eMLR - model fitting

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Last updated: 2021-03-04

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Knit directory: emlr_mod_v_XXX/

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---

1 Required data

Required are:

• cleaned and prepared GLODAP-based synthetic model subsetting file

GLODAP <-
  read_csv(paste(path_version_data,
                 "GLODAPv2.2020_MLR_fitting_ready.csv",
                 sep = ""))

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

• sal, temp, aou, nitrate, silicate, phosphate, phosphate_star

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

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

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

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

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

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

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

# convert to tibble
lm_all <- as_tibble(lm_all)

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

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

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

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

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


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

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

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

3 Apply predictor threshold

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

• Minimum: 3
  
• Maximum: 9

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

This results in a total number of MLR models of:

• 45

4 Fit all models

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

• cstar_tref

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

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

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

5 Prepare coeffcients

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

5.1 Formatting

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

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

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

5.2 Predictor selection

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

• 5

The criterion used to select the best models was:

• aic

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

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

# remove models with predictors fitted as NA

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

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

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

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

5.3 RMSE tables

5.3.1 per model

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

basin	gamma_slab	model	nr_obs	rmse	aic	resid_max	eras	rmse_sum	aic_sum
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	281	1.5970497	1074.5482	5.875642	1982-1990 –> 1991-2014	2.8795435	1452.117
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	281	1.0960503	860.9862	4.424911	1982-1990 –> 1991-2014	2.0703119	1176.630
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	281	1.0946847	862.2856	4.363468	1982-1990 –> 1991-2014	2.0682944	1179.784
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	281	1.5046238	1039.0446	7.418118	1982-1990 –> 1991-2014	2.6631295	1392.448
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	281	1.4977854	1038.4845	7.157446	1982-1990 –> 1991-2014	2.6482942	1392.378
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	48	1.2963422	173.1346	3.559537	1991-2014 –> 2015-2019	2.3923925	1034.121
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	48	1.1767705	165.8444	3.129669	1991-2014 –> 2015-2019	2.2714552	1028.130
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate_star	48	1.6723887	197.5864	3.701869	1991-2014 –> 2015-2019	3.2707700	1270.603
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	48	1.6823912	198.1588	5.164384	1991-2014 –> 2015-2019	3.1870150	1237.203
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	48	1.5812099	194.2044	4.461200	1991-2014 –> 2015-2019	3.0789953	1232.689
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1966	3.5233536	10545.2792	13.102326	1982-1990 –> 1991-2014	6.7273892	14604.805
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1966	4.1918832	11226.4125	14.679512	1982-1990 –> 1991-2014	8.1225145	15604.011
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	1966	4.0484955	11089.5602	17.060255	1982-1990 –> 1991-2014	7.9203491	15443.564
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1966	4.0441047	11087.2934	17.587936	1982-1990 –> 1991-2014	7.9050840	15438.893
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1966	4.2825005	11312.5061	14.621009	1982-1990 –> 1991-2014	8.3106200	15730.471
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	389	3.7055748	2136.9884	10.789649	1991-2014 –> 2015-2019	7.2289284	12682.268
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	389	4.1214445	2217.7407	11.335208	1991-2014 –> 2015-2019	8.3133277	13444.153
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	389	3.9337989	2181.4873	12.837679	1991-2014 –> 2015-2019	7.9822945	13271.048
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	389	3.9021294	2177.1986	13.677281	1991-2014 –> 2015-2019	7.9462341	13264.492
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	389	4.2683212	2246.9838	11.089308	1991-2014 –> 2015-2019	8.5508217	13559.490
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2571	3.2707332	13401.5249	11.597074	1982-1990 –> 1991-2014	6.2375318	18050.406
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	2571	3.2695097	13399.6010	11.272296	1982-1990 –> 1991-2014	6.3120152	18095.098
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2571	3.2048798	13298.9386	11.602630	1982-1990 –> 1991-2014	6.1423154	17931.418
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2571	3.2817369	13420.7950	10.510535	1982-1990 –> 1991-2014	6.3050670	18106.595
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2571	3.1545751	13217.5882	10.240198	1982-1990 –> 1991-2014	6.0058253	17794.976
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	454	3.5529188	2451.5309	11.528924	1991-2014 –> 2015-2019	6.8236521	15853.056
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	454	3.4518490	2425.3265	10.422776	1991-2014 –> 2015-2019	6.7213587	15824.928
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	454	3.4335594	2422.5027	10.688996	1991-2014 –> 2015-2019	6.6384392	15721.441
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	454	3.5029857	2440.6792	9.732434	1991-2014 –> 2015-2019	6.7847226	15861.474
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	454	3.4078423	2415.6762	11.246610	1991-2014 –> 2015-2019	6.5624174	15633.264
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4308	2.0192666	18292.3336	24.415011	1982-1990 –> 1991-2014	3.5341792	24075.030
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4308	1.9473419	17981.8397	23.294561	1982-1990 –> 1991-2014	3.4500119	23741.008
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4308	2.1148970	18693.0112	21.732554	1982-1990 –> 1991-2014	3.7647656	24746.180
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	4308	2.1278543	18743.6374	25.188019	1982-1990 –> 1991-2014	3.7666335	24773.590
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4308	1.9965941	18197.0453	29.931685	1982-1990 –> 1991-2014	3.3331186	23587.594
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	920	2.5300093	4330.7772	17.628304	1991-2014 –> 2015-2019	4.5492758	22623.111
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	920	2.4976736	4307.1088	15.637246	1991-2014 –> 2015-2019	4.6336582	23083.604
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	920	2.4377288	4264.4098	16.501545	1991-2014 –> 2015-2019	4.3850707	22246.249
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	920	2.6177264	4395.4902	13.486569	1991-2014 –> 2015-2019	4.7326234	23088.501
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	920	2.1790130	4057.9715	15.347220	1991-2014 –> 2015-2019	4.1756071	22255.017
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	3715	2.1372788	16200.0466	10.896405	1982-1990 –> 1991-2014	4.4474409	21886.275
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	3715	1.8970672	15312.2099	10.691809	1982-1990 –> 1991-2014	3.5298360	20123.978
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3715	1.8478236	15118.7964	10.457644	1982-1990 –> 1991-2014	3.2804294	19603.778
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3715	2.0285304	15812.0383	19.125736	1982-1990 –> 1991-2014	3.5007731	20365.632
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3715	2.2555753	16600.3128	22.155256	1982-1990 –> 1991-2014	4.1503801	21788.261
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	812	2.2225970	3615.4065	11.815881	1991-2014 –> 2015-2019	4.3598758	19815.453
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	812	2.3083874	3674.9121	13.926205	1991-2014 –> 2015-2019	4.2054546	18987.122
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	812	2.2983822	3669.8579	14.337448	1991-2014 –> 2015-2019	4.1462057	18788.654
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	812	2.3348320	3693.4106	15.182007	1991-2014 –> 2015-2019	4.5098292	20021.437
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	812	2.6050612	3873.2650	19.387030	1991-2014 –> 2015-2019	4.6335915	19685.303
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	3732	2.5388851	17557.3528	13.187909	1982-1990 –> 1991-2014	5.2446256	24590.178
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	3732	2.4113475	17174.6633	13.868034	1982-1990 –> 1991-2014	5.0602590	24147.761
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3732	2.6683418	17930.5541	21.318709	1982-1990 –> 1991-2014	4.6230922	24019.951
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	3732	2.2200185	16555.6132	12.206475	1982-1990 –> 1991-2014	3.8094265	22041.342
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3732	2.0866502	16095.1770	16.105288	1982-1990 –> 1991-2014	3.6659055	21564.271
Atlantic	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	826	3.1231742	4237.4664	20.774319	1991-2014 –> 2015-2019	5.7928271	22169.687
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	826	2.9996057	4170.7768	16.886815	1991-2014 –> 2015-2019	5.5384907	21728.130
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	826	2.8794169	4105.2215	15.347919	1991-2014 –> 2015-2019	5.2907644	21279.885
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	826	3.1761584	4265.2573	12.392938	1991-2014 –> 2015-2019	5.3961769	20820.871
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	826	2.9050667	4119.8724	14.809197	1991-2014 –> 2015-2019	4.9917169	20215.049
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	5157	2.7500121	25078.6292	13.726799	1982-1990 –> 1991-2014	5.1173390	33408.623
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5157	2.7076980	24920.6951	14.283002	1982-1990 –> 1991-2014	4.7553820	32723.539
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	5157	2.4686086	23967.2264	15.019467	1982-1990 –> 1991-2014	4.7797909	32211.660
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5157	2.3773223	23580.5957	14.669631	1982-1990 –> 1991-2014	4.3087512	31172.216
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5157	2.9980522	25973.3203	15.681982	1982-1990 –> 1991-2014	5.0926535	33860.805
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1072	3.2539734	5585.8602	14.985024	1991-2014 –> 2015-2019	6.0866911	30974.106
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	1072	3.4913525	5732.8243	14.794275	1991-2014 –> 2015-2019	6.2413646	30811.453
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1072	3.4866881	5731.9580	14.513260	1991-2014 –> 2015-2019	6.1943861	30652.653
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	1072	2.9351550	5362.7782	15.988010	1991-2014 –> 2015-2019	5.4037636	29330.005
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1072	2.9347624	5364.4914	15.956338	1991-2014 –> 2015-2019	5.3120846	28945.087
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	1798	1.9632966	7540.4545	13.814538	1982-1990 –> 1991-2014	4.0157042	10472.897
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1798	1.9129872	7449.1058	14.706514	1982-1990 –> 1991-2014	3.9231962	10355.170
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1798	1.9249308	7469.4875	12.924585	1982-1990 –> 1991-2014	3.6233666	10143.338
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	1798	1.7788535	7185.6877	12.707965	1982-1990 –> 1991-2014	3.6428524	9986.599
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1798	1.5988572	6804.0667	13.326789	1982-1990 –> 1991-2014	3.2697013	9457.544
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	388	1.9377000	1626.4216	12.861648	1991-2014 –> 2015-2019	3.9009966	9166.876
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	388	1.9240349	1622.9297	13.214866	1991-2014 –> 2015-2019	3.8370221	9072.036
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	388	2.4064533	1794.5438	11.603279	1991-2014 –> 2015-2019	4.3313842	9264.031
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	388	1.7783613	1559.8336	11.935868	1991-2014 –> 2015-2019	3.5572149	8745.521
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	388	1.6657663	1511.0776	12.251134	1991-2014 –> 2015-2019	3.2646235	8315.144
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1846	3.3161267	9676.6813	39.654130	1982-1990 –> 1991-2014	6.1933002	12818.025
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1846	3.3139048	9674.2067	49.157410	1982-1990 –> 1991-2014	6.1000285	12774.904
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1846	3.3069740	9668.4770	46.300562	1982-1990 –> 1991-2014	6.0910062	12770.225
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1846	3.1543325	9492.0053	24.179391	1982-1990 –> 1991-2014	6.0650918	12648.019
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1846	3.1235955	9457.8527	23.883862	1982-1990 –> 1991-2014	5.9935225	12598.009
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	410	3.5342728	2210.7858	23.010237	1991-2014 –> 2015-2019	6.8503996	11887.467
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	410	3.0920214	2101.1661	20.417292	1991-2014 –> 2015-2019	6.4059262	11775.373
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	410	3.0009171	2078.6423	20.359135	1991-2014 –> 2015-2019	6.3078911	11747.119
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	410	3.4823993	2198.6612	22.611128	1991-2014 –> 2015-2019	6.6367318	11690.667
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	410	3.4676728	2197.1862	22.301119	1991-2014 –> 2015-2019	6.5912683	11655.039
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2233	4.7693006	13325.7632	25.970236	1982-1990 –> 1991-2014	9.4903802	18406.248
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2233	4.6961681	13258.7510	25.199285	1982-1990 –> 1991-2014	9.3288340	18308.984
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2233	4.1218059	12674.1368	23.182302	1982-1990 –> 1991-2014	8.1736376	17493.828
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2233	3.7552909	12260.2378	28.317404	1982-1990 –> 1991-2014	7.5088933	16951.500
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2233	4.7510773	13310.6662	22.489256	1982-1990 –> 1991-2014	9.4174969	18373.284
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	460	4.1127155	2618.3803	23.347732	1991-2014 –> 2015-2019	8.8820161	15944.143
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	460	4.0167547	2598.6598	22.883115	1991-2014 –> 2015-2019	8.7129228	15857.411
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	460	3.4687913	2461.7252	15.116927	1991-2014 –> 2015-2019	7.5905972	15135.862
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	460	3.0480487	2344.7649	16.197499	1991-2014 –> 2015-2019	6.8033396	14605.003
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	460	4.1844332	2636.2850	24.305825	1991-2014 –> 2015-2019	8.9355105	15946.951
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1452	1.0913755	4386.5198	11.296660	1982-1990 –> 1991-2014	2.0055753	5836.749
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1452	1.0144309	4174.2052	8.300201	1982-1990 –> 1991-2014	1.8560074	5534.875
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1452	1.0027386	4142.5395	7.631696	1982-1990 –> 1991-2014	1.8436861	5504.400
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1452	1.0455690	4262.0033	11.521015	1982-1990 –> 1991-2014	1.9553590	5707.001
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1452	0.9575190	4008.5357	12.592388	1982-1990 –> 1991-2014	1.7831768	5350.543
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	321	1.2664670	1074.6189	11.543084	1991-2014 –> 2015-2019	2.3578425	5461.139
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	321	1.1416732	1008.0203	7.946765	1991-2014 –> 2015-2019	2.1561041	5182.225
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	321	1.0609196	962.9239	6.432098	1991-2014 –> 2015-2019	2.0636582	5105.463
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	321	1.2025847	1041.3903	12.216957	1991-2014 –> 2015-2019	2.2481537	5303.394
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	321	1.1680948	1024.7087	12.938304	1991-2014 –> 2015-2019	2.1256138	5033.244
Atlantic	(28.1,28.15]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1681	0.8020092	4040.6957	10.234036	1982-1990 –> 1991-2014	1.4492943	5410.574
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1681	0.7955252	4015.4048	6.805246	1982-1990 –> 1991-2014	1.4626648	5428.977
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1681	0.7354492	3749.4170	6.172766	1982-1990 –> 1991-2014	1.3754610	5103.701
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1681	0.7151105	3657.1316	6.149630	1982-1990 –> 1991-2014	1.3064060	4904.160
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1681	0.7012166	3591.1684	10.505609	1982-1990 –> 1991-2014	1.2740214	4794.353
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	357	1.0044822	1030.3153	6.762019	1991-2014 –> 2015-2019	1.8000075	5045.720
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	357	0.9124974	959.7411	6.058897	1991-2014 –> 2015-2019	1.6479467	4709.158
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	357	0.9122466	961.5449	6.061880	1991-2014 –> 2015-2019	1.6273571	4618.676
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	357	1.0291394	1045.6303	11.372665	1991-2014 –> 2015-2019	1.8317057	5088.661
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	357	0.9656260	1002.1473	11.485840	1991-2014 –> 2015-2019	1.6668426	4593.316
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2895	0.6351539	5599.6429	6.617855	1982-1990 –> 1991-2014	1.1027395	7075.420
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2895	0.6237294	5496.5502	7.684933	1982-1990 –> 1991-2014	1.0577785	6808.956
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2895	0.7005408	6166.9780	11.171208	1982-1990 –> 1991-2014	1.1613097	7610.123
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	2895	0.6899008	6078.3630	11.858579	1982-1990 –> 1991-2014	1.1299717	7419.384
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2895	0.6898771	6080.1641	11.900029	1982-1990 –> 1991-2014	1.1246070	7396.052
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	577	0.6751002	1196.0552	2.128076	1991-2014 –> 2015-2019	1.3102541	6795.698
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	577	0.6367983	1130.6522	1.963683	1991-2014 –> 2015-2019	1.2605277	6627.202
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	577	0.7156504	1263.3688	2.327378	1991-2014 –> 2015-2019	1.4161913	7430.347
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	577	0.6800742	1204.5265	2.284496	1991-2014 –> 2015-2019	1.3699750	7282.889
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	577	0.6626252	1176.5313	2.352024	1991-2014 –> 2015-2019	1.3525023	7256.695
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	4966	0.3540822	3791.2358	3.366024	1982-1990 –> 1991-2014	0.6279599	4265.977
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	4966	0.3454367	3547.7197	2.132448	1982-1990 –> 1991-2014	0.6189923	4020.046
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	4966	0.3510484	3707.7711	2.443183	1982-1990 –> 1991-2014	0.6247137	4181.601
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4966	0.3408491	3416.9331	2.868623	1982-1990 –> 1991-2014	0.6085809	3810.520
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4966	0.5641655	8421.7457	10.759763	1982-1990 –> 1991-2014	0.9490573	10177.219
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	1119	0.4312848	1303.4562	2.458907	1991-2014 –> 2015-2019	0.7853670	5094.692
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1119	0.4111185	1198.2850	2.439762	1991-2014 –> 2015-2019	0.7565552	4746.005
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	1119	0.4243147	1268.9919	2.481994	1991-2014 –> 2015-2019	0.7753631	4976.763
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1119	0.4036559	1159.2877	2.464821	1991-2014 –> 2015-2019	0.7445050	4576.221
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1119	0.6622974	2267.4375	3.700595	1991-2014 –> 2015-2019	1.2264629	10689.183
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	9682	6.3357720	63238.3686	30.583791	1982-1990 –> 1991-2014	12.8487055	86859.232
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	9682	6.2826960	63077.4692	30.088806	1982-1990 –> 1991-2014	12.7518171	86651.937
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	9682	7.3183138	66032.0431	31.865284	1982-1990 –> 1991-2014	14.8161830	90664.650
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	9682	7.3941920	66231.7804	29.848080	1982-1990 –> 1991-2014	14.9474321	90917.142
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	9682	7.5062285	66520.9823	29.068724	1982-1990 –> 1991-2014	15.1884533	91325.751
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2030	5.8246152	12926.9878	17.898043	1991-2014 –> 2015-2019	12.1603872	76165.356
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2030	5.7529203	12878.7033	17.937836	1991-2014 –> 2015-2019	12.0356163	75956.173
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2030	6.8332763	13577.4157	22.857113	1991-2014 –> 2015-2019	14.1515901	79609.459
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2030	6.8945420	13613.6546	22.139530	1991-2014 –> 2015-2019	14.2887340	79845.435
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2030	7.0324952	13692.0893	22.299311	1991-2014 –> 2015-2019	14.5387237	80213.072
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	10181	4.7623662	60684.3089	42.834511	1982-1990 –> 1991-2014	9.4337794	83621.648
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	10181	4.3923698	59039.5168	44.800735	1982-1990 –> 1991-2014	8.6474833	81256.029
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	10181	4.5738978	59864.1139	48.951685	1982-1990 –> 1991-2014	9.0229643	82425.798
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	10181	4.7543070	60649.8219	41.564739	1982-1990 –> 1991-2014	9.3844962	83518.519
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	10181	4.7487443	60627.9837	42.175668	1982-1990 –> 1991-2014	9.3775599	83496.383
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2102	4.8234643	12592.1797	38.721833	1991-2014 –> 2015-2019	9.5858305	73276.489
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2102	4.5030555	12305.2126	44.909536	1991-2014 –> 2015-2019	8.8954253	71344.729
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2102	4.6064664	12400.6639	43.468136	1991-2014 –> 2015-2019	9.1803642	72264.778
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	2102	4.8376270	12604.5054	35.243135	1991-2014 –> 2015-2019	9.5919340	73254.327
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2102	4.8199225	12591.0916	37.796306	1991-2014 –> 2015-2019	9.5686668	73219.075
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	8419	4.1013445	47667.8063	22.612674	1982-1990 –> 1991-2014	7.8694431	64971.022
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	8419	3.9675083	47111.1789	20.124177	1982-1990 –> 1991-2014	7.5263664	64056.585
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	8419	4.1090842	47701.5517	37.670707	1982-1990 –> 1991-2014	7.9029437	65049.678
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	8419	4.0110840	47295.1050	23.270512	1982-1990 –> 1991-2014	7.7202964	64501.121
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	8419	4.1128271	47714.8820	37.173326	1982-1990 –> 1991-2014	8.0401191	65278.707
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1711	4.4364980	9965.9268	23.642868	1991-2014 –> 2015-2019	8.5378425	57633.733
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1711	4.3115843	9870.1948	23.468371	1991-2014 –> 2015-2019	8.2790925	56981.374
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1711	4.3533536	9903.1866	30.751376	1991-2014 –> 2015-2019	8.4624378	57604.738
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1711	4.3020551	9862.6233	21.657742	1991-2014 –> 2015-2019	8.3131390	57157.728
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	1711	4.3805774	9922.5195	34.223910	1991-2014 –> 2015-2019	8.4934045	57637.401
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	9983	4.4326724	58071.9538	18.312081	1982-1990 –> 1991-2014	8.2225993	78619.547
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	9983	4.1834150	56916.4261	21.387704	1982-1990 –> 1991-2014	7.6520827	76802.887
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	9983	4.1677886	56843.7075	20.495882	1982-1990 –> 1991-2014	7.6241626	76705.667
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	9983	4.1082617	56554.4846	22.096742	1982-1990 –> 1991-2014	7.5920723	76473.459
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	9983	4.0748418	56393.4011	20.483095	1982-1990 –> 1991-2014	7.5366191	76267.020
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2038	4.8846870	12260.5583	17.949083	1991-2014 –> 2015-2019	9.3173594	70332.512
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2038	4.6621122	12070.4675	19.567208	1991-2014 –> 2015-2019	8.8455271	68986.894
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2038	4.6496425	12061.5509	18.753486	1991-2014 –> 2015-2019	8.8174311	68905.258
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2038	4.5822019	11999.9977	16.144415	1991-2014 –> 2015-2019	8.6904636	68554.482
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2038	4.5578519	11980.2800	17.365499	1991-2014 –> 2015-2019	8.6326938	68373.681
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	11834	4.3374785	68323.3324	35.609176	1982-1990 –> 1991-2014	7.6043485	91484.376
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	11834	4.2839531	68031.4470	38.131627	1982-1990 –> 1991-2014	7.4422106	90893.768
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	11834	4.1109470	67055.7860	43.672039	1982-1990 –> 1991-2014	7.0077363	89149.510
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	11834	4.2917010	68072.2139	42.731701	1982-1990 –> 1991-2014	7.4957610	91060.594
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	11834	3.8409175	65447.7318	28.428207	1982-1990 –> 1991-2014	6.8453114	87865.846
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2492	5.1797276	15281.4360	34.389108	1991-2014 –> 2015-2019	9.5172061	83604.768
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2492	5.1268059	15232.2521	36.702709	1991-2014 –> 2015-2019	9.4107590	83263.699
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2492	4.9812685	15088.7216	41.007621	1991-2014 –> 2015-2019	9.0922154	82144.508
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2492	5.1671995	15269.3666	42.648953	1991-2014 –> 2015-2019	9.4589004	83341.581
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2492	4.5560825	14644.0420	27.382998	1991-2014 –> 2015-2019	8.3970000	80091.774
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	10730	3.3485267	56399.2697	32.223299	1982-1990 –> 1991-2014	6.0432043	75251.527
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	10730	3.5816330	57843.4934	32.193147	1982-1990 –> 1991-2014	6.3895220	77017.413
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	10730	3.5975737	57936.7928	31.699283	1982-1990 –> 1991-2014	6.4084439	77117.006
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	10730	3.5579309	57701.0058	33.237855	1982-1990 –> 1991-2014	6.3849210	76927.915
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	10730	3.3214847	56225.2596	33.410846	1982-1990 –> 1991-2014	5.9786969	74968.084
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2228	4.0580440	12578.3141	31.954794	1991-2014 –> 2015-2019	7.4065706	68977.584
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2228	4.3731039	12911.4980	32.992534	1991-2014 –> 2015-2019	7.9547370	70754.991
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	2228	4.4198370	12956.8643	31.533857	1991-2014 –> 2015-2019	8.0174107	70893.657
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2228	4.3082666	12844.9370	32.622370	1991-2014 –> 2015-2019	7.8661975	70545.943
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2228	3.8900060	12389.8682	34.380147	1991-2014 –> 2015-2019	7.2114907	68615.128
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	10806	3.0537537	54807.1218	30.553558	1982-1990 –> 1991-2014	5.0847796	71806.919
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	10806	3.0522422	54796.4217	32.203765	1982-1990 –> 1991-2014	5.1024941	71871.441
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	10806	3.1555075	55513.5148	29.651791	1982-1990 –> 1991-2014	5.2135179	72616.690
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	10806	3.1598324	55543.1161	30.027069	1982-1990 –> 1991-2014	5.2677058	72837.427
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	10806	3.1983702	55805.1051	29.029922	1982-1990 –> 1991-2014	5.2676435	72951.855
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2247	3.9976483	12618.0737	24.999766	1991-2014 –> 2015-2019	7.0514021	67425.196
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2247	3.8351836	12431.6223	10.833538	1991-2014 –> 2015-2019	6.8874258	67228.044
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	2247	4.1595818	12794.5228	23.535439	1991-2014 –> 2015-2019	7.3150893	68308.038
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	2247	4.2544544	12895.8713	32.118875	1991-2014 –> 2015-2019	7.4142868	68438.987
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2247	4.0489791	12675.4105	19.554817	1991-2014 –> 2015-2019	7.2553457	68536.481
Indo-Pacific	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4260	2.6051555	20259.1913	24.652727	1982-1990 –> 1991-2014	4.2583900	26151.508
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4260	2.6036022	20256.1097	24.952806	1982-1990 –> 1991-2014	4.2356334	26110.927
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4260	2.6047039	20259.7143	25.247303	1982-1990 –> 1991-2014	4.2639326	26165.106
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate	4260	2.6179623	20300.9726	24.216157	1982-1990 –> 1991-2014	4.2821454	26213.488
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4260	2.5354031	20029.9609	24.814201	1982-1990 –> 1991-2014	4.1776173	25903.812
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	922	3.0579229	4691.6276	36.382754	1991-2014 –> 2015-2019	5.6740088	24988.492
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	922	3.1055539	4720.1289	35.090044	1991-2014 –> 2015-2019	5.7091561	24976.239
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	922	3.1449104	4743.3509	33.954853	1991-2014 –> 2015-2019	5.7496143	25003.065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	922	3.0725864	4698.4489	34.402860	1991-2014 –> 2015-2019	5.6863827	24985.853
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	922	3.0364046	4678.6058	31.402096	1991-2014 –> 2015-2019	5.5718078	24708.567
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	5309	2.5668371	25087.6067	30.182329	1982-1990 –> 1991-2014	4.6284820	33896.476
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5309	2.5654989	25084.0697	29.989493	1982-1990 –> 1991-2014	4.6254104	33891.486
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5309	2.5807858	25147.1508	35.369284	1982-1990 –> 1991-2014	4.6922237	34056.010
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + phosphate_star	5309	2.5722729	25108.0686	32.003273	1982-1990 –> 1991-2014	4.6429213	33932.831
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	5309	2.5702526	25101.7257	31.637318	1982-1990 –> 1991-2014	4.6396366	33925.980
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1097	3.4259098	5826.7705	31.197717	1991-2014 –> 2015-2019	5.9927469	30914.377
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	1097	3.4213687	5823.8604	30.819141	1991-2014 –> 2015-2019	5.9938100	30934.624
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1097	3.4058252	5815.8702	30.764342	1991-2014 –> 2015-2019	5.9713241	30899.940
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + phosphate_star	1097	3.4339878	5829.9377	33.280103	1991-2014 –> 2015-2019	6.0062607	30938.006
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	1097	3.4091222	5815.9931	32.021227	1991-2014 –> 2015-2019	5.9793748	30917.719
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4586	2.1812140	20179.5782	8.166104	1982-1990 –> 1991-2014	4.0282687	27476.169
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4586	2.1379896	19997.9948	8.949083	1982-1990 –> 1991-2014	4.0658894	27450.120
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4586	2.1340646	19981.1408	8.674285	1982-1990 –> 1991-2014	3.9532668	27225.275
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4586	2.1895679	20216.6395	8.037144	1982-1990 –> 1991-2014	4.0437604	27529.053
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4586	2.1061976	19860.5825	7.765903	1982-1990 –> 1991-2014	3.9226533	27099.302
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate_star	986	2.4382660	4567.7650	8.209457	1991-2014 –> 2015-2019	4.6027272	24676.626
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	986	2.4323280	4564.9567	8.377699	1991-2014 –> 2015-2019	4.5703176	24562.951
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	986	2.5002629	4619.2795	8.378546	1991-2014 –> 2015-2019	4.6343275	24600.420
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	986	2.4894027	4608.6952	8.844160	1991-2014 –> 2015-2019	4.6714034	24791.581
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	986	2.4497862	4579.0603	8.657077	1991-2014 –> 2015-2019	4.5559838	24439.643
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	3263	1.8690111	13353.4151	8.710475	1982-1990 –> 1991-2014	3.3994600	18153.736
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3263	1.8089790	13142.3616	8.857639	1982-1990 –> 1991-2014	3.3135675	17900.442
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	3263	1.8748441	13373.7505	8.849840	1982-1990 –> 1991-2014	3.4383664	18229.574
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3263	1.8307351	13220.3799	9.821157	1982-1990 –> 1991-2014	3.3458588	17996.575
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3263	1.8002711	13110.8713	8.504391	1982-1990 –> 1991-2014	3.3260671	17905.288
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	677	2.0488347	2904.4280	8.825797	1991-2014 –> 2015-2019	3.9256783	16285.135
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	677	2.0489747	2906.5205	9.016007	1991-2014 –> 2015-2019	3.9243558	16284.140
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	677	1.9929778	2869.0017	8.610574	1991-2014 –> 2015-2019	3.8019569	16011.363
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	677	2.0391799	2900.0324	8.467085	1991-2014 –> 2015-2019	3.8699150	16120.412
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	677	1.9232619	2820.7895	6.757174	1991-2014 –> 2015-2019	3.7235330	15931.661
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	27122	1.4027036	95337.1527	13.674494	1982-1990 –> 1991-2014	2.6288396	128094.139
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	27122	1.3045930	91405.9010	16.121120	1982-1990 –> 1991-2014	2.4237594	122322.965
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	27122	1.3229805	92165.0990	13.015308	1982-1990 –> 1991-2014	2.3788879	121908.134
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	27122	1.3659606	93899.3208	16.927242	1982-1990 –> 1991-2014	2.5534529	126012.126
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	27122	1.5219023	99761.2715	17.446244	1982-1990 –> 1991-2014	2.7775521	132998.198
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5555	1.6233951	21161.4208	9.689660	1991-2014 –> 2015-2019	3.1230324	120125.255
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	5555	1.5730131	20809.1588	10.335174	1991-2014 –> 2015-2019	2.9757167	116146.312
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5555	1.5004212	20286.2438	12.496018	1991-2014 –> 2015-2019	2.8050143	111692.145
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5555	1.5822876	20876.4711	10.782557	1991-2014 –> 2015-2019	2.9052681	113041.570
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5555	1.5619408	20732.6801	13.601766	1991-2014 –> 2015-2019	2.9279014	114632.001

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]	1982-1990 –> 1991-2014	2.4659147	1318.671
Atlantic	(-Inf,26]	1991-2014 –> 2015-2019	2.8401256	1160.549
Atlantic	(26,26.5]	1982-1990 –> 1991-2014	7.7971914	15364.349
Atlantic	(26,26.5]	1991-2014 –> 2015-2019	8.0043213	13244.290
Atlantic	(26.5,26.75]	1982-1990 –> 1991-2014	6.2005510	17995.699
Atlantic	(26.5,26.75]	1991-2014 –> 2015-2019	6.7061180	15778.833
Atlantic	(26.75,27]	1982-1990 –> 1991-2014	3.5697418	24184.681
Atlantic	(26.75,27]	1991-2014 –> 2015-2019	4.4952471	22659.297
Atlantic	(27,27.25]	1982-1990 –> 1991-2014	3.7817719	20753.585
Atlantic	(27,27.25]	1991-2014 –> 2015-2019	4.3709914	19459.594
Atlantic	(27.25,27.5]	1982-1990 –> 1991-2014	4.4806618	23272.701
Atlantic	(27.25,27.5]	1991-2014 –> 2015-2019	5.4019952	21242.724
Atlantic	(27.5,27.75]	1982-1990 –> 1991-2014	4.8107833	32675.369
Atlantic	(27.5,27.75]	1991-2014 –> 2015-2019	5.8476580	30142.661
Atlantic	(27.75,27.85]	1982-1990 –> 1991-2014	3.6949641	10083.110
Atlantic	(27.75,27.85]	1991-2014 –> 2015-2019	3.7782482	8912.722
Atlantic	(27.85,27.95]	1982-1990 –> 1991-2014	6.0885898	12721.837
Atlantic	(27.85,27.95]	1991-2014 –> 2015-2019	6.5584434	11751.133
Atlantic	(27.95,28.05]	1982-1990 –> 1991-2014	8.7838484	17906.769
Atlantic	(27.95,28.05]	1991-2014 –> 2015-2019	8.1848772	15497.874
Atlantic	(28.05,28.1]	1982-1990 –> 1991-2014	1.8887609	5586.714
Atlantic	(28.05,28.1]	1991-2014 –> 2015-2019	2.1902745	5217.093
Atlantic	(28.1,28.15]	1982-1990 –> 1991-2014	1.3735695	5128.353
Atlantic	(28.1,28.15]	1991-2014 –> 2015-2019	1.7147719	4811.106
Atlantic	(28.15,28.2]	1982-1990 –> 1991-2014	1.1152813	7261.987
Atlantic	(28.15,28.2]	1991-2014 –> 2015-2019	1.3418901	7078.566
Atlantic	(28.2, Inf]	1982-1990 –> 1991-2014	0.6858608	5291.073
Atlantic	(28.2, Inf]	1991-2014 –> 2015-2019	0.8576507	6016.573
Indo-Pacific	(-Inf,26]	1982-1990 –> 1991-2014	14.1105182	89283.742
Indo-Pacific	(-Inf,26]	1991-2014 –> 2015-2019	13.4350103	78357.899
Indo-Pacific	(26,26.5]	1982-1990 –> 1991-2014	9.1732566	82863.675
Indo-Pacific	(26,26.5]	1991-2014 –> 2015-2019	9.3644442	72671.880
Indo-Pacific	(26.5,26.75]	1982-1990 –> 1991-2014	7.8118337	64771.423
Indo-Pacific	(26.5,26.75]	1991-2014 –> 2015-2019	8.4171833	57402.995
Indo-Pacific	(26.75,27]	1982-1990 –> 1991-2014	7.7255072	76973.716
Indo-Pacific	(26.75,27]	1991-2014 –> 2015-2019	8.8606950	69030.566
Indo-Pacific	(27,27.25]	1982-1990 –> 1991-2014	7.2790736	90090.819
Indo-Pacific	(27,27.25]	1991-2014 –> 2015-2019	9.1752162	82489.266
Indo-Pacific	(27.25,27.5]	1982-1990 –> 1991-2014	6.2409576	76256.389
Indo-Pacific	(27.25,27.5]	1991-2014 –> 2015-2019	7.6912813	69957.461
Indo-Pacific	(27.5,27.75]	1982-1990 –> 1991-2014	5.1872282	72416.866
Indo-Pacific	(27.5,27.75]	1991-2014 –> 2015-2019	7.1847099	67987.349
Indo-Pacific	(27.75,27.85]	1982-1990 –> 1991-2014	4.2435437	26108.968
Indo-Pacific	(27.75,27.85]	1991-2014 –> 2015-2019	5.6781939	24932.443
Indo-Pacific	(27.85,27.95]	1982-1990 –> 1991-2014	4.6457348	33940.557
Indo-Pacific	(27.85,27.95]	1991-2014 –> 2015-2019	5.9887033	30920.933
Indo-Pacific	(27.95,28.05]	1982-1990 –> 1991-2014	4.0027677	27355.984
Indo-Pacific	(27.95,28.05]	1991-2014 –> 2015-2019	4.6069519	24614.244
Indo-Pacific	(28.05,28.1]	1982-1990 –> 1991-2014	3.3646639	18037.123
Indo-Pacific	(28.05,28.1]	1991-2014 –> 2015-2019	3.8490878	16126.542
Indo-Pacific	(28.1, Inf]	1982-1990 –> 1991-2014	2.5524984	126267.112
Indo-Pacific	(28.1, Inf]	1991-2014 –> 2015-2019	2.9473866	115127.456

5.4 Target variable coefficients

A data frame to map the target variable is prepared.

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

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

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

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

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.5 Plot selected model residuals

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

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

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

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

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

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

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

5.6 Cant coeffcients

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

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

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

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

5.7 Write files

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

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

6 Model diagnotics

6.1 Selection criterion vs predictors

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

6.1.1 All models

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

Past versions of eMLR_predictor_model_quality_all-1.png

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

6.1.2 Best models

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

Past versions of eMLR_predictor_model_quality_best-1.png

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

6.2 RMSE correlation between eras

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

6.2.1 All models

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

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

Past versions of rmse_correlation_across_eras_all_models-1.png

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

rm(max_rmse)

6.2.2 Best models

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

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

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
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 - 1982-1990 --> 1991-2014
(-Inf,26]	5	1	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	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	53.00	28.00
Atlantic - 1991-2014 --> 2015-2019
(-Inf,26]	5	0	4	5	3	3	2
(26,26.5]	5	3	2	4	1	4	4
(26.5,26.75]	5	1	4	4	2	5	2
(26.75,27]	5	1	4	4	2	5	2
(27,27.25]	5	2	2	4	4	5	1
(27.25,27.5]	5	5	0	3	2	5	2
(27.5,27.75]	5	1	4	3	5	3	0
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	3	5	2	3	3
(28.05,28.1]	5	0	5	5	2	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	28.00	40.00	57.00	39.00	52.00	26.00
Indo-Pacific - 1982-1990 --> 1991-2014
(-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]	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	2	3	5	2	5	2
(28.05,28.1]	4	1	4	4	3	5	2
(28.1, Inf]	4	2	3	4	2	5	3
total	52.00	19.00	39.00	56.00	23.00	54.00	31.00
Indo-Pacific - 1991-2014 --> 2015-2019
(-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]	5	2	3	5	2	4	3
(27.85,27.95]	3	5	0	4	0	3	5
(27.95,28.05]	5	2	3	5	3	3	2
(28.05,28.1]	5	2	3	5	2	5	2
(28.1, Inf]	5	2	3	4	3	5	2
total	55.00	22.00	36.00	57.00	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)

Past versions of aic_vs_rmse_all_models-1.png

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

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

Past versions of aic_vs_rmse_selected_models-1.png

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

Session information

sessionInfo()

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

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

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

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

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

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