835.9888
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1088	3.4970317	5825.7763	11.382695	2000-2008 –> 2009-2019	6.5970818	10761.9649
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1088	3.5173399	5838.3763	9.303961	2000-2008 –> 2009-2019	6.6890638	10818.6790
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1088	3.4808595	5815.6899	10.801616	2000-2008 –> 2009-2019	6.5256783	10717.1831
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1657	2.0639034	7115.6835	14.125744	1982-1999 –> 2000-2008	3.7364407	19268.6843
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1657	1.9677382	6959.5584	13.449850	1982-1999 –> 2000-2008	3.6207272	19040.7271
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1657	2.1735515	7289.2275	15.480311	1982-1999 –> 2000-2008	3.9692177	19890.3232
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	1657	2.1677049	7278.3012	14.596637	1982-1999 –> 2000-2008	3.9552964	19849.0936
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1657	2.0627635	7115.8527	14.751576	1982-1999 –> 2000-2008	3.5762127	18643.1640
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2004	2.4497762	9290.2603	27.463653	2000-2008 –> 2009-2019	4.5136796	16405.9438
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	2004	2.4126150	9228.9963	24.703523	2000-2008 –> 2009-2019	4.5882586	16519.4121
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2004	2.3482362	9122.5930	25.940225	2000-2008 –> 2009-2019	4.3159744	16082.1514
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2004	2.5042136	9380.3485	23.426544	2000-2008 –> 2009-2019	4.6777651	16669.5760
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2004	2.1044039	8683.1870	22.765287	2000-2008 –> 2009-2019	4.1671674	15799.0396
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1403	2.0537007	6014.8608	9.421835	1982-1999 –> 2000-2008	4.2879821	17636.6263
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1403	1.8593301	5733.8684	9.146139	1982-1999 –> 2000-2008	3.5757053	15976.5660
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1403	1.8318571	5694.0982	9.660601	1982-1999 –> 2000-2008	3.4018426	15473.2641
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1403	2.0001436	5940.7140	13.323132	1982-1999 –> 2000-2008	3.6767223	16062.9069
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1403	2.2298791	6245.8059	14.287388	1982-1999 –> 2000-2008	4.3063013	17484.9379
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1770	2.1957025	7821.2597	11.870716	2000-2008 –> 2009-2019	4.2494032	13836.1205
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1770	2.1848856	7801.7771	13.569860	2000-2008 –> 2009-2019	4.0442157	13535.6455
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1770	2.1848757	7803.7610	13.557213	2000-2008 –> 2009-2019	4.0167327	13497.8592
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	1770	2.2804983	7953.3970	14.908620	2000-2008 –> 2009-2019	4.3742676	14020.4770
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1770	2.3928360	8125.6190	19.363213	2000-2008 –> 2009-2019	4.3929796	14066.3330
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1432	2.4907687	6689.5017	12.826044	1982-1999 –> 2000-2008	5.1072729	20405.2580
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1432	2.4077228	6594.3836	12.290135	1982-1999 –> 2000-2008	4.9426914	20129.9170
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1432	2.5668051	6777.6239	20.256556	1982-1999 –> 2000-2008	4.7338531	19410.5281
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1432	2.2302104	6373.0427	11.116059	1982-1999 –> 2000-2008	3.9502899	17674.3375
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1432	2.1206350	6230.7534	14.412780	1982-1999 –> 2000-2008	3.8365337	17520.0406
Atlantic	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	1702	2.9549498	8530.2384	21.650262	2000-2008 –> 2009-2019	5.6584972	15454.5117
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1702	2.8677604	8428.2875	16.040376	2000-2008 –> 2009-2019	5.3585291	15117.7892
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1702	2.7136930	8242.3155	17.246937	2000-2008 –> 2009-2019	5.1214158	14836.6991
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1702	3.0012510	8583.1622	11.700791	2000-2008 –> 2009-2019	5.2314614	14956.2049
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1702	2.7021751	8227.8369	17.252150	2000-2008 –> 2009-2019	4.8228101	14458.5903
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	1979	2.7318315	9603.8390	13.412723	1982-1999 –> 2000-2008	5.2068813	26978.4255
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1979	2.7065774	9569.0795	13.943817	1982-1999 –> 2000-2008	4.9724453	26286.2217
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	1979	2.4346321	9149.9698	13.506431	1982-1999 –> 2000-2008	4.8018169	26193.7891
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1979	2.3627628	9033.3723	14.367622	1982-1999 –> 2000-2008	4.4633308	25186.8128
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1979	2.9949305	9971.7722	15.808719	1982-1999 –> 2000-2008	5.3810915	27077.2186
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate	2340	3.1460588	12016.6166	16.554630	2000-2008 –> 2009-2019	5.9266722	21692.5094
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2340	3.1208758	11981.0043	15.244357	2000-2008 –> 2009-2019	5.8915958	21644.7894
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2340	3.2193457	12124.3861	13.894909	2000-2008 –> 2009-2019	5.9259231	21693.4656
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	2340	2.7289817	11351.0180	14.950042	2000-2008 –> 2009-2019	5.1636138	20500.9878
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2340	2.7164500	11331.4775	14.798604	2000-2008 –> 2009-2019	5.0792128	20364.8498
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	688	1.8822594	2834.7420	13.350662	1982-1999 –> 2000-2008	3.8869076	8428.7769
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	688	1.8187205	2789.4907	14.229361	1982-1999 –> 2000-2008	3.7703681	8314.7877
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	688	1.8530923	2813.2529	12.537840	1982-1999 –> 2000-2008	3.5363892	7946.0421
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	688	1.6885881	2685.3358	12.338165	1982-1999 –> 2000-2008	3.4972653	8007.7864
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	688	1.4850215	2510.5701	12.906742	1982-1999 –> 2000-2008	3.0820664	7506.4970
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	861	2.0091785	3656.8962	12.547977	2000-2008 –> 2009-2019	3.8914378	6491.6382
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	861	1.9932243	3645.1678	12.962072	2000-2008 –> 2009-2019	3.8119448	6434.6585
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	861	2.3474123	3924.8181	11.404366	2000-2008 –> 2009-2019	4.2005046	6738.0710
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	861	1.8364097	3502.0651	11.597744	2000-2008 –> 2009-2019	3.5249977	6187.4009
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	861	1.7164355	3387.7222	11.994150	2000-2008 –> 2009-2019	3.2014570	5898.2923
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	659	3.2692448	3443.4097	31.189168	1982-1999 –> 2000-2008	6.1468429	10070.9998
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	659	3.2412466	3432.0737	24.556990	1982-1999 –> 2000-2008	5.9712539	9918.9784
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	659	3.2312069	3429.9848	22.832095	1982-1999 –> 2000-2008	5.9610850	9918.7632
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	659	2.8864969	3279.2985	21.562532	1982-1999 –> 2000-2008	5.8033025	9943.0490
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	659	2.8805779	3278.5930	21.426742	1982-1999 –> 2000-2008	5.7448332	9895.7649
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	893	3.6388755	4853.1553	24.564776	2000-2008 –> 2009-2019	6.9081203	8296.5650
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	893	3.2764028	4665.7528	31.808520	2000-2008 –> 2009-2019	6.5176494	8097.8264
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	893	3.2010827	4626.2158	30.563544	2000-2008 –> 2009-2019	6.4322896	8056.2006
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	893	3.5763422	4822.1964	23.280568	2000-2008 –> 2009-2019	6.4628391	8101.4949
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	893	3.5520614	4812.0294	24.376118	2000-2008 –> 2009-2019	6.4326393	8090.6225
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	818	4.7047102	4866.8344	26.101591	1982-1999 –> 2000-2008	9.5365696	14915.2919
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	818	4.6216768	4839.7028	25.161279	1982-1999 –> 2000-2008	9.3669537	14829.5509
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	818	4.1997782	4681.0953	22.430457	1982-1999 –> 2000-2008	8.2305079	14121.8891
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	818	4.0418371	4620.3835	23.852350	1982-1999 –> 2000-2008	7.5736465	13620.2536
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	818	4.5670350	4820.2453	21.600448	1982-1999 –> 2000-2008	9.4214040	14886.2821
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1052	4.3783749	6104.3764	24.778686	2000-2008 –> 2009-2019	9.0830851	10971.2108
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1052	4.3189470	6077.6231	24.715518	2000-2008 –> 2009-2019	8.9406238	10917.3260
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1052	3.8344411	5825.2725	22.665961	2000-2008 –> 2009-2019	8.0342193	10506.3678
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1052	3.4529907	5606.8092	27.139851	2000-2008 –> 2009-2019	7.4948278	10227.1927
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1052	4.4232551	6127.8335	23.229057	2000-2008 –> 2009-2019	8.9902901	10948.0788
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	565	1.1868409	1808.9639	9.898592	1982-1999 –> 2000-2008	2.1399091	4771.0756
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	565	1.0497520	1670.2665	6.601232	1982-1999 –> 2000-2008	1.9426413	4492.0165
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	565	1.0102726	1628.9493	5.552406	1982-1999 –> 2000-2008	1.9026282	4451.4127
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	565	1.1387134	1762.1865	10.155131	1982-1999 –> 2000-2008	2.0795224	4696.4376
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	565	1.0871626	1711.8360	10.964604	1982-1999 –> 2000-2008	1.9264395	4402.3298
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	673	1.1480158	2109.6865	8.049134	2000-2008 –> 2009-2019	2.2560949	3843.0566
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	673	1.0731011	2016.8552	9.691677	2000-2008 –> 2009-2019	2.1228531	3687.1217
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	673	1.0390706	1975.4790	8.643193	2000-2008 –> 2009-2019	2.0493432	3604.4283
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	673	1.0632974	2004.5018	13.201907	2000-2008 –> 2009-2019	2.2020109	3766.6883
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	673	1.0029755	1927.8904	13.995196	2000-2008 –> 2009-2019	2.0901381	3639.7263
Atlantic	(28.1,28.15]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	663	0.8738857	1714.7601	8.841534	1982-1999 –> 2000-2008	1.5587943	4421.5741
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	663	0.8421206	1667.6632	5.498270	1982-1999 –> 2000-2008	1.5504168	4463.4412
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	663	0.7666921	1541.2340	5.064981	1982-1999 –> 2000-2008	1.4385674	4198.2872
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	663	0.7487168	1511.7754	4.939418	1982-1999 –> 2000-2008	1.3781696	4001.9040
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	663	0.7991257	1598.1742	8.836000	1982-1999 –> 2000-2008	1.3879154	3915.3379
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	770	0.8961317	2030.2768	7.973080	2000-2008 –> 2009-2019	1.7382523	3697.9400
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	770	0.8166830	1885.3088	7.028213	2000-2008 –> 2009-2019	1.5833751	3426.5429
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	770	0.8154600	1885.0009	7.017951	2000-2008 –> 2009-2019	1.5641768	3396.7763
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	770	0.8766659	1994.4562	11.848627	2000-2008 –> 2009-2019	1.7498948	3708.2194
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	770	0.7933963	1842.7593	12.250467	2000-2008 –> 2009-2019	1.5925220	3440.9335
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1061	0.5794269	1864.9786	1.969688	1982-1999 –> 2000-2008	1.1121633	5387.3849
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1061	0.5341524	1694.3364	1.999332	1982-1999 –> 2000-2008	1.0518513	5091.3826
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1061	0.5822300	1875.2196	2.120487	1982-1999 –> 2000-2008	1.1460192	5649.6210
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1061	0.5540176	1769.8217	2.133061	1982-1999 –> 2000-2008	1.1046685	5439.3422
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1061	0.5427548	1728.2384	2.247413	1982-1999 –> 2000-2008	1.0928040	5394.8958
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1298	0.7148302	2824.0606	5.571969	2000-2008 –> 2009-2019	1.2942571	4689.0393
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1298	0.7054925	2791.9262	6.356481	2000-2008 –> 2009-2019	1.2396450	4486.2627
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1298	0.8189368	3177.0178	9.752451	2000-2008 –> 2009-2019	1.4011668	5052.2374
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1298	0.8075260	3140.5916	10.459046	2000-2008 –> 2009-2019	1.3615436	4910.4133
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1298	0.8075158	3142.5587	10.484177	2000-2008 –> 2009-2019	1.3502706	4870.7971
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	1894	0.3478881	1385.2869	1.901627	1982-1999 –> 2000-2008	0.6541565	3144.2453
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1894	0.3436789	1341.1751	1.880270	1982-1999 –> 2000-2008	0.6456295	2996.7524
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	1894	0.3477023	1385.2635	1.900515	1982-1999 –> 2000-2008	0.6524897	3110.2447
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1894	0.3356062	1253.1367	1.842246	1982-1999 –> 2000-2008	0.6346935	2839.9984
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1894	0.5035510	2790.1052	2.925171	1982-1999 –> 2000-2008	0.9625571	7556.0165
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	2356	0.4048932	2435.7681	2.383068	2000-2008 –> 2009-2019	0.7527813	3821.0550
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2356	0.3912592	2276.3681	2.329236	2000-2008 –> 2009-2019	0.7349381	3617.5433
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	2356	0.4002060	2382.9022	2.376657	2000-2008 –> 2009-2019	0.7479083	3768.1657
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2356	0.3839474	2189.4776	2.545602	2000-2008 –> 2009-2019	0.7195536	3442.6143
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2356	0.6695335	4809.7061	10.072546	2000-2008 –> 2009-2019	1.1730845	7599.8113
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3645	6.2800447	23750.5409	30.230794	1982-1999 –> 2000-2008	12.8095859	71168.3703
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3645	6.2366403	23701.9814	29.760266	1982-1999 –> 2000-2008	12.7154916	71009.6939
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3645	7.2084570	24757.6702	31.572854	1982-1999 –> 2000-2008	14.7368140	74225.2048
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3645	7.2998380	24849.5041	29.330385	1982-1999 –> 2000-2008	14.8840176	74423.3171
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	3645	7.4017617	24948.5864	28.658407	1982-1999 –> 2000-2008	15.1160648	74765.1296
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4459	6.0310286	28691.0048	24.778598	2000-2008 –> 2009-2019	12.3110733	52441.5457
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4459	5.9692539	28601.1884	24.098032	2000-2008 –> 2009-2019	12.2058942	52303.1697
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4459	7.0467156	30081.0385	25.923585	2000-2008 –> 2009-2019	14.2551726	54838.7088
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4459	7.1134116	30165.0489	25.398300	2000-2008 –> 2009-2019	14.4132496	55014.5531
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	4459	7.2315127	30309.8953	24.429455	2000-2008 –> 2009-2019	14.6332744	55258.4817
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3829	4.8018565	22893.6533	41.112188	1982-1999 –> 2000-2008	9.4490406	68486.6582
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3829	4.4591298	22328.5862	44.055448	1982-1999 –> 2000-2008	8.7055025	66532.4029
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3829	4.6772167	22694.2524	48.793195	1982-1999 –> 2000-2008	9.0888586	67486.9851
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	3829	4.8139267	22912.8787	39.342352	1982-1999 –> 2000-2008	9.4336871	68414.5945
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3829	4.7961752	22886.5875	40.610595	1982-1999 –> 2000-2008	9.4158443	68389.9984
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4614	4.9091889	27788.7162	41.959096	2000-2008 –> 2009-2019	9.7110454	50682.3695
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4614	4.5485519	27086.6215	45.085074	2000-2008 –> 2009-2019	9.0076817	49415.2077
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4614	4.7038052	27396.3397	47.887037	2000-2008 –> 2009-2019	9.3810219	50090.5922
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	4614	4.8959995	27763.8901	40.766362	2000-2008 –> 2009-2019	9.7099261	50676.7688
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4614	4.8929016	27760.0494	41.227023	2000-2008 –> 2009-2019	9.6890768	50646.6369
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3155	3.9625071	17653.5955	20.911911	1982-1999 –> 2000-2008	7.9115745	52783.0441
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3155	4.1522917	17948.7992	16.771288	1982-1999 –> 2000-2008	8.0864731	53030.7531
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3155	3.8616436	17492.8983	18.914735	1982-1999 –> 2000-2008	7.6190382	51998.6450
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3155	3.9611210	17653.3879	32.520264	1982-1999 –> 2000-2008	7.9520007	52917.2898
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3155	3.8815654	17525.3672	19.148818	1982-1999 –> 2000-2008	7.7587575	52425.8166
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3836	4.3185308	22121.5823	25.159708	2000-2008 –> 2009-2019	8.2810379	39775.1779
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3836	4.1788159	21871.2707	25.715301	2000-2008 –> 2009-2019	8.0404595	39364.1690
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3836	4.2292460	21963.3024	33.372085	2000-2008 –> 2009-2019	8.1903669	39616.6903
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3836	4.1844077	21881.5300	23.557925	2000-2008 –> 2009-2019	8.0659731	39406.8973
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	3836	4.2320442	21966.3768	34.676735	2000-2008 –> 2009-2019	8.1933235	39618.0169
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3602	4.4276782	20952.6872	18.675688	1982-1999 –> 2000-2008	8.4246624	63205.7447
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3602	4.1974239	20567.9622	21.823544	1982-1999 –> 2000-2008	7.8852310	61608.4061
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3602	4.1830712	20545.2866	20.925760	1982-1999 –> 2000-2008	7.8569689	61530.8136
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3602	4.0982507	20395.7091	20.585046	1982-1999 –> 2000-2008	7.7784464	61405.0342
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3602	4.0663351	20341.3875	19.148134	1982-1999 –> 2000-2008	7.7187988	61238.7836
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4620	4.8346391	27683.4439	18.928175	2000-2008 –> 2009-2019	9.2623173	48636.1311
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4620	4.6186014	27261.0415	21.294506	2000-2008 –> 2009-2019	8.8160253	47829.0037
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4620	4.6042741	27234.3336	20.417790	2000-2008 –> 2009-2019	8.7873453	47779.6201
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4620	4.5195678	27060.7592	22.587891	2000-2008 –> 2009-2019	8.6178185	47456.4683
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4620	4.4910489	27004.2693	21.096126	2000-2008 –> 2009-2019	8.5573840	47345.6567
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4568	4.2292066	26151.6661	40.359235	1982-1999 –> 2000-2008	7.7949415	73714.1824
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4568	4.0055429	25655.2588	49.799294	1982-1999 –> 2000-2008	7.3721959	72202.3843
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4568	4.2126690	26113.8712	43.196336	1982-1999 –> 2000-2008	7.8207376	73882.9839
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4568	3.8257666	25235.7315	28.555206	1982-1999 –> 2000-2008	7.1285974	71444.5911
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	4568	4.4625769	26640.3786	72.276444	1982-1999 –> 2000-2008	7.9568018	73842.8445
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5368	4.9996749	32523.9515	33.137375	2000-2008 –> 2009-2019	9.2907167	58806.2277
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5368	4.9630411	32446.9967	35.215683	2000-2008 –> 2009-2019	9.1922477	58598.6628
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5368	4.8065903	32103.1149	38.756934	2000-2008 –> 2009-2019	8.8121332	57758.3737
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5368	4.9677680	32455.2170	41.181662	2000-2008 –> 2009-2019	9.1804370	58569.0882
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5368	4.3759429	31095.3701	26.859631	2000-2008 –> 2009-2019	8.2017095	56331.1016
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4039	3.3644463	21276.9271	31.943258	1982-1999 –> 2000-2008	6.2858318	60608.8167
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4039	3.6148276	21856.7722	31.787265	1982-1999 –> 2000-2008	6.6853031	61974.3012
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	4039	3.6290799	21886.5590	31.201192	1982-1999 –> 2000-2008	6.7002103	62005.4540
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4039	3.5505971	21711.9469	32.714186	1982-1999 –> 2000-2008	6.6340860	61896.2304
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4039	3.2730327	21054.4073	32.962584	1982-1999 –> 2000-2008	6.1973260	60401.9994
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4935	3.7984566	27191.3742	30.763268	2000-2008 –> 2009-2019	7.1629028	48468.3013
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4935	4.1106150	27970.8855	32.033024	2000-2008 –> 2009-2019	7.7254426	49827.6577
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	4935	4.1456000	28052.5325	30.395240	2000-2008 –> 2009-2019	7.7746799	49939.0916
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4935	4.0646343	27859.8589	30.502849	2000-2008 –> 2009-2019	7.6152314	49571.8058
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4935	3.6825512	26885.5122	32.539426	2000-2008 –> 2009-2019	6.9555839	47939.9195
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4064	3.0861626	20706.8068	22.095058	1982-1999 –> 2000-2008	5.4001237	57321.3554
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4064	3.0443640	20595.9700	9.327871	1982-1999 –> 2000-2008	5.3879214	57416.5342
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	4064	3.1804065	20949.3017	20.678327	1982-1999 –> 2000-2008	5.5419993	57892.1371
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	4064	3.2498349	21124.8272	27.387013	1982-1999 –> 2000-2008	5.6349372	58228.2340
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	4064	3.2368427	21092.2680	23.477959	1982-1999 –> 2000-2008	5.6140649	58142.0306
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4876	3.8360163	26962.4128	26.671827	2000-2008 –> 2009-2019	6.9221789	47669.2196
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4876	3.7213482	26666.4554	10.513159	2000-2008 –> 2009-2019	6.7657122	47262.4254
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	4876	3.9928783	27351.2531	24.983842	2000-2008 –> 2009-2019	7.1732848	48300.5548
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	4876	3.9962227	27359.4179	32.475641	2000-2008 –> 2009-2019	7.2460576	48484.2451
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4876	3.9296820	27197.6711	19.536419	2000-2008 –> 2009-2019	7.1045490	48134.8034
Indo-Pacific	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1555	2.6839109	7495.3242	18.741605	1982-1999 –> 2000-2008	4.6157998	20516.2332
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1555	2.6836540	7497.0264	18.642565	1982-1999 –> 2000-2008	4.6053778	20486.8995
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1555	2.6866482	7500.4944	18.596488	1982-1999 –> 2000-2008	4.6230658	20538.0656
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate	1555	2.6925693	7505.3410	18.400293	1982-1999 –> 2000-2008	4.6378569	20569.5303
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1555	2.5956168	7393.2920	18.533639	1982-1999 –> 2000-2008	4.5031991	20336.9140
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2026	2.9681471	10171.8633	31.686491	2000-2008 –> 2009-2019	5.6568984	17674.7912
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2026	3.0026006	10218.6269	30.980275	2000-2008 –> 2009-2019	5.6862545	17715.6533
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	2026	2.9867207	10195.1402	28.760017	2000-2008 –> 2009-2019	5.6813878	17702.9033
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2026	2.9577599	10155.6582	31.706119	2000-2008 –> 2009-2019	5.6758613	17690.3506
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2026	2.9108359	10092.8590	29.031327	2000-2008 –> 2009-2019	5.5064527	17486.1510
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1964	2.8296725	9671.3428	24.941384	1982-1999 –> 2000-2008	4.9510654	27094.8546
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1964	2.8253047	9667.2750	24.624299	1982-1999 –> 2000-2008	4.9459782	27090.0667
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1964	2.9226142	9800.2861	31.450314	1982-1999 –> 2000-2008	5.0639019	27300.6604
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + phosphate_star	1964	2.8842446	9744.3757	30.089390	1982-1999 –> 2000-2008	5.0067268	27170.0047
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	1964	2.8746435	9733.2784	29.310870	1982-1999 –> 2000-2008	4.9965208	27158.6210
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate	2485	2.9957879	12515.2447	34.344816	2000-2008 –> 2009-2019	5.8325346	22194.3953
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2485	2.9891703	12506.2540	34.512839	2000-2008 –> 2009-2019	5.8188428	22177.5968
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	2485	2.9841143	12497.8404	33.884360	2000-2008 –> 2009-2019	5.8176753	22174.5774
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2485	2.9784354	12490.3733	34.058594	2000-2008 –> 2009-2019	5.8037401	22157.6483
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2485	2.9350011	12417.3624	38.832321	2000-2008 –> 2009-2019	5.8576153	22217.6485
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1700	2.2099405	7532.4740	8.300638	1982-1999 –> 2000-2008	4.1321042	22229.4297
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1700	2.1706324	7473.4541	8.502508	1982-1999 –> 2000-2008	4.0613511	22055.5300
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1700	2.2132827	7539.6122	8.135234	1982-1999 –> 2000-2008	4.1482806	22285.7233
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	1700	2.2240383	7554.0946	8.348214	1982-1999 –> 2000-2008	4.1569272	22290.4785
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1700	2.1509590	7442.4978	8.001836	1982-1999 –> 2000-2008	4.0266185	21967.9095
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2121	2.3344559	9627.4152	8.114849	2000-2008 –> 2009-2019	4.5412987	17155.1199
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2121	2.3295082	9620.4150	8.254005	2000-2008 –> 2009-2019	4.5107108	17110.3857
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2121	2.4048197	9755.3859	8.396749	2000-2008 –> 2009-2019	4.5754520	17228.8399
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2121	2.3980224	9741.3788	8.922395	2000-2008 –> 2009-2019	4.6245468	17299.2719
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2121	2.3597710	9675.1682	8.699549	2000-2008 –> 2009-2019	4.5107300	17117.6661
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	1204	1.9361704	5019.7985	8.586962	1982-1999 –> 2000-2008	3.5567398	14745.7644
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1204	1.8505923	4912.9419	9.143550	1982-1999 –> 2000-2008	3.4470375	14564.2970
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1204	1.9408263	5025.5820	8.727570	1982-1999 –> 2000-2008	3.5819108	14815.8051
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1204	1.8672540	4934.5251	9.942146	1982-1999 –> 2000-2008	3.4767239	14627.3853
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1204	1.8153765	4866.6773	8.948253	1982-1999 –> 2000-2008	3.4419856	14613.6447
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1480	2.0189887	6291.7443	9.987210	2000-2008 –> 2009-2019	3.9129613	11258.4815
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1480	1.9639299	6211.9027	9.739216	2000-2008 –> 2009-2019	3.8145222	11124.8446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1480	1.9976364	6262.2735	10.515985	2000-2008 –> 2009-2019	3.8648904	11196.7986
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	1480	2.0305789	6308.6880	10.033303	2000-2008 –> 2009-2019	3.9341136	11287.5517
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1480	1.9240869	6151.2346	9.194710	2000-2008 –> 2009-2019	3.7394634	11017.9118
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	10112	1.3942708	35430.4957	13.436590	1982-1999 –> 2000-2008	2.6710714	103088.7417
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	10112	1.3022101	34051.0208	15.782178	1982-1999 –> 2000-2008	2.4733465	98198.0752
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	10112	1.3244424	34393.3857	12.768469	1982-1999 –> 2000-2008	2.4502983	96936.7828
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	10112	1.3593151	34918.9958	16.549331	1982-1999 –> 2000-2008	2.5993386	101390.5784
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	10112	1.5189133	37162.1461	17.072914	1982-1999 –> 2000-2008	2.8481821	106458.2405
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	12319	1.6225597	46898.7219	9.024654	2000-2008 –> 2009-2019	3.1046139	83566.0449
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	12319	1.5499918	45769.4022	10.853455	2000-2008 –> 2009-2019	2.9442626	81199.8979
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	12319	1.4654909	44390.2118	13.078916	2000-2008 –> 2009-2019	2.7677010	78441.2326
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	12319	1.5412287	45631.7127	12.618266	2000-2008 –> 2009-2019	2.8656711	80025.0985
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	12319	1.5232127	45342.0128	14.186735	2000-2008 –> 2009-2019	2.8825278	80261.0087

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 –> 2000-2008	2.8606816	1162.9097
Atlantic	(-Inf,26]	2000-2008 –> 2009-2019	2.7024907	811.0608
Atlantic	(26,26.5]	1982-1999 –> 2000-2008	8.0388930	12658.7669
Atlantic	(26,26.5]	2000-2008 –> 2009-2019	8.0020539	9067.8095
Atlantic	(26.5,26.75]	1982-1999 –> 2000-2008	6.2215471	14628.6182
Atlantic	(26.5,26.75]	2000-2008 –> 2009-2019	6.6580076	10797.6308
Atlantic	(26.75,27]	1982-1999 –> 2000-2008	3.7715789	19338.3984
Atlantic	(26.75,27]	2000-2008 –> 2009-2019	4.4525690	16295.2246
Atlantic	(27,27.25]	1982-1999 –> 2000-2008	3.8497107	16526.8602
Atlantic	(27,27.25]	2000-2008 –> 2009-2019	4.2155198	13791.2870
Atlantic	(27.25,27.5]	1982-1999 –> 2000-2008	4.5141282	19028.0162
Atlantic	(27.25,27.5]	2000-2008 –> 2009-2019	5.2385427	14964.7590
Atlantic	(27.5,27.75]	1982-1999 –> 2000-2008	4.9651132	26344.4935
Atlantic	(27.5,27.75]	2000-2008 –> 2009-2019	5.5974036	21179.3204
Atlantic	(27.75,27.85]	1982-1999 –> 2000-2008	3.5545993	8040.7780
Atlantic	(27.75,27.85]	2000-2008 –> 2009-2019	3.7260684	6350.0122
Atlantic	(27.85,27.95]	1982-1999 –> 2000-2008	5.9254635	9949.5110
Atlantic	(27.85,27.95]	2000-2008 –> 2009-2019	6.5507075	8128.5419
Atlantic	(27.95,28.05]	1982-1999 –> 2000-2008	8.8258163	14474.6535
Atlantic	(27.95,28.05]	2000-2008 –> 2009-2019	8.5086092	10714.0352
Atlantic	(28.05,28.1]	1982-1999 –> 2000-2008	1.9982281	4562.6544
Atlantic	(28.05,28.1]	2000-2008 –> 2009-2019	2.1440880	3708.2042
Atlantic	(28.1,28.15]	1982-1999 –> 2000-2008	1.4627727	4200.1089
Atlantic	(28.1,28.15]	2000-2008 –> 2009-2019	1.6456442	3534.0824
Atlantic	(28.15,28.2]	1982-1999 –> 2000-2008	1.1015012	5392.5253
Atlantic	(28.15,28.2]	2000-2008 –> 2009-2019	1.3293766	4801.7499
Atlantic	(28.2, Inf]	1982-1999 –> 2000-2008	0.7099053	3929.4515
Atlantic	(28.2, Inf]	2000-2008 –> 2009-2019	0.8256531	4449.8379
Indo-Pacific	(-Inf,26]	1982-1999 –> 2000-2008	14.0523948	73118.3431
Indo-Pacific	(-Inf,26]	2000-2008 –> 2009-2019	13.5637328	53971.2918
Indo-Pacific	(26,26.5]	1982-1999 –> 2000-2008	9.2185866	67862.1278
Indo-Pacific	(26,26.5]	2000-2008 –> 2009-2019	9.4997504	50302.3150
Indo-Pacific	(26.5,26.75]	1982-1999 –> 2000-2008	7.8655688	52631.1097
Indo-Pacific	(26.5,26.75]	2000-2008 –> 2009-2019	8.1542322	39556.1903
Indo-Pacific	(26.75,27]	1982-1999 –> 2000-2008	7.9328215	61797.7564
Indo-Pacific	(26.75,27]	2000-2008 –> 2009-2019	8.8081781	47809.3760
Indo-Pacific	(27,27.25]	1982-1999 –> 2000-2008	7.6146548	73017.3972
Indo-Pacific	(27,27.25]	2000-2008 –> 2009-2019	8.9354488	58012.6908
Indo-Pacific	(27.25,27.5]	1982-1999 –> 2000-2008	6.5005514	61377.3603
Indo-Pacific	(27.25,27.5]	2000-2008 –> 2009-2019	7.4467681	49149.3552
Indo-Pacific	(27.5,27.75]	1982-1999 –> 2000-2008	5.5158093	57800.0583
Indo-Pacific	(27.5,27.75]	2000-2008 –> 2009-2019	7.0423565	47970.2497
Indo-Pacific	(27.75,27.85]	1982-1999 –> 2000-2008	4.5970599	20489.5285
Indo-Pacific	(27.75,27.85]	2000-2008 –> 2009-2019	5.6413710	17653.9699
Indo-Pacific	(27.85,27.95]	1982-1999 –> 2000-2008	4.9928386	27162.8415
Indo-Pacific	(27.85,27.95]	2000-2008 –> 2009-2019	5.8260816	22184.3733
Indo-Pacific	(27.95,28.05]	1982-1999 –> 2000-2008	4.1050563	22165.8142
Indo-Pacific	(27.95,28.05]	2000-2008 –> 2009-2019	4.5525476	17182.2567
Indo-Pacific	(28.05,28.1]	1982-1999 –> 2000-2008	3.5008795	14673.3793
Indo-Pacific	(28.05,28.1]	2000-2008 –> 2009-2019	3.8531902	11177.1176
Indo-Pacific	(28.1, Inf]	1982-1999 –> 2000-2008	2.6084474	101214.4837
Indo-Pacific	(28.1, Inf]	2000-2008 –> 2009-2019	2.9129553	80698.6565

5.4 Target variable coefficients

A data frame to map the target variable is prepared.

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

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

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

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

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.5 Plot selected model residuals

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

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

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

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

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

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

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

5.6 Cant coeffcients

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

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

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

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

5.7 Write files

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

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

6 Model diagnotics

6.1 Selection criterion vs predictors

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

6.1.1 All models

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

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

6.1.2 Best models

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

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

6.2 RMSE correlation between eras

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

6.2.1 All models

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

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

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

rm(max_rmse)

6.2.2 Best models

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

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

Version	Author	Date
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 - 1982-1999 --> 2000-2008
(-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 - 2000-2008 --> 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	2	3	3	5	4	0
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	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]	5	5	0	3	4	3	1
total	70.00	30.00	38.00	57.00	40.00	53.00	26.00
Indo-Pacific - 1982-1999 --> 2000-2008
(-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	4	1	5	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	18.00	40.00	55.00	23.00	53.00	32.00
Indo-Pacific - 2000-2008 --> 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]	5	4	1	3	0	3	5
(27.95,28.05]	5	2	3	5	3	3	2
(28.05,28.1]	5	1	4	4	1	5	3
(28.1, Inf]	5	2	3	4	3	5	2
total	56.00	20.00	38.00	55.00	24.00	51.00	31.00

6.4 RMSE alternatives

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

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

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

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

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

sessionInfo()

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

Matrix products: default
BLAS:   /usr/local/R-4.0.3/lib64/R/lib/libRblas.so
LAPACK: /usr/local/R-4.0.3/lib64/R/lib/libRlapack.so

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

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

other attached packages:
 [1] gt_0.2.2         corrr_0.4.3      broom_0.7.5      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.3   
[21] tidyverse_1.3.0  workflowr_1.6.2 

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

eMLR - model fitting

Jens Daniel Müller and Donghe Zhu

03 March, 2021