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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

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 ~ sal + aou + nitrate + phosphate_star	124	3.2615075	657.0798	6.744848	1982-2000 –> 2001-2010	8.4129747	2026.929
Atlantic	(-Inf,26]	cstar ~ sal + aou + phosphate + phosphate_star	124	3.1227341	646.2966	7.531486	1982-2000 –> 2001-2010	8.3054226	2018.829
Atlantic	(-Inf,26]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	124	3.1213666	648.1879	7.456981	1982-2000 –> 2001-2010	8.2678686	2019.610
Atlantic	(-Inf,26]	cstar ~ sal + nitrate + silicate	124	3.2577132	654.7911	6.550723	1982-2000 –> 2001-2010	8.4528089	2026.385
Atlantic	(-Inf,26]	cstar ~ sal + nitrate + silicate + phosphate_star	124	3.2563367	656.6863	6.548670	1982-2000 –> 2001-2010	8.4012564	2025.971
Atlantic	(-Inf,26]	cstar ~ sal + aou + nitrate + phosphate_star	92	3.3239644	494.0978	9.221507	2001-2010 –> 2011-2019	6.5854720	1151.178
Atlantic	(-Inf,26]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	92	3.2734428	493.2797	7.972642	2001-2010 –> 2011-2019	6.5294545	1151.941
Atlantic	(-Inf,26]	cstar ~ sal + aou + phosphate + phosphate_star	92	3.1116309	481.9517	8.044232	2001-2010 –> 2011-2019	6.2343651	1128.248
Atlantic	(-Inf,26]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	92	3.1114626	483.9418	8.026167	2001-2010 –> 2011-2019	6.2328291	1132.130
Atlantic	(-Inf,26]	cstar ~ sal + aou + silicate + phosphate_star	92	3.2941035	492.4374	8.650620	2001-2010 –> 2011-2019	6.5797101	1151.343
Atlantic	(26,26.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	822	4.5565124	4839.9555	18.021194	1982-2000 –> 2001-2010	10.2635651	15005.935
Atlantic	(26,26.5]	cstar ~ temp + aou + nitrate + phosphate_star	822	5.1516800	5039.7817	14.408152	1982-2000 –> 2001-2010	11.3476331	15467.767
Atlantic	(26,26.5]	cstar ~ temp + aou + nitrate + silicate	822	5.0444837	5005.2124	15.701845	1982-2000 –> 2001-2010	11.2316144	15428.621
Atlantic	(26,26.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	822	5.0437134	5006.9614	15.874667	1982-2000 –> 2001-2010	11.2171342	15425.245
Atlantic	(26,26.5]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	822	5.1943783	5055.3514	17.528160	1982-2000 –> 2001-2010	11.3894855	15484.899
Atlantic	(26,26.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	710	4.4069435	4135.0103	14.276064	2001-2010 –> 2011-2019	8.9634560	8974.966
Atlantic	(26,26.5]	cstar ~ temp + aou + nitrate + phosphate_star	710	4.8712630	4275.2543	14.717480	2001-2010 –> 2011-2019	10.0229430	9315.036
Atlantic	(26,26.5]	cstar ~ temp + aou + nitrate + silicate	710	4.7601060	4242.4760	13.435422	2001-2010 –> 2011-2019	9.8045897	9247.688
Atlantic	(26,26.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	710	4.7524309	4242.1846	13.675144	2001-2010 –> 2011-2019	9.7961443	9249.146
Atlantic	(26,26.5]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	710	4.9734585	4306.7367	15.099740	2001-2010 –> 2011-2019	10.1678368	9362.088
Atlantic	(26.5,26.75]	cstar ~ aou + silicate + phosphate + phosphate_star	1090	4.0963788	6179.3113	14.996817	1982-2000 –> 2001-2010	8.9294369	18121.072
Atlantic	(26.5,26.75]	cstar ~ sal + aou + silicate + phosphate	1090	4.0664046	6163.3011	13.681185	1982-2000 –> 2001-2010	8.9490045	18145.693
Atlantic	(26.5,26.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1090	4.0224818	6141.6260	14.317077	1982-2000 –> 2001-2010	8.8366354	18069.773
Atlantic	(26.5,26.75]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1090	4.1083135	6187.6535	14.147802	1982-2000 –> 2001-2010	8.9744854	18158.618
Atlantic	(26.5,26.75]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1090	3.9778979	6117.3287	14.003233	1982-2000 –> 2001-2010	8.7524866	18012.598
Atlantic	(26.5,26.75]	cstar ~ aou + silicate + phosphate + phosphate_star	868	4.2142810	4972.4768	13.355454	2001-2010 –> 2011-2019	8.3106598	11151.788
Atlantic	(26.5,26.75]	cstar ~ sal + aou + silicate + phosphate	868	4.2052645	4968.7587	12.686203	2001-2010 –> 2011-2019	8.2716691	11132.060
Atlantic	(26.5,26.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	868	4.1600002	4951.9716	13.106978	2001-2010 –> 2011-2019	8.1824820	11093.598
Atlantic	(26.5,26.75]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	868	4.1770474	4959.0709	12.912416	2001-2010 –> 2011-2019	8.2853609	11146.724
Atlantic	(26.5,26.75]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	868	4.1649044	4954.0169	12.389670	2001-2010 –> 2011-2019	8.1428023	11071.346
Atlantic	(26.75,27]	cstar ~ aou + silicate + phosphate + phosphate_star	1822	2.8892277	9048.8567	13.895402	1982-2000 –> 2001-2010	6.3103047	26676.002
Atlantic	(26.75,27]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1822	2.8430134	8992.0985	13.316922	1982-2000 –> 2001-2010	6.2561891	26605.866
Atlantic	(26.75,27]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1822	2.9795269	9163.0020	16.760421	1982-2000 –> 2001-2010	6.4619297	26910.298
Atlantic	(26.75,27]	cstar ~ temp + aou + silicate + phosphate	1822	2.9705911	9150.0569	14.379929	1982-2000 –> 2001-2010	6.4466780	26883.281
Atlantic	(26.75,27]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1822	2.8867576	9047.7401	16.059596	1982-2000 –> 2001-2010	6.2418828	26547.434
Atlantic	(26.75,27]	cstar ~ aou + silicate + phosphate + phosphate_star	1654	3.2220990	8576.3178	26.569855	2001-2010 –> 2011-2019	6.1113266	17625.175
Atlantic	(26.75,27]	cstar ~ sal + aou + silicate + phosphate	1654	3.2198641	8574.0226	23.817368	2001-2010 –> 2011-2019	6.2399648	17784.312
Atlantic	(26.75,27]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1654	3.1585755	8512.4493	25.201992	2001-2010 –> 2011-2019	6.0015889	17504.548
Atlantic	(26.75,27]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1654	3.2872719	8644.5606	23.091359	2001-2010 –> 2011-2019	6.2667988	17807.563
Atlantic	(26.75,27]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1654	2.9265633	8260.0743	21.532652	2001-2010 –> 2011-2019	5.8133209	17307.814
Atlantic	(27,27.25]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1552	2.5868034	7368.4980	10.847592	1982-2000 –> 2001-2010	5.7132922	21594.346
Atlantic	(27,27.25]	cstar ~ sal + aou + silicate + phosphate	1552	2.4258421	7167.0840	10.346353	1982-2000 –> 2001-2010	5.2266026	20779.883
Atlantic	(27,27.25]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1552	2.4008307	7136.9143	10.810762	1982-2000 –> 2001-2010	5.1309290	20609.790
Atlantic	(27,27.25]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1552	2.5198693	7287.1238	14.581964	1982-2000 –> 2001-2010	5.3279223	20916.366
Atlantic	(27,27.25]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1552	2.7203651	7524.7632	14.715048	1982-2000 –> 2001-2010	5.7896235	21648.003
Atlantic	(27,27.25]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1455	2.7785376	7116.9121	12.538430	2001-2010 –> 2011-2019	5.3653410	14485.410
Atlantic	(27,27.25]	cstar ~ sal + aou + silicate + phosphate	1455	2.7801169	7116.5657	14.223889	2001-2010 –> 2011-2019	5.2059590	14283.650
Atlantic	(27,27.25]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1455	2.7798233	7118.2584	14.302337	2001-2010 –> 2011-2019	5.1806540	14255.173
Atlantic	(27,27.25]	cstar ~ sal + aou + silicate + phosphate_star	1455	2.8458939	7184.6138	15.576280	2001-2010 –> 2011-2019	5.4648033	14589.400
Atlantic	(27,27.25]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1455	2.9675779	7308.4522	19.540078	2001-2010 –> 2011-2019	5.4874471	14595.576
Atlantic	(27.25,27.5]	cstar ~ sal + aou + nitrate + silicate	1572	2.7954446	7705.1469	14.341594	1982-2000 –> 2001-2010	6.0809825	23639.241
Atlantic	(27.25,27.5]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1572	2.7198300	7620.9329	14.115124	1982-2000 –> 2001-2010	5.9510353	23455.242
Atlantic	(27.25,27.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1572	2.9727185	7900.4580	22.454907	1982-2000 –> 2001-2010	5.8843731	23099.135
Atlantic	(27.25,27.5]	cstar ~ temp + aou + nitrate + silicate	1572	2.6780366	7570.2466	11.886778	1982-2000 –> 2001-2010	5.3059577	22141.090
Atlantic	(27.25,27.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1572	2.5274618	7390.3085	16.182826	1982-2000 –> 2001-2010	5.1544840	21961.063
Atlantic	(27.25,27.5]	cstar ~ aou + nitrate + silicate + phosphate_star	1388	3.2398790	7214.2613	21.420038	2001-2010 –> 2011-2019	6.2498838	15151.909
Atlantic	(27.25,27.5]	cstar ~ sal + aou + nitrate + silicate	1388	3.1947000	7175.2784	16.113960	2001-2010 –> 2011-2019	5.9901445	14880.425
Atlantic	(27.25,27.5]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1388	3.0311596	7031.4054	14.190786	2001-2010 –> 2011-2019	5.7509896	14652.338
Atlantic	(27.25,27.5]	cstar ~ temp + aou + nitrate + silicate	1388	3.3421933	7300.5706	11.982809	2001-2010 –> 2011-2019	6.0202299	14870.817
Atlantic	(27.25,27.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1388	3.0508656	7049.3942	14.188674	2001-2010 –> 2011-2019	5.5783275	14439.703
Atlantic	(27.5,27.75]	cstar ~ sal + aou + phosphate	2162	2.9719746	10855.3060	14.808840	1982-2000 –> 2001-2010	5.9360653	30678.870
Atlantic	(27.5,27.75]	cstar ~ sal + aou + phosphate + phosphate_star	2162	2.9557048	10833.5695	15.007127	1982-2000 –> 2001-2010	5.7667488	30239.896
Atlantic	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate	2162	2.6744184	10401.1470	15.025557	1982-2000 –> 2001-2010	5.5571004	30006.480
Atlantic	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	2162	2.6209321	10315.7940	15.936130	1982-2000 –> 2001-2010	5.3132883	29382.976
Atlantic	(27.5,27.75]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	2162	3.2690284	11271.2371	16.146506	1982-2000 –> 2001-2010	6.2343768	31102.156
Atlantic	(27.5,27.75]	cstar ~ sal + aou + nitrate + silicate	1937	3.4178724	10270.1846	17.732251	2001-2010 –> 2011-2019	6.4319272	21188.285
Atlantic	(27.5,27.75]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1937	3.3829074	10232.3493	15.984540	2001-2010 –> 2011-2019	6.3934636	21147.427
Atlantic	(27.5,27.75]	cstar ~ sal + aou + phosphate + phosphate_star	1937	3.4824823	10342.7333	15.860193	2001-2010 –> 2011-2019	6.4381871	21176.303
Atlantic	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate	1937	3.0214721	9792.6207	16.830331	2001-2010 –> 2011-2019	5.6958904	20193.768
Atlantic	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1937	3.0134444	9784.3143	16.708738	2001-2010 –> 2011-2019	5.6343765	20100.108
Atlantic	(27.75,27.85]	cstar ~ sal + aou + nitrate + silicate	785	2.0784547	3388.3842	13.393032	1982-2000 –> 2001-2010	4.3376754	9610.789
Atlantic	(27.75,27.85]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	785	2.0234457	3348.2724	14.294729	1982-2000 –> 2001-2010	4.2388889	9518.279
Atlantic	(27.75,27.85]	cstar ~ sal + aou + phosphate + phosphate_star	785	2.1719254	3457.4476	12.529922	1982-2000 –> 2001-2010	4.1517166	9312.813
Atlantic	(27.75,27.85]	cstar ~ sal + aou + silicate + phosphate	785	1.9124483	3257.6968	12.361213	1982-2000 –> 2001-2010	3.9856881	9241.279
Atlantic	(27.75,27.85]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	785	1.7409273	3112.1696	12.951823	1982-2000 –> 2001-2010	3.6277818	8835.872
Atlantic	(27.75,27.85]	cstar ~ sal + aou + nitrate + silicate	694	2.1648813	3053.5300	12.588858	2001-2010 –> 2011-2019	4.2433360	6441.914
Atlantic	(27.75,27.85]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	694	2.1524624	3047.5448	12.955422	2001-2010 –> 2011-2019	4.1759082	6395.817
Atlantic	(27.75,27.85]	cstar ~ sal + aou + phosphate + phosphate_star	694	2.5183116	3263.4278	11.886566	2001-2010 –> 2011-2019	4.6902371	6720.875
Atlantic	(27.75,27.85]	cstar ~ sal + aou + silicate + phosphate	694	2.0164884	2954.9710	11.662886	2001-2010 –> 2011-2019	3.9289367	6212.668
Atlantic	(27.75,27.85]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	694	1.9155470	2885.6911	12.025857	2001-2010 –> 2011-2019	3.6564743	5997.861
Atlantic	(27.85,27.95]	cstar ~ aou + silicate + phosphate + phosphate_star	750	3.3545533	3955.8857	33.678139	1982-2000 –> 2001-2010	6.3223158	11021.871
Atlantic	(27.85,27.95]	cstar ~ sal + aou + phosphate + phosphate_star	750	3.3452324	3951.7120	28.827922	1982-2000 –> 2001-2010	6.1596094	10868.366
Atlantic	(27.85,27.95]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	750	3.3314274	3947.5091	26.554649	1982-2000 –> 2001-2010	6.1457685	10866.127
Atlantic	(27.85,27.95]	cstar ~ temp + aou + phosphate + phosphate_star	750	3.0000941	3788.3733	21.479747	1982-2000 –> 2001-2010	5.9997323	10884.422
Atlantic	(27.85,27.95]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	750	2.9873236	3783.9746	21.513521	1982-2000 –> 2001-2010	5.9420944	10839.615
Atlantic	(27.85,27.95]	cstar ~ aou + silicate + phosphate + phosphate_star	731	3.7998786	4038.2130	23.414136	2001-2010 –> 2011-2019	7.1544319	7994.099
Atlantic	(27.85,27.95]	cstar ~ sal + aou + phosphate + phosphate_star	731	3.4386336	3892.1666	30.630629	2001-2010 –> 2011-2019	6.7838660	7843.879
Atlantic	(27.85,27.95]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	731	3.3620842	3861.2524	29.398203	2001-2010 –> 2011-2019	6.6935116	7808.762
Atlantic	(27.85,27.95]	cstar ~ temp + aou + phosphate + phosphate_star	731	3.7219690	4007.9258	22.631514	2001-2010 –> 2011-2019	6.7220632	7796.299
Atlantic	(27.85,27.95]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	731	3.6935819	3998.7325	23.285560	2001-2010 –> 2011-2019	6.6809055	7782.707
Atlantic	(27.95,28.05]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	924	4.6980424	5495.3240	25.160690	1982-2000 –> 2001-2010	9.4526472	16039.716
Atlantic	(27.95,28.05]	cstar ~ temp + aou + nitrate + phosphate_star	924	4.2013468	5286.8271	22.206275	1982-2000 –> 2001-2010	8.2709407	15279.123
Atlantic	(27.95,28.05]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	924	4.0064687	5201.0565	25.022177	1982-2000 –> 2001-2010	7.6043480	14759.722
Atlantic	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	924	4.6596686	5480.1675	21.661342	1982-2000 –> 2001-2010	9.5112810	16095.978
Atlantic	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate_star	924	4.7226299	5502.9705	24.237775	1982-2000 –> 2001-2010	9.5945376	16131.542
Atlantic	(27.95,28.05]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	854	4.3349976	4942.7066	24.370650	2001-2010 –> 2011-2019	9.0330400	10438.031
Atlantic	(27.95,28.05]	cstar ~ temp + aou + nitrate + phosphate_star	854	3.8616953	4743.2365	22.414073	2001-2010 –> 2011-2019	8.0630421	10030.064
Atlantic	(27.95,28.05]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	854	3.4985961	4576.5809	26.627224	2001-2010 –> 2011-2019	7.5050648	9777.637
Atlantic	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	854	4.4438079	4985.0489	22.928085	2001-2010 –> 2011-2019	9.1034765	10465.216
Atlantic	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate_star	854	4.4443554	4983.2593	23.217101	2001-2010 –> 2011-2019	9.1669854	10486.230
Atlantic	(28.05,28.1]	cstar ~ aou + silicate + phosphate + phosphate_star	625	1.2248218	2039.1673	10.101485	1982-2000 –> 2001-2010	2.4204436	5680.926
Atlantic	(28.05,28.1]	cstar ~ sal + aou + phosphate + phosphate_star	625	1.1139452	1920.5581	7.148025	1982-2000 –> 2001-2010	2.2622163	5470.507
Atlantic	(28.05,28.1]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	625	1.0803183	1884.2428	6.138916	1982-2000 –> 2001-2010	2.2282632	5435.546
Atlantic	(28.05,28.1]	cstar ~ temp + aou + phosphate + phosphate_star	625	1.1702602	1982.2058	10.430649	1982-2000 –> 2001-2010	2.3539376	5601.153
Atlantic	(28.05,28.1]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	625	1.1158650	1924.7105	11.408976	1982-2000 –> 2001-2010	2.2121652	5371.429
Atlantic	(28.05,28.1]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	553	1.2938561	1868.2815	9.004752	2001-2010 –> 2011-2019	2.4795021	3868.814
Atlantic	(28.05,28.1]	cstar ~ sal + aou + phosphate + phosphate_star	553	1.2237224	1804.6445	10.666527	2001-2010 –> 2011-2019	2.3376676	3725.203
Atlantic	(28.05,28.1]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	553	1.1877437	1773.6393	9.478772	2001-2010 –> 2011-2019	2.2680620	3657.882
Atlantic	(28.05,28.1]	cstar ~ temp + aou + phosphate + phosphate_star	553	1.2498655	1828.0238	14.596752	2001-2010 –> 2011-2019	2.4201257	3810.230
Atlantic	(28.05,28.1]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	553	1.2040330	1788.7045	15.347053	2001-2010 –> 2011-2019	2.3198980	3713.415
Atlantic	(28.1,28.15]	cstar ~ aou + silicate + phosphate + phosphate_star	730	0.9168587	1956.9195	11.412156	1982-2000 –> 2001-2010	1.7984757	5496.062
Atlantic	(28.1,28.15]	cstar ~ sal + aou + phosphate + phosphate_star	730	0.8449045	1837.5940	7.258465	1982-2000 –> 2001-2010	1.7041519	5306.625
Atlantic	(28.1,28.15]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	730	0.8302277	1814.0096	7.117191	1982-2000 –> 2001-2010	1.6520987	5163.717
Atlantic	(28.1,28.15]	cstar ~ temp + aou + silicate + phosphate	730	0.9286604	1975.5925	11.497046	1982-2000 –> 2001-2010	1.8214229	5549.007
Atlantic	(28.1,28.15]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	730	0.8374219	1826.6064	11.501958	1982-2000 –> 2001-2010	1.6439400	5124.872
Atlantic	(28.1,28.15]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	634	1.0154724	1832.6829	8.297395	2001-2010 –> 2011-2019	1.9248481	3779.637
Atlantic	(28.1,28.15]	cstar ~ sal + aou + phosphate + phosphate_star	634	0.9270373	1715.1485	7.388159	2001-2010 –> 2011-2019	1.7719418	3552.743
Atlantic	(28.1,28.15]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	634	0.9259444	1715.6528	7.387751	2001-2010 –> 2011-2019	1.7561721	3529.662
Atlantic	(28.1,28.15]	cstar ~ temp + aou + phosphate + phosphate_star	634	0.9990473	1810.0055	12.519106	2001-2010 –> 2011-2019	1.9124313	3761.381
Atlantic	(28.1,28.15]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	634	0.9191637	1706.3330	12.985587	2001-2010 –> 2011-2019	1.7565856	3532.939
Atlantic	(28.15,28.2]	cstar ~ sal + aou + nitrate + phosphate_star	1187	0.6279269	2275.8630	2.949173	1982-2000 –> 2001-2010	1.2363706	6586.636
Atlantic	(28.15,28.2]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1187	0.5786561	2083.8705	2.322577	1982-2000 –> 2001-2010	1.1765290	6314.936
Atlantic	(28.15,28.2]	cstar ~ temp + aou + nitrate + phosphate_star	1187	0.6233521	2258.5037	2.403297	1982-2000 –> 2001-2010	1.2593614	6775.844
Atlantic	(28.15,28.2]	cstar ~ temp + aou + nitrate + silicate	1187	0.5948620	2147.4433	2.237198	1982-2000 –> 2001-2010	1.2213490	6594.456
Atlantic	(28.15,28.2]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1187	0.5834551	2103.4780	2.272568	1982-2000 –> 2001-2010	1.2097995	6551.429
Atlantic	(28.15,28.2]	cstar ~ sal + aou + nitrate + phosphate_star	1065	0.7555426	2437.2593	4.997412	2001-2010 –> 2011-2019	1.3834695	4713.122
Atlantic	(28.15,28.2]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1065	0.7483863	2418.9883	5.639219	2001-2010 –> 2011-2019	1.3270423	4502.859
Atlantic	(28.15,28.2]	cstar ~ temp + aou + nitrate + phosphate_star	1065	0.8589612	2710.5120	9.016889	2001-2010 –> 2011-2019	1.4823133	4969.016
Atlantic	(28.15,28.2]	cstar ~ temp + aou + nitrate + silicate	1065	0.8519989	2693.1769	9.669208	2001-2010 –> 2011-2019	1.4468609	4840.620
Atlantic	(28.15,28.2]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1065	0.8517471	2694.5474	9.554421	2001-2010 –> 2011-2019	1.4352023	4798.025
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate	2075	0.3796799	1879.6236	2.015903	1982-2000 –> 2001-2010	0.7417682	5048.897
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate + phosphate_star	2075	0.3742434	1821.7718	1.991831	1982-2000 –> 2001-2010	0.7330349	4921.353
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate + silicate	2075	0.3791162	1875.4575	2.014214	1982-2000 –> 2001-2010	0.7399747	5020.065
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	2075	0.3672065	1744.9961	2.077596	1982-2000 –> 2001-2010	0.7241868	4806.911
Atlantic	(28.2, Inf]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	2075	0.5379025	3329.2717	3.121041	1982-2000 –> 2001-2010	1.0376970	9028.802
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate	1967	0.4372635	2337.8235	2.439187	2001-2010 –> 2011-2019	0.8169434	4217.447
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate + phosphate_star	1967	0.4203312	2184.4576	2.396465	2001-2010 –> 2011-2019	0.7945745	4006.229
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate + silicate	1967	0.4310142	2283.1938	2.392120	2001-2010 –> 2011-2019	0.8101304	4158.651
Atlantic	(28.2, Inf]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1967	0.4120641	2108.3132	2.647270	2001-2010 –> 2011-2019	0.7792706	3853.309
Atlantic	(28.2, Inf]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1967	0.7080347	4237.8427	8.997608	2001-2010 –> 2011-2019	1.2459372	7567.114
Indo-Pacific	(-Inf,26]	cstar ~ sal + aou + phosphate + phosphate_star	4077	6.8428599	27263.8446	30.476653	1982-2000 –> 2001-2010	14.6650404	80109.553
Indo-Pacific	(-Inf,26]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4077	6.8078550	27224.0254	30.053282	1982-2000 –> 2001-2010	14.5931044	79999.800
Indo-Pacific	(-Inf,26]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	4077	7.7159477	28245.0059	32.151612	1982-2000 –> 2001-2010	16.4075686	82694.735
Indo-Pacific	(-Inf,26]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4077	7.8361951	28371.1000	29.711490	1982-2000 –> 2001-2010	16.5603622	82877.640
Indo-Pacific	(-Inf,26]	cstar ~ temp + silicate + phosphate + phosphate_star	4077	7.9166124	28452.3522	29.041725	1982-2000 –> 2001-2010	16.7718230	83183.510
Indo-Pacific	(-Inf,26]	cstar ~ sal + aou + phosphate + phosphate_star	3620	6.6650059	24018.4599	26.444799	2001-2010 –> 2011-2019	13.5078659	51282.304
Indo-Pacific	(-Inf,26]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	3620	6.6163104	23967.3691	25.792991	2001-2010 –> 2011-2019	13.4241653	51191.395
Indo-Pacific	(-Inf,26]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	3620	7.6893503	25055.5297	27.389652	2001-2010 –> 2011-2019	15.4052980	53300.536
Indo-Pacific	(-Inf,26]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	3620	7.7183993	25082.8296	27.030017	2001-2010 –> 2011-2019	15.5545944	53453.930
Indo-Pacific	(-Inf,26]	cstar ~ temp + silicate + phosphate + phosphate_star	3620	7.8401647	25194.1562	26.057010	2001-2010 –> 2011-2019	15.7567771	53646.508
Indo-Pacific	(26,26.5]	cstar ~ aou + silicate + phosphate + phosphate_star	4220	5.3263709	26105.1771	43.904943	1982-2000 –> 2001-2010	11.0442349	77609.553
Indo-Pacific	(26,26.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4220	4.9959668	25566.6865	48.187075	1982-2000 –> 2001-2010	10.3844491	76107.026
Indo-Pacific	(26,26.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	4220	5.1799142	25871.8561	50.518458	1982-2000 –> 2001-2010	10.7039017	76816.579
Indo-Pacific	(26,26.5]	cstar ~ temp + aou + silicate + phosphate	4220	5.3260159	26104.6145	41.418559	1982-2000 –> 2001-2010	11.0205249	77542.349
Indo-Pacific	(26,26.5]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4220	5.3161660	26090.9912	42.819641	1982-2000 –> 2001-2010	11.0106228	77530.577
Indo-Pacific	(26,26.5]	cstar ~ aou + silicate + phosphate + phosphate_star	3794	5.3733764	23537.7972	45.536348	2001-2010 –> 2011-2019	10.6997473	49642.974
Indo-Pacific	(26,26.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	3794	5.0586719	23081.8425	45.933471	2001-2010 –> 2011-2019	10.0546387	48648.529
Indo-Pacific	(26,26.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	3794	5.1967576	23286.1943	51.404996	2001-2010 –> 2011-2019	10.3766718	49158.050
Indo-Pacific	(26,26.5]	cstar ~ temp + aou + silicate + phosphate	3794	5.3626602	23522.6493	44.447825	2001-2010 –> 2011-2019	10.6886761	49627.264
Indo-Pacific	(26,26.5]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	3794	5.3595329	23520.2230	44.892901	2001-2010 –> 2011-2019	10.6756989	49611.214
Indo-Pacific	(26.5,26.75]	cstar ~ aou + silicate + phosphate + phosphate_star	3488	4.3515566	20168.9577	23.877070	1982-2000 –> 2001-2010	9.0978234	59753.802
Indo-Pacific	(26.5,26.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	3488	4.2503108	20006.7322	21.960404	1982-2000 –> 2001-2010	8.8376086	59140.618
Indo-Pacific	(26.5,26.75]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	3488	4.3114441	20106.3550	30.460588	1982-2000 –> 2001-2010	9.1012744	59814.679
Indo-Pacific	(26.5,26.75]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	3488	4.2742249	20045.8722	21.963387	1982-2000 –> 2001-2010	8.9550947	59448.242
Indo-Pacific	(26.5,26.75]	cstar ~ temp + nitrate + silicate + phosphate_star	3488	4.3117148	20104.7929	30.146256	1982-2000 –> 2001-2010	9.1626404	59979.638
Indo-Pacific	(26.5,26.75]	cstar ~ aou + silicate + phosphate + phosphate_star	3143	4.7279420	18696.6859	25.375135	2001-2010 –> 2011-2019	9.0794986	38865.644
Indo-Pacific	(26.5,26.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	3143	4.6034133	18530.9002	26.234361	2001-2010 –> 2011-2019	8.8537241	38537.632
Indo-Pacific	(26.5,26.75]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	3143	4.6625834	18611.1826	33.294084	2001-2010 –> 2011-2019	8.9740275	38717.538
Indo-Pacific	(26.5,26.75]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	3143	4.6087871	18538.2338	24.409574	2001-2010 –> 2011-2019	8.8830120	38584.106
Indo-Pacific	(26.5,26.75]	cstar ~ temp + nitrate + silicate + phosphate_star	3143	4.6743102	18624.9726	35.801289	2001-2010 –> 2011-2019	8.9860250	38729.766
Indo-Pacific	(26.75,27]	cstar ~ aou + silicate + phosphate + phosphate_star	4075	4.7061189	24199.5870	19.637534	1982-2000 –> 2001-2010	9.4295372	71297.521
Indo-Pacific	(26.75,27]	cstar ~ sal + aou + phosphate + phosphate_star	4075	4.4824000	23802.6417	22.715888	1982-2000 –> 2001-2010	8.9378918	69975.244
Indo-Pacific	(26.75,27]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4075	4.4686641	23779.6285	21.907678	1982-2000 –> 2001-2010	8.9073277	69894.267
Indo-Pacific	(26.75,27]	cstar ~ temp + aou + phosphate + phosphate_star	4075	4.3998975	23651.2363	22.224691	1982-2000 –> 2001-2010	8.8581963	69833.818
Indo-Pacific	(26.75,27]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4075	4.3698710	23597.4269	20.901397	1982-2000 –> 2001-2010	8.7981063	69674.793
Indo-Pacific	(26.75,27]	cstar ~ aou + silicate + phosphate + phosphate_star	3755	5.1488424	22975.4054	21.838728	2001-2010 –> 2011-2019	9.8549612	47174.992
Indo-Pacific	(26.75,27]	cstar ~ sal + aou + phosphate + phosphate_star	3755	4.9333639	22654.3468	23.814311	2001-2010 –> 2011-2019	9.4157639	46456.988
Indo-Pacific	(26.75,27]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	3755	4.9243970	22642.6842	23.050839	2001-2010 –> 2011-2019	9.3930612	46422.313
Indo-Pacific	(26.75,27]	cstar ~ temp + aou + phosphate + phosphate_star	3755	4.8303776	22495.9124	20.897629	2001-2010 –> 2011-2019	9.2302751	46147.149
Indo-Pacific	(26.75,27]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	3755	4.8092795	22465.0384	19.911142	2001-2010 –> 2011-2019	9.1791504	46062.465
Indo-Pacific	(27,27.25]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	5035	4.5504270	29560.9872	46.044668	1982-2000 –> 2001-2010	8.9222622	83660.328
Indo-Pacific	(27,27.25]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	5035	4.2686966	28917.3880	56.817049	1982-2000 –> 2001-2010	8.4991660	82402.456
Indo-Pacific	(27,27.25]	cstar ~ temp + aou + phosphate + phosphate_star	5035	4.5608034	29581.9239	48.934144	1982-2000 –> 2001-2010	9.0001897	83965.813
Indo-Pacific	(27,27.25]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	5035	4.2410652	28851.9928	34.437415	1982-2000 –> 2001-2010	8.4216004	82115.165
Indo-Pacific	(27,27.25]	cstar ~ temp + nitrate + silicate + phosphate_star	5035	4.5858348	29637.0406	78.292868	1982-2000 –> 2001-2010	8.9489951	83697.263
Indo-Pacific	(27,27.25]	cstar ~ aou + silicate + phosphate + phosphate_star	4394	5.3237703	27176.7652	31.926570	2001-2010 –> 2011-2019	9.9309084	56860.477
Indo-Pacific	(27,27.25]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4394	5.2829317	27111.0926	34.134451	2001-2010 –> 2011-2019	9.8333587	56672.080
Indo-Pacific	(27,27.25]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	4394	5.1339127	26859.6405	37.191688	2001-2010 –> 2011-2019	9.4026093	55777.028
Indo-Pacific	(27,27.25]	cstar ~ temp + aou + phosphate + phosphate_star	4394	5.2852844	27113.0054	40.729059	2001-2010 –> 2011-2019	9.8460879	56694.929
Indo-Pacific	(27,27.25]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4394	4.6890173	26063.0518	26.211339	2001-2010 –> 2011-2019	8.9300825	54915.045
Indo-Pacific	(27.25,27.5]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	4525	3.7195506	24743.4996	32.137050	1982-2000 –> 2001-2010	7.3602789	69946.486
Indo-Pacific	(27.25,27.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4525	3.9793937	25354.6155	32.260023	1982-2000 –> 2001-2010	7.7606643	71188.925
Indo-Pacific	(27.25,27.5]	cstar ~ sal + aou + silicate + phosphate_star	4525	3.9932800	25384.1410	31.544624	1982-2000 –> 2001-2010	7.7745735	71216.551
Indo-Pacific	(27.25,27.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	4525	3.8932218	25156.4889	32.630203	1982-2000 –> 2001-2010	7.6387007	70832.275
Indo-Pacific	(27.25,27.5]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4525	3.6667715	24614.1634	33.059077	1982-2000 –> 2001-2010	7.3507532	70014.005
Indo-Pacific	(27.25,27.5]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	4007	4.1137078	22719.7721	31.039838	2001-2010 –> 2011-2019	7.8332585	47463.272
Indo-Pacific	(27.25,27.5]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4007	4.4221644	23299.2203	32.192748	2001-2010 –> 2011-2019	8.4015581	48653.836
Indo-Pacific	(27.25,27.5]	cstar ~ sal + aou + silicate + phosphate_star	4007	4.4599021	23365.3197	30.581432	2001-2010 –> 2011-2019	8.4531822	48749.461
Indo-Pacific	(27.25,27.5]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	4007	4.3710730	23206.0917	31.013092	2001-2010 –> 2011-2019	8.2642948	48362.581
Indo-Pacific	(27.25,27.5]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4007	4.0072348	22509.6183	32.993931	2001-2010 –> 2011-2019	7.6740063	47123.782
Indo-Pacific	(27.5,27.75]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	4480	3.4251650	23758.7901	23.149497	1982-2000 –> 2001-2010	6.3941340	66690.240
Indo-Pacific	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4480	3.4152828	23732.9016	11.213435	1982-2000 –> 2001-2010	6.4130403	66829.536
Indo-Pacific	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate_star	4480	3.5313202	24030.2686	21.541236	1982-2000 –> 2001-2010	6.5466023	67224.682
Indo-Pacific	(27.5,27.75]	cstar ~ sal + nitrate + silicate + phosphate_star	4480	3.5590812	24100.4310	28.476354	1982-2000 –> 2001-2010	6.5924841	67397.410
Indo-Pacific	(27.5,27.75]	cstar ~ sal + silicate + phosphate + phosphate_star	4480	3.5801484	24153.3113	24.488002	1982-2000 –> 2001-2010	6.6101814	67431.262
Indo-Pacific	(27.5,27.75]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	4006	4.1604953	22804.7162	26.146725	2001-2010 –> 2011-2019	7.5856603	46563.506
Indo-Pacific	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	4006	4.0245862	22538.6214	10.945458	2001-2010 –> 2011-2019	7.4398690	46271.523
Indo-Pacific	(27.5,27.75]	cstar ~ sal + aou + silicate + phosphate_star	4006	4.3179926	23100.4140	24.511363	2001-2010 –> 2011-2019	7.8493128	47130.683
Indo-Pacific	(27.5,27.75]	cstar ~ sal + nitrate + silicate + phosphate_star	4006	4.3433675	23147.3591	32.302340	2001-2010 –> 2011-2019	7.9024487	47247.790
Indo-Pacific	(27.5,27.75]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	4006	4.2305828	22938.5617	18.679475	2001-2010 –> 2011-2019	7.7681793	46986.741
Indo-Pacific	(27.75,27.85]	cstar ~ aou + silicate + phosphate + phosphate_star	1772	2.9170149	8834.7856	21.055032	1982-2000 –> 2001-2010	5.3737515	24106.999
Indo-Pacific	(27.75,27.85]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1772	2.9161606	8835.7475	21.293384	1982-2000 –> 2001-2010	5.3650443	24088.882
Indo-Pacific	(27.75,27.85]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1772	2.9136257	8832.6655	21.486044	1982-2000 –> 2001-2010	5.3702408	24106.554
Indo-Pacific	(27.75,27.85]	cstar ~ temp + aou + silicate + phosphate	1772	2.9274071	8847.3891	20.650526	1982-2000 –> 2001-2010	5.3913652	24138.928
Indo-Pacific	(27.75,27.85]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1772	2.8363586	8737.4127	20.879844	1982-2000 –> 2001-2010	5.2797724	23975.824
Indo-Pacific	(27.75,27.85]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1648	3.2450479	8570.6423	29.981525	2001-2010 –> 2011-2019	6.1594031	17404.195
Indo-Pacific	(27.75,27.85]	cstar ~ sal + nitrate + silicate + phosphate_star	1648	3.2533312	8577.0449	28.060881	2001-2010 –> 2011-2019	6.1676885	17408.600
Indo-Pacific	(27.75,27.85]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1648	3.2740679	8599.9869	29.326154	2001-2010 –> 2011-2019	6.1876935	17432.652
Indo-Pacific	(27.75,27.85]	cstar ~ temp + aou + phosphate + phosphate_star	1648	3.2216485	8544.7894	30.662953	2001-2010 –> 2011-2019	6.1454636	17387.827
Indo-Pacific	(27.75,27.85]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1648	3.1700595	8493.5825	27.788882	2001-2010 –> 2011-2019	6.0064181	17230.995
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate + phosphate_star	2176	2.8510566	10746.7658	26.157736	1982-2000 –> 2001-2010	5.1641296	29888.952
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate + silicate	2176	2.8444030	10736.5976	25.745680	1982-2000 –> 2001-2010	5.1960116	30018.797
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	2176	2.8407088	10732.9418	25.535864	1982-2000 –> 2001-2010	5.1513289	29868.137
Indo-Pacific	(27.85,27.95]	cstar ~ temp + nitrate + phosphate_star	2176	2.8878899	10800.6300	30.561785	1982-2000 –> 2001-2010	5.2034100	29949.777
Indo-Pacific	(27.85,27.95]	cstar ~ temp + nitrate + silicate + phosphate_star	2176	2.8732077	10780.4477	29.520555	1982-2000 –> 2001-2010	5.1866819	29924.104
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate	2046	3.1951398	10569.6898	35.387658	2001-2010 –> 2011-2019	6.0485509	21318.048
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate + phosphate_star	2046	3.1893940	10564.3247	35.529099	2001-2010 –> 2011-2019	6.0404506	21311.091
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate + silicate	2046	3.1820229	10554.8566	34.980600	2001-2010 –> 2011-2019	6.0264258	21291.454
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	2046	3.1770142	10550.4104	35.124053	2001-2010 –> 2011-2019	6.0177230	21283.352
Indo-Pacific	(27.85,27.95]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	2046	3.1197138	10475.9338	40.168786	2001-2010 –> 2011-2019	6.0369065	21324.500
Indo-Pacific	(27.95,28.05]	cstar ~ aou + silicate + phosphate + phosphate_star	1910	2.2725300	8568.1593	9.137309	1982-2000 –> 2001-2010	4.3474766	24460.338
Indo-Pacific	(27.95,28.05]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1910	2.2277338	8494.1072	9.349733	1982-2000 –> 2001-2010	4.2751074	24289.425
Indo-Pacific	(27.95,28.05]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1910	2.2758565	8575.7469	8.969487	1982-2000 –> 2001-2010	4.3631957	24513.931
Indo-Pacific	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate	1910	2.2863589	8591.3345	9.186238	1982-2000 –> 2001-2010	4.3716998	24520.440
Indo-Pacific	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1910	2.2108376	8465.0241	8.812504	1982-2000 –> 2001-2010	4.2391905	24191.366
Indo-Pacific	(27.95,28.05]	cstar ~ sal + aou + nitrate + phosphate_star	1759	2.4658781	8178.9895	9.983524	2001-2010 –> 2011-2019	4.7038680	16688.643
Indo-Pacific	(27.95,28.05]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	1759	2.4583937	8170.2955	10.166360	2001-2010 –> 2011-2019	4.6771350	16648.952
Indo-Pacific	(27.95,28.05]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1759	2.5231094	8261.7067	10.100622	2001-2010 –> 2011-2019	4.7508432	16755.814
Indo-Pacific	(27.95,28.05]	cstar ~ temp + aou + phosphate + phosphate_star	1759	2.5191024	8254.1153	10.179165	2001-2010 –> 2011-2019	4.7917918	16822.543
Indo-Pacific	(27.95,28.05]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1759	2.4756829	8194.9501	9.928208	2001-2010 –> 2011-2019	4.6865206	16659.974
Indo-Pacific	(28.05,28.1]	cstar ~ sal + aou + silicate + phosphate	1321	1.9818871	5568.0943	9.523772	1982-2000 –> 2001-2010	3.7197113	16198.983
Indo-Pacific	(28.05,28.1]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1321	1.8869350	5440.3836	10.150907	1982-2000 –> 2001-2010	3.6017358	16001.440
Indo-Pacific	(28.05,28.1]	cstar ~ sal + silicate + phosphate + phosphate_star	1321	1.9824370	5568.8273	9.278758	1982-2000 –> 2001-2010	3.7375846	16253.140
Indo-Pacific	(28.05,28.1]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1321	1.9019277	5461.2927	10.903283	1982-2000 –> 2001-2010	3.6246876	16047.290
Indo-Pacific	(28.05,28.1]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1321	1.8582913	5399.9705	9.841824	1982-2000 –> 2001-2010	3.5904399	16015.241
Indo-Pacific	(28.05,28.1]	cstar ~ aou + silicate + phosphate + phosphate_star	1224	2.1021750	5304.3583	9.338380	2001-2010 –> 2011-2019	4.0279576	10796.582
Indo-Pacific	(28.05,28.1]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	1224	2.0441555	5237.8441	9.052582	2001-2010 –> 2011-2019	3.9310905	10678.228
Indo-Pacific	(28.05,28.1]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	1224	2.0855455	5286.9161	9.819478	2001-2010 –> 2011-2019	3.9874732	10748.209
Indo-Pacific	(28.05,28.1]	cstar ~ temp + aou + silicate + phosphate	1224	2.1143730	5318.5219	9.470052	2001-2010 –> 2011-2019	4.0489454	10822.777
Indo-Pacific	(28.05,28.1]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	1224	1.9950662	5178.3393	8.422468	2001-2010 –> 2011-2019	3.8533574	10578.310
Indo-Pacific	(28.1, Inf]	cstar ~ sal + aou + silicate + phosphate	11307	1.4222626	40065.6345	12.448422	1982-2000 –> 2001-2010	2.7125094	111815.504
Indo-Pacific	(28.1, Inf]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	11307	1.3241226	38450.7580	14.922637	1982-2000 –> 2001-2010	2.5124113	106674.423
Indo-Pacific	(28.1, Inf]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	11307	1.3584530	39029.5967	13.107193	1982-2000 –> 2001-2010	2.5013676	105584.614
Indo-Pacific	(28.1, Inf]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	11307	1.3760657	39320.9097	15.711661	1982-2000 –> 2001-2010	2.6336117	109972.506
Indo-Pacific	(28.1, Inf]	cstar ~ temp + nitrate + silicate + phosphate_star	11307	1.5492538	41999.6842	16.692830	1982-2000 –> 2001-2010	2.8960757	115588.852
Indo-Pacific	(28.1, Inf]	cstar ~ sal + aou + nitrate + silicate + phosphate_star	10029	1.6385108	38379.4638	9.314138	2001-2010 –> 2011-2019	3.1508314	79835.515
Indo-Pacific	(28.1, Inf]	cstar ~ sal + aou + silicate + phosphate	10029	1.5753489	37588.9638	11.239773	2001-2010 –> 2011-2019	2.9976115	77654.598
Indo-Pacific	(28.1, Inf]	cstar ~ sal + aou + silicate + phosphate + phosphate_star	10029	1.4949035	36539.6218	13.624735	2001-2010 –> 2011-2019	2.8190261	74990.380
Indo-Pacific	(28.1, Inf]	cstar ~ temp + aou + nitrate + silicate + phosphate_star	10029	1.5777186	37621.1137	12.446204	2001-2010 –> 2011-2019	2.9361716	76650.710
Indo-Pacific	(28.1, Inf]	cstar ~ temp + aou + silicate + phosphate + phosphate_star	10029	1.5527536	37301.1885	14.748217	2001-2010 –> 2011-2019	2.9288194	76622.098

5.3.2 per fitting unit

lm_best %>%
  group_by(basin, gamma_slab, eras) %>% 
  summarise(rmse_sum_mean = mean(rmse_sum),
            ais_sum_mean = mean(aic_sum)) %>% 
  ungroup() %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	gamma_slab	eras	rmse_sum_mean	ais_sum_mean
Atlantic	(-Inf,26]	1982-2000 –> 2001-2010	8.3680662	2023.545
Atlantic	(-Inf,26]	2001-2010 –> 2011-2019	6.4323661	1142.968
Atlantic	(26,26.5]	1982-2000 –> 2001-2010	11.0898864	15362.493
Atlantic	(26,26.5]	2001-2010 –> 2011-2019	9.7509940	9229.785
Atlantic	(26.5,26.75]	1982-2000 –> 2001-2010	8.8884098	18101.551
Atlantic	(26.5,26.75]	2001-2010 –> 2011-2019	8.2385948	11119.103
Atlantic	(26.75,27]	1982-2000 –> 2001-2010	6.3433969	26724.576
Atlantic	(26.75,27]	2001-2010 –> 2011-2019	6.0866000	17605.882
Atlantic	(27,27.25]	1982-2000 –> 2001-2010	5.4376739	21109.678
Atlantic	(27,27.25]	2001-2010 –> 2011-2019	5.3408409	14441.842
Atlantic	(27.25,27.5]	1982-2000 –> 2001-2010	5.6753665	22859.154
Atlantic	(27.25,27.5]	2001-2010 –> 2011-2019	5.9179151	14799.038
Atlantic	(27.5,27.75]	1982-2000 –> 2001-2010	5.7615159	30282.075
Atlantic	(27.5,27.75]	2001-2010 –> 2011-2019	6.1187689	20761.178
Atlantic	(27.75,27.85]	1982-2000 –> 2001-2010	4.0683502	9303.806
Atlantic	(27.75,27.85]	2001-2010 –> 2011-2019	4.1389784	6353.827
Atlantic	(27.85,27.95]	1982-2000 –> 2001-2010	6.1139041	10896.080
Atlantic	(27.85,27.95]	2001-2010 –> 2011-2019	6.8069556	7845.149
Atlantic	(27.95,28.05]	1982-2000 –> 2001-2010	8.8867509	15661.216
Atlantic	(27.95,28.05]	2001-2010 –> 2011-2019	8.5743217	10239.436
Atlantic	(28.05,28.1]	1982-2000 –> 2001-2010	2.2954052	5511.912
Atlantic	(28.05,28.1]	2001-2010 –> 2011-2019	2.3650511	3755.109
Atlantic	(28.1,28.15]	1982-2000 –> 2001-2010	1.7240178	5328.057
Atlantic	(28.1,28.15]	2001-2010 –> 2011-2019	1.8243958	3631.273
Atlantic	(28.15,28.2]	1982-2000 –> 2001-2010	1.2206819	6564.660
Atlantic	(28.15,28.2]	2001-2010 –> 2011-2019	1.4149777	4764.728
Atlantic	(28.2, Inf]	1982-2000 –> 2001-2010	0.7953323	5765.206
Atlantic	(28.2, Inf]	2001-2010 –> 2011-2019	0.8893712	4760.550
Indo-Pacific	(-Inf,26]	1982-2000 –> 2001-2010	15.7995797	81773.048
Indo-Pacific	(-Inf,26]	2001-2010 –> 2011-2019	14.7297401	52574.935
Indo-Pacific	(26,26.5]	1982-2000 –> 2001-2010	10.8327467	77121.217
Indo-Pacific	(26,26.5]	2001-2010 –> 2011-2019	10.4990866	49337.606
Indo-Pacific	(26.5,26.75]	1982-2000 –> 2001-2010	9.0308883	59627.396
Indo-Pacific	(26.5,26.75]	2001-2010 –> 2011-2019	8.9552574	38686.937
Indo-Pacific	(26.75,27]	1982-2000 –> 2001-2010	8.9862119	70135.129
Indo-Pacific	(26.75,27]	2001-2010 –> 2011-2019	9.4146424	46452.782
Indo-Pacific	(27,27.25]	1982-2000 –> 2001-2010	8.7584427	83168.205
Indo-Pacific	(27,27.25]	2001-2010 –> 2011-2019	9.5886094	56183.912
Indo-Pacific	(27.25,27.5]	1982-2000 –> 2001-2010	7.5769941	70639.648
Indo-Pacific	(27.25,27.5]	2001-2010 –> 2011-2019	8.1252600	48070.586
Indo-Pacific	(27.5,27.75]	1982-2000 –> 2001-2010	6.5112884	67114.626
Indo-Pacific	(27.5,27.75]	2001-2010 –> 2011-2019	7.7090940	46840.049
Indo-Pacific	(27.75,27.85]	1982-2000 –> 2001-2010	5.3560348	24083.437
Indo-Pacific	(27.75,27.85]	2001-2010 –> 2011-2019	6.1333334	17372.854
Indo-Pacific	(27.85,27.95]	1982-2000 –> 2001-2010	5.1803124	29929.953
Indo-Pacific	(27.85,27.95]	2001-2010 –> 2011-2019	6.0340114	21305.689
Indo-Pacific	(27.95,28.05]	1982-2000 –> 2001-2010	4.3193340	24395.100
Indo-Pacific	(27.95,28.05]	2001-2010 –> 2011-2019	4.7220317	16715.185
Indo-Pacific	(28.05,28.1]	1982-2000 –> 2001-2010	3.6548318	16103.219
Indo-Pacific	(28.05,28.1]	2001-2010 –> 2011-2019	3.9697648	10724.821
Indo-Pacific	(28.1, Inf]	1982-2000 –> 2001-2010	2.6511951	109927.180
Indo-Pacific	(28.1, Inf]	2001-2010 –> 2011-2019	2.9664920	77150.660

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

6.1.2 Best models

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

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

6.2 RMSE correlation between eras

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

6.2.1 All models

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

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

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

rm(max_rmse)

6.2.2 Best models

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

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

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

rm(max_rmse)

6.3 Predictor counts

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

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

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

	aou	nitrate	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-2000 --> 2001-2010
(-Inf,26]	3	3	2	4	5	3	0
(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	2	5	1	4	4
(28.05,28.1]	5	0	5	5	2	3	2
(28.1,28.15]	5	0	5	4	2	4	2
(28.15,28.2]	5	5	0	4	2	3	3
(28.2, Inf]	5	5	0	3	4	3	1
total	68.00	29.00	40.00	55.00	37.00	54.00	28.00
Atlantic - 2001-2010 --> 2011-2019
(-Inf,26]	5	2	2	5	5	3	0
(26,26.5]	5	3	2	4	1	4	4
(26.5,26.75]	5	1	4	4	2	5	2
(26.75,27]	5	1	4	4	2	5	2
(27,27.25]	5	2	2	4	4	5	1
(27.25,27.5]	5	5	0	3	2	5	2
(27.5,27.75]	5	2	3	3	5	4	0
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	2	5	1	4	4
(28.05,28.1]	5	1	4	5	3	3	2
(28.1,28.15]	5	1	4	5	3	3	2
(28.15,28.2]	5	5	0	4	2	3	3
(28.2, Inf]	5	5	0	3	4	3	1
total	70.00	32.00	35.00	57.00	41.00	54.00	25.00
Indo-Pacific - 1982-2000 --> 2001-2010
(-Inf,26]	4	1	4	5	2	4	3
(26,26.5]	5	1	4	4	1	5	3
(26.5,26.75]	4	2	3	5	1	5	3
(26.75,27]	5	0	5	5	2	3	2
(27,27.25]	4	2	3	5	1	4	4
(27.25,27.5]	5	2	2	5	3	5	2
(27.5,27.75]	3	2	2	5	5	5	0
(27.75,27.85]	5	1	4	4	1	5	3
(27.85,27.95]	3	5	0	4	0	3	5
(27.95,28.05]	5	1	4	4	1	5	3
(28.05,28.1]	4	1	4	4	3	5	2
(28.1, Inf]	4	2	3	4	2	5	3
total	51.00	20.00	38.00	54.00	22.00	54.00	33.00
Indo-Pacific - 2001-2010 --> 2011-2019
(-Inf,26]	4	1	4	5	2	4	3
(26,26.5]	5	1	4	4	1	5	3
(26.5,26.75]	4	2	3	5	1	5	3
(26.75,27]	5	0	5	5	2	3	2
(27,27.25]	5	1	4	5	1	4	3
(27.25,27.5]	5	2	2	5	3	5	2
(27.5,27.75]	4	2	2	5	4	5	1
(27.75,27.85]	4	3	2	5	2	4	3
(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	21.00	37.00	55.00	23.00	51.00	32.00

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

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

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

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

05 March, 2021