eMLR - model fitting

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Last updated: 2021-03-03

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Knit directory: emlr_mod_v_XXX/

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---

1 Required data

Required are:

• cleaned and prepared GLODAP-based synthetic model subsetting file

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

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

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

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

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

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

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

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

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

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

# convert to tibble
lm_all <- as_tibble(lm_all)

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

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

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

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

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


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

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

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

3 Apply predictor threshold

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

• Minimum: 3
  
• Maximum: 9

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

This results in a total number of MLR models of:

• 45

4 Fit all models

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

• cstar_tref

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

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

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

5 Prepare coeffcients

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

5.1 Formatting

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

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

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

5.2 Predictor selection

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

• 5

The criterion used to select the best models was:

• aic

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

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

# remove models with predictors fitted as NA

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

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

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

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

5.3 RMSE tables

5.3.1 per model

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

basin	gamma_slab	model	nr_obs	rmse	aic	resid_max	eras	rmse_sum	aic_sum
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate_star	138	1.5621609	526.7424	6.535028	1982-1999 –> 2000-2010	3.2518625	1347.2344
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	138	1.0341977	412.9078	4.179751	1982-1999 –> 2000-2010	2.3705461	1135.8016
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	138	1.0338079	414.8038	4.140896	1982-1999 –> 2000-2010	2.3695004	1139.4933
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	138	1.4508864	506.3472	7.012112	1982-1999 –> 2000-2010	3.1131566	1320.0303
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	138	1.4369443	505.6822	6.608482	1982-1999 –> 2000-2010	3.0984327	1321.1696
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	92	1.2425411	313.0419	3.684842	2000-2010 –> 2011-2019	2.2767388	725.9497
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	92	1.1737104	304.5560	3.337674	2000-2010 –> 2011-2019	2.2075183	719.3597
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate_star	92	1.7091191	371.7047	4.482545	2000-2010 –> 2011-2019	3.2709906	898.3959
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	92	1.5863943	357.9940	6.073868	2000-2010 –> 2011-2019	3.0372808	864.3413
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	92	1.5384000	354.3414	5.490783	2000-2010 –> 2011-2019	2.9753443	860.0236
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	903	3.5569805	4868.2581	13.513007	1982-1999 –> 2000-2010	7.0037255	12984.1830
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	903	4.2332931	5180.6252	10.528465	1982-1999 –> 2000-2010	8.3917062	13867.0450
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	903	4.0489733	5100.2278	12.346901	1982-1999 –> 2000-2010	8.1333495	13731.8558
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	903	4.0372383	5096.9859	12.952352	1982-1999 –> 2000-2010	8.1188942	13728.5819
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	903	4.3331358	5224.7254	13.107752	1982-1999 –> 2000-2010	8.5682351	13968.8786
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	710	3.5876836	3842.9523	11.056693	2000-2010 –> 2011-2019	7.1446642	8711.2104
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	710	4.0777394	4022.7635	12.865584	2000-2010 –> 2011-2019	8.3110326	9203.3887
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	710	3.9167692	3965.5721	16.808870	2000-2010 –> 2011-2019	7.9657425	9065.7998
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	710	3.9000219	3961.4874	18.379640	2000-2010 –> 2011-2019	7.9372602	9058.4733
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	710	4.1918274	4063.9469	11.602249	2000-2010 –> 2011-2019	8.5249632	9288.6724
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1185	3.2352167	6157.4917	10.813474	1982-1999 –> 2000-2010	6.3338302	15843.7868
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	1185	3.2467194	6165.9031	9.916606	1982-1999 –> 2000-2010	6.3936674	15910.9231
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1185	3.1712045	6112.1286	10.266114	1982-1999 –> 2000-2010	6.2303546	15751.7936
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1185	3.2452216	6166.8096	10.029110	1982-1999 –> 2000-2010	6.3899646	15911.1701
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1185	3.1158141	6070.3668	9.939754	1982-1999 –> 2000-2010	6.0988478	15614.4369
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	868	3.6003392	4699.1420	11.802729	2000-2010 –> 2011-2019	6.8355559	10856.6337
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	868	3.5314345	4665.5957	11.416965	2000-2010 –> 2011-2019	6.7781539	10831.4988
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	868	3.5028068	4653.4654	11.671917	2000-2010 –> 2011-2019	6.6740113	10765.5940
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	868	3.5201255	4662.0275	9.397928	2000-2010 –> 2011-2019	6.7653472	10828.8370
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	868	3.4940939	4649.1419	11.129108	2000-2010 –> 2011-2019	6.6099080	10719.5087
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2007	2.0756941	8639.0257	14.498483	1982-1999 –> 2000-2010	3.7482314	20792.0266
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2007	1.9862990	8464.3195	13.838369	1982-1999 –> 2000-2010	3.6392879	20545.4882
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2007	2.1812067	8840.0506	15.840559	1982-1999 –> 2000-2010	3.9768728	21441.1462
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	2007	2.1781623	8832.4442	15.001238	1982-1999 –> 2000-2010	3.9657538	21403.2367
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2007	2.0727203	8635.2710	16.865464	1982-1999 –> 2000-2010	3.5861696	20162.5823
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1654	2.5494966	7801.7924	27.697323	2000-2010 –> 2011-2019	4.6251906	16440.8181
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	1654	2.4887515	7722.0208	24.985488	2000-2010 –> 2011-2019	4.6734377	16566.4695
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1654	2.4378718	7655.6917	26.094232	2000-2010 –> 2011-2019	4.4241708	16120.0111
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1654	2.5970570	7864.9341	23.518921	2000-2010 –> 2011-2019	4.7782637	16704.9847
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1654	2.1639596	7261.4252	22.660033	2000-2010 –> 2011-2019	4.2366800	15896.6962
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1718	2.0725267	7393.5213	9.772313	1982-1999 –> 2000-2010	4.3068081	19015.2868
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1718	1.8811325	7058.5918	9.293604	1982-1999 –> 2000-2010	3.5975076	17301.2894
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1718	1.8537326	7010.1762	9.767083	1982-1999 –> 2000-2010	3.4237181	16789.3421
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1718	2.0295409	7321.5066	13.600022	1982-1999 –> 2000-2010	3.7061196	17443.6995
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1718	2.2806548	7722.3263	13.827815	1982-1999 –> 2000-2010	4.3570770	18961.4584
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1455	2.2352316	6483.7546	11.845042	2000-2010 –> 2011-2019	4.3077582	13877.2759
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1455	2.2644017	6519.4849	13.764140	2000-2010 –> 2011-2019	4.1455342	13578.0768
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1455	2.2629528	6519.6223	13.921405	2000-2010 –> 2011-2019	4.1166854	13529.7985
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	1455	2.3287999	6601.0886	15.070391	2000-2010 –> 2011-2019	4.4437747	14062.2728
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1455	2.4732508	6778.2133	19.985420	2000-2010 –> 2011-2019	4.5027917	14099.7199
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1746	2.5146894	8187.0787	13.276443	1982-1999 –> 2000-2010	5.1311935	21902.8349
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1746	2.4441909	8089.7831	12.544299	1982-1999 –> 2000-2010	4.9791595	21625.3166
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1746	2.6274808	8342.2945	21.211260	1982-1999 –> 2000-2010	4.7945288	20975.1987
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1746	2.3305489	7921.5279	11.900975	1982-1999 –> 2000-2010	4.0506284	19222.8227
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1746	2.1999537	7722.1530	15.366013	1982-1999 –> 2000-2010	3.9158524	19011.4402
Atlantic	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	1388	2.9677724	6970.7385	21.519349	2000-2010 –> 2011-2019	5.7216853	15475.1474
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1388	2.9418952	6946.4273	16.058883	2000-2010 –> 2011-2019	5.4565846	15133.5059
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1388	2.7521896	6763.3870	17.076695	2000-2010 –> 2011-2019	5.1963805	14853.1701
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1388	3.0777910	7071.7862	11.915546	2000-2010 –> 2011-2019	5.4083399	14993.3141
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1388	2.7598039	6771.0565	16.780096	2000-2010 –> 2011-2019	4.9597576	14493.2095
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	2382	2.7621827	11610.1481	13.618961	1982-1999 –> 2000-2010	5.2372325	28984.7346
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2382	2.7395207	11572.9013	14.121872	1982-1999 –> 2000-2010	5.0053886	28290.0435
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	2382	2.4448440	11030.7501	13.704940	1982-1999 –> 2000-2010	4.8120289	28074.5694
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2382	2.3786567	10902.0003	14.526193	1982-1999 –> 2000-2010	4.4792246	27055.4408
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2382	3.0563377	12096.2467	16.041191	1982-1999 –> 2000-2010	5.4424987	29201.6932
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate	1937	3.2145883	10032.6349	16.577579	2000-2010 –> 2011-2019	6.0243842	21726.2030
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1937	3.1752800	9986.9713	14.945718	2000-2010 –> 2011-2019	5.9793618	21672.8413
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1937	3.3297137	10168.9495	14.066023	2000-2010 –> 2011-2019	6.0692344	21741.8508
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	1937	2.8098769	9511.3548	15.377731	2000-2010 –> 2011-2019	5.2547209	20542.1050
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1937	2.8042018	9505.5226	15.279124	2000-2010 –> 2011-2019	5.1828584	20407.5228
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	855	1.9005157	3536.4191	13.314813	1982-1999 –> 2000-2010	3.9051640	9130.4540
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	855	1.8423572	3485.2733	14.186977	1982-1999 –> 2000-2010	3.7940048	9010.5702
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	855	1.9476121	3578.2778	12.448725	1982-1999 –> 2000-2010	3.6309090	8711.0670
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	855	1.7125124	3358.2991	12.282404	1982-1999 –> 2000-2010	3.5211896	8680.7497
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	855	1.5238470	3160.7020	12.854686	1982-1999 –> 2000-2010	3.1208919	8156.6289
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	694	2.0171038	2955.3945	12.602743	2000-2010 –> 2011-2019	3.9176195	6491.8136
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	694	2.0083437	2951.3535	12.900020	2000-2010 –> 2011-2019	3.8507009	6436.6267
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	694	2.3686529	3178.3888	11.418228	2000-2010 –> 2011-2019	4.3162650	6756.6666
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	694	1.8392362	2827.2650	11.670593	2000-2010 –> 2011-2019	3.5517485	6185.5640
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	694	1.7303093	2744.5274	12.029848	2000-2010 –> 2011-2019	3.2541563	5905.2293
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	821	3.2700339	4287.3392	34.820621	1982-1999 –> 2000-2010	6.1476320	10914.9293
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	821	3.2604694	4282.5295	30.069446	1982-1999 –> 2000-2010	5.9904767	10769.4343
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	821	3.2505442	4279.5235	28.085684	1982-1999 –> 2000-2010	5.9804223	10768.3018
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	821	2.9167858	4099.6289	21.501124	1982-1999 –> 2000-2010	5.8335914	10763.3794
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	821	2.9057458	4095.4022	21.303891	1982-1999 –> 2000-2010	5.7700012	10712.5740
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	731	3.7755824	4028.8350	24.278071	2000-2010 –> 2011-2019	7.0456163	8316.1743
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	731	3.4079754	3879.0732	31.539245	2000-2010 –> 2011-2019	6.6684448	8161.6028
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	731	3.3293057	3846.9288	30.295708	2000-2010 –> 2011-2019	6.5798499	8126.4523
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	731	3.6982911	3998.5953	22.983455	2000-2010 –> 2011-2019	6.6150769	8098.2242
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	731	3.6706108	3989.6117	24.150702	2000-2010 –> 2011-2019	6.5763566	8085.0139
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1016	4.6609329	6022.9692	26.327926	1982-1999 –> 2000-2010	9.4927923	16071.4267
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1016	4.5787836	5988.8357	25.413868	1982-1999 –> 2000-2010	9.3240605	15978.6838
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1016	4.1596314	5791.7497	22.697412	1982-1999 –> 2000-2010	8.1903611	15232.5434
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1016	3.9731188	5700.5315	24.698690	1982-1999 –> 2000-2010	7.5049281	14700.4016
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1016	4.5626775	5981.6755	21.968274	1982-1999 –> 2000-2010	9.4170465	16047.7123
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	854	4.3591190	4950.1841	24.482101	2000-2010 –> 2011-2019	9.0200518	10973.1533
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	854	4.3034100	4930.2154	24.473348	2000-2010 –> 2011-2019	8.8821937	10919.0512
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	854	3.8115314	4720.9041	22.515294	2000-2010 –> 2011-2019	7.9711628	10512.6537
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	854	3.4333251	4544.4149	26.895103	2000-2010 –> 2011-2019	7.4064439	10244.9464
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	854	4.4106534	4972.2580	22.938388	2000-2010 –> 2011-2019	8.9733309	10953.9335
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	685	1.1739244	2175.6285	10.447220	1982-1999 –> 2000-2010	2.1269926	5137.7401
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	685	1.0543254	2028.4204	7.246283	1982-1999 –> 2000-2010	1.9472148	4850.1704
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	685	1.0206197	1985.9075	6.267908	1982-1999 –> 2000-2010	1.9129753	4808.3708
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	685	1.1180870	2108.8640	10.759600	1982-1999 –> 2000-2010	2.0588959	5043.1151
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	685	1.0592663	2036.8256	11.651813	1982-1999 –> 2000-2010	1.8985432	4727.3194
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	553	1.1578690	1745.4649	7.747201	2000-2010 –> 2011-2019	2.2758741	3856.2286
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	553	1.0938294	1680.5373	9.449358	2000-2010 –> 2011-2019	2.1481548	3708.9577
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	553	1.0491050	1636.3648	8.200998	2000-2010 –> 2011-2019	2.0697247	3622.2723
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	553	1.1005139	1687.2756	13.167362	2000-2010 –> 2011-2019	2.2186009	3796.1397
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	553	1.0518980	1639.3054	13.891084	2000-2010 –> 2011-2019	2.1111643	3676.1309
Atlantic	(28.1,28.15]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	799	0.8736417	2063.5981	9.651179	1982-1999 –> 2000-2010	1.5585504	4770.4120
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	799	0.8422901	2007.1977	6.163232	1982-1999 –> 2000-2010	1.5505862	4802.9758
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	799	0.7731525	1868.3319	5.676689	1982-1999 –> 2000-2010	1.4450278	4525.3851
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	799	0.7583594	1839.4605	5.549422	1982-1999 –> 2000-2010	1.3878123	4329.5891
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	799	0.8001503	1925.1805	9.633101	1982-1999 –> 2000-2010	1.3889400	4242.3443
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	634	0.9257911	1715.4428	7.538886	2000-2010 –> 2011-2019	1.7680812	3722.6405
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	634	0.8400290	1590.1777	6.642030	2000-2010 –> 2011-2019	1.6131814	3458.5096
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	634	0.8391551	1590.8579	6.641684	2000-2010 –> 2011-2019	1.5975145	3430.3184
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	634	0.9112747	1693.4030	11.656765	2000-2010 –> 2011-2019	1.7815510	3750.8334
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	634	0.8256471	1570.2807	12.116337	2000-2010 –> 2011-2019	1.6257974	3495.4612
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1294	0.5909516	2322.8701	2.369480	1982-1999 –> 2000-2010	1.1236880	5845.2763
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1294	0.5407499	2095.1145	2.009350	1982-1999 –> 2000-2010	1.0584487	5492.1606
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1294	0.5919253	2327.1310	2.114490	1982-1999 –> 2000-2010	1.1557145	6101.5324
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1294	0.5610862	2188.6577	2.126762	1982-1999 –> 2000-2010	1.1117371	5858.1782
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1294	0.5486132	2132.4772	2.245858	1982-1999 –> 2000-2010	1.0986624	5799.1345
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1065	0.7329106	2372.4808	5.199994	2000-2010 –> 2011-2019	1.3238622	4695.3509
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1065	0.7275030	2358.7071	5.749767	2000-2010 –> 2011-2019	1.2682529	4453.8215
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1065	0.8596180	2712.1399	9.457165	2000-2010 –> 2011-2019	1.4515433	5039.2709
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1065	0.8514553	2691.8173	10.098604	2000-2010 –> 2011-2019	1.4125415	4880.4751
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1065	0.8513703	2693.6049	10.031960	2000-2010 –> 2011-2019	1.3999836	4826.0821
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	2283	0.3539537	1746.6747	1.941307	1982-1999 –> 2000-2010	0.6602221	3505.6331
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2283	0.3493314	1688.6551	1.914590	1982-1999 –> 2000-2010	0.6512820	3344.2324
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	2283	0.3536404	1744.6316	1.938967	1982-1999 –> 2000-2010	0.6584278	3469.6129
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2283	0.3412651	1583.9865	1.874295	1982-1999 –> 2000-2010	0.6403524	3170.8483
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2283	0.5126025	3441.6225	3.103768	1982-1999 –> 2000-2010	0.9716085	8207.5338
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	1967	0.4147946	2130.2948	2.430540	2000-2010 –> 2011-2019	0.7687482	3876.9695
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1967	0.3962301	1952.1633	2.371006	2000-2010 –> 2011-2019	0.7455615	3640.8184
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	1967	0.4077495	2064.9043	2.421900	2000-2010 –> 2011-2019	0.7613899	3809.5359
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1967	0.3876841	1868.3856	2.430333	2000-2010 –> 2011-2019	0.7289492	3452.3721
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1967	0.6964403	4172.8882	9.154760	2000-2010 –> 2011-2019	1.2090427	7614.5107
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4484	6.2624515	29189.4800	30.122873	1982-1999 –> 2000-2010	12.7919928	76607.3094
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4484	6.2211537	29132.1445	29.691492	1982-1999 –> 2000-2010	12.7000049	76439.8570
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4484	7.1900224	30430.1631	31.792635	1982-1999 –> 2000-2010	14.7183794	79897.6977
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4484	7.3021929	30568.9915	29.394245	1982-1999 –> 2000-2010	14.8863726	80142.8045
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	4484	7.4011572	30687.7157	28.721206	1982-1999 –> 2000-2010	15.1154602	80504.2589
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3620	5.9822711	23236.0290	24.783697	2000-2010 –> 2011-2019	12.2447226	52425.5090
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3620	5.9125324	23153.1324	24.045503	2000-2010 –> 2011-2019	12.1336861	52285.2770
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3620	7.0143253	24390.3058	25.654692	2000-2010 –> 2011-2019	14.2043477	54820.4689
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3620	7.0552862	24432.4615	25.263739	2000-2010 –> 2011-2019	14.3574791	55001.4531
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	3620	7.1801867	24557.5108	24.268755	2000-2010 –> 2011-2019	14.5813439	55245.2264
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4649	4.8024551	27795.0358	41.501394	1982-1999 –> 2000-2010	9.4496392	73388.0407
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4649	4.4408878	27069.2538	44.888541	1982-1999 –> 2000-2010	8.6872605	71273.0705
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4649	4.6481645	27493.4109	49.192612	1982-1999 –> 2000-2010	9.0598064	72286.1436
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	4649	4.8090257	27807.7484	39.710764	1982-1999 –> 2000-2010	9.4287860	73309.4642
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4649	4.7948461	27782.2925	40.888279	1982-1999 –> 2000-2010	9.4145152	73285.7034
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3794	4.9439290	22905.7463	41.470670	2000-2010 –> 2011-2019	9.7463840	50700.7821
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3794	4.6050429	22368.9348	44.026694	2000-2010 –> 2011-2019	9.0459307	49438.1886
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3794	4.7582837	22617.3285	47.149314	2000-2010 –> 2011-2019	9.4064482	50110.7394
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	3794	4.9331516	22889.1871	40.344940	2000-2010 –> 2011-2019	9.7421773	50696.9355
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3794	4.9294606	22885.5075	40.824625	2000-2010 –> 2011-2019	9.7243067	50667.8000
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3848	3.9905621	21582.8924	21.745319	1982-1999 –> 2000-2010	7.9396295	56712.3410
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3848	3.8807513	21370.1483	19.849239	1982-1999 –> 2000-2010	7.6381460	55875.8951
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3848	3.9660697	21537.5120	33.064789	1982-1999 –> 2000-2010	7.9569494	56801.4139
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3848	3.9017846	21411.7473	20.726166	1982-1999 –> 2000-2010	7.7789766	56312.1967
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	3848	3.9664102	21536.1727	32.900429	1982-1999 –> 2000-2010	8.0279408	57018.7608
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3143	4.3952443	18238.0159	24.561008	2000-2010 –> 2011-2019	8.3858064	39820.9083
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3143	4.2668415	18053.6406	24.765936	2000-2010 –> 2011-2019	8.1475928	39423.7890
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3143	4.3240503	18137.3618	31.696967	2000-2010 –> 2011-2019	8.2901199	39674.8738
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3143	4.2646943	18050.4766	22.795115	2000-2010 –> 2011-2019	8.1664789	39462.2239
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	3143	4.3368573	18153.9523	34.262429	2000-2010 –> 2011-2019	8.3032675	39690.1250
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4467	4.4742662	26074.9876	18.384173	1982-1999 –> 2000-2010	8.4712504	68328.0451
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4467	4.2513273	25618.3608	21.539668	1982-1999 –> 2000-2010	7.9391344	66658.8047
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4467	4.2322670	25580.2163	20.575508	1982-1999 –> 2000-2010	7.9061647	66565.7433
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4467	4.1568978	25417.6838	22.680123	1982-1999 –> 2000-2010	7.8370935	66427.0089
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4467	4.1192889	25338.4869	20.988542	1982-1999 –> 2000-2010	7.7717526	66235.8830
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3755	4.9077345	22615.2297	19.517122	2000-2010 –> 2011-2019	9.3820007	48690.2172
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3755	4.6853329	22266.9500	21.537757	2000-2010 –> 2011-2019	8.9366602	47885.3108
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3755	4.6745542	22251.6532	20.722111	2000-2010 –> 2011-2019	8.9068212	47831.8695
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3755	4.5848207	22104.0884	17.762636	2000-2010 –> 2011-2019	8.7417185	47521.7721
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3755	4.5607657	22066.5823	16.916459	2000-2010 –> 2011-2019	8.6800546	47405.0692
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5542	4.3330765	31993.7377	42.631683	1982-1999 –> 2000-2010	7.8988114	79556.2541
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5542	4.1023515	31387.2497	50.065974	1982-1999 –> 2000-2010	7.4690045	77934.3751
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5542	4.3171626	31950.9551	46.277928	1982-1999 –> 2000-2010	7.9252312	79720.0678
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5542	3.9178231	30877.1176	31.968831	1982-1999 –> 2000-2010	7.2206538	77085.9772
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	5542	4.5822791	32611.5406	72.682445	1982-1999 –> 2000-2010	8.0765040	79814.0065
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4394	5.0667861	26741.9784	31.695512	2000-2010 –> 2011-2019	9.4506952	58862.9891
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4394	5.0220198	26665.9892	33.949988	2000-2010 –> 2011-2019	9.3550963	58659.7269
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4394	4.8756983	26406.1379	36.885352	2000-2010 –> 2011-2019	8.9780498	57793.3876
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4394	5.0361214	26688.6309	40.506889	2000-2010 –> 2011-2019	9.3532840	58639.5860
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4394	4.4115113	25526.9337	26.045742	2000-2010 –> 2011-2019	8.3293344	56404.0513
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4967	3.4111729	26299.3116	32.135867	1982-1999 –> 2000-2010	6.3325585	65631.2012
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4967	3.6744463	27037.8673	32.194731	1982-1999 –> 2000-2010	6.7449218	67155.3963
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	4967	3.6889493	27074.9995	31.509697	1982-1999 –> 2000-2010	6.7600796	67193.8945
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4967	3.6017395	26839.3312	32.763063	1982-1999 –> 2000-2010	6.6852283	67023.6147
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4967	3.3185383	26025.8109	33.178319	1982-1999 –> 2000-2010	6.2428316	65373.4031
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4007	3.8895971	22270.8344	30.979101	2000-2010 –> 2011-2019	7.3007701	48570.1460
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4007	4.2014468	22888.9009	32.220987	2000-2010 –> 2011-2019	7.8758930	49926.7682
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	4007	4.2453334	22970.1777	30.526464	2000-2010 –> 2011-2019	7.9342826	50045.1772
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4007	4.1765503	22841.2712	31.079200	2000-2010 –> 2011-2019	7.7782898	49680.6023
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4007	3.7690403	22018.5122	33.027470	2000-2010 –> 2011-2019	7.0875786	48044.3231
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4934	3.1622396	25376.9216	23.467655	1982-1999 –> 2000-2010	5.4762007	61991.4701
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4934	3.1334691	25286.7303	9.803062	1982-1999 –> 2000-2010	5.4770265	62107.2946
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	4934	3.2646972	25689.5776	21.916582	1982-1999 –> 2000-2010	5.6262901	62632.4131
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	4934	3.3053682	25811.7519	28.662766	1982-1999 –> 2000-2010	5.6904705	62915.1587
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	4934	3.3173711	25847.5210	24.791454	1982-1999 –> 2000-2010	5.6945934	62897.2836
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4006	3.9723248	22433.8999	26.174799	2000-2010 –> 2011-2019	7.1345644	47810.8215
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4006	3.8155457	22111.2740	10.753469	2000-2010 –> 2011-2019	6.9490148	47398.0044
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	4006	4.1351566	22753.7714	24.548760	2000-2010 –> 2011-2019	7.3998538	48443.3490
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	4006	4.1639733	22809.4111	32.338700	2000-2010 –> 2011-2019	7.4693415	48621.1630
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4006	4.0318574	22553.0836	20.361122	2000-2010 –> 2011-2019	7.3040861	48267.4000
Indo-Pacific	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1933	2.6958504	9331.5815	20.445281	1982-1999 –> 2000-2010	4.6277393	22352.4905
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1933	2.6952714	9332.7511	20.622527	1982-1999 –> 2000-2010	4.6169952	22322.6241
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1933	2.6957403	9333.4236	20.654923	1982-1999 –> 2000-2010	4.6321579	22370.9948
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate	1933	2.7062245	9346.4300	20.056930	1982-1999 –> 2000-2010	4.6515120	22410.6193
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1933	2.6092118	9207.2966	20.356568	1982-1999 –> 2000-2010	4.5167940	22150.9186
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1648	3.1007702	8420.7415	30.298833	2000-2010 –> 2011-2019	5.7973354	17755.3480
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1648	3.1316820	8453.4369	29.493657	2000-2010 –> 2011-2019	5.8269534	17786.1880
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	1648	3.1100170	8428.5559	28.314959	2000-2010 –> 2011-2019	5.8075401	17762.5355
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1648	3.0782123	8394.6758	30.602797	2000-2010 –> 2011-2019	5.7911352	17750.6629
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1648	3.0255771	8339.8291	27.765869	2000-2010 –> 2011-2019	5.6347889	17547.1257
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2403	2.7869568	11757.3295	26.027700	1982-1999 –> 2000-2010	4.9083498	29180.8413
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	2403	2.7856813	11755.1294	25.850462	1982-1999 –> 2000-2010	4.9613234	29381.1535
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2403	2.7808081	11748.7146	25.609707	1982-1999 –> 2000-2010	4.9014816	29171.5062
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + phosphate_star	2403	2.8279763	11825.5505	30.583391	1982-1999 –> 2000-2010	4.9504586	29251.1795
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2403	2.8173376	11809.4365	29.735866	1982-1999 –> 2000-2010	4.9392148	29234.7791
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate	2046	3.1312405	10487.0250	35.046588	2000-2010 –> 2011-2019	5.9219592	22248.8374
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2046	3.1228292	10478.0181	35.215964	2000-2010 –> 2011-2019	5.9097860	22235.3476
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	2046	3.1187952	10472.7286	34.654059	2000-2010 –> 2011-2019	5.9044765	22227.8580
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2046	3.1112502	10464.8172	34.828329	2000-2010 –> 2011-2019	5.8920583	22213.5318
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2046	3.1117790	10463.5128	34.254667	2000-2010 –> 2011-2019	5.9291166	22272.9493
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2062	2.2219750	9156.2894	8.230091	1982-1999 –> 2000-2010	4.1441387	23853.2450
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2062	2.1759231	9071.9187	8.437911	1982-1999 –> 2000-2010	4.0666418	23653.9946
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2062	2.2238776	9161.8192	8.040775	1982-1999 –> 2000-2010	4.1588755	23907.9303
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	2062	2.2370247	9184.1277	8.281478	1982-1999 –> 2000-2010	4.1699136	23920.5115
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2062	2.1521797	9026.6708	7.877935	1982-1999 –> 2000-2010	4.0278393	23552.0825
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1759	2.4104487	8099.0076	8.219622	2000-2010 –> 2011-2019	4.5903149	17176.3927
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1759	2.4042735	8091.9835	8.383840	2000-2010 –> 2011-2019	4.5650409	17135.0772
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1759	2.4709066	8188.1563	8.414649	2000-2010 –> 2011-2019	4.6468297	17260.0749
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1759	2.4660466	8179.2299	8.996953	2000-2010 –> 2011-2019	4.6844172	17328.8242
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1759	2.4261389	8123.8329	8.758843	2000-2010 –> 2011-2019	4.5783186	17150.5037
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	1460	1.9413556	6092.3890	8.704942	1982-1999 –> 2000-2010	3.5619250	15818.3549
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1460	1.8501241	5953.8384	9.254259	1982-1999 –> 2000-2010	3.4465693	15605.1936
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1460	1.9448354	6097.6184	8.852501	1982-1999 –> 2000-2010	3.5859199	15887.8414
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1460	1.8656290	5978.2074	10.070772	1982-1999 –> 2000-2010	3.4750989	15671.0676
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1460	1.8167075	5900.6159	9.108315	1982-1999 –> 2000-2010	3.4433166	15647.5833
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1224	2.0621585	5257.3095	10.073863	2000-2010 –> 2011-2019	3.9562304	11277.6985
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1224	2.0058896	5191.5841	9.838746	2000-2010 –> 2011-2019	3.8560137	11145.4226
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1224	2.0461176	5240.1928	10.585784	2000-2010 –> 2011-2019	3.9117466	11218.4002
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	1224	2.0743598	5271.7510	10.122214	2000-2010 –> 2011-2019	3.9780796	11306.9760
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1224	1.9585274	5133.0896	9.225019	2000-2010 –> 2011-2019	3.7752349	11033.7055
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	12402	1.4118609	43762.4641	13.678755	1982-1999 –> 2000-2010	2.6886614	111420.7100
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	12402	1.3174986	42048.6812	16.081939	1982-1999 –> 2000-2010	2.4886350	106195.7355
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	12402	1.3461653	42582.5894	12.957947	1982-1999 –> 2000-2010	2.4720212	105125.9864
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	12402	1.3743872	43097.2215	16.873378	1982-1999 –> 2000-2010	2.6144108	109568.8040
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	12402	1.5425796	45958.7954	17.365225	1982-1999 –> 2000-2010	2.8718484	115254.8897
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	10029	1.6342281	38326.9691	9.304087	2000-2010 –> 2011-2019	3.1380281	83656.2340
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	10029	1.5705643	37527.9526	10.813075	2000-2010 –> 2011-2019	2.9824252	81290.4167
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	10029	1.4904452	36479.7127	12.918817	2000-2010 –> 2011-2019	2.8079438	78528.3939
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	10029	1.5745823	37581.2007	11.169511	2000-2010 –> 2011-2019	2.9207476	80163.7901
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	10029	1.5486196	37247.7156	14.043850	2000-2010 –> 2011-2019	2.9230069	80344.9370

5.3.2 per fitting unit

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

basin	gamma_slab	eras	rmse_sum_mean	ais_sum_mean
Atlantic	(-Inf,26]	1982-1999 –> 2000-2010	2.8406997	1252.746
Atlantic	(-Inf,26]	2000-2010 –> 2011-2019	2.7535745	813.614
Atlantic	(26,26.5]	1982-1999 –> 2000-2010	8.0431821	13656.109
Atlantic	(26,26.5]	2000-2010 –> 2011-2019	7.9767325	9065.509
Atlantic	(26.5,26.75]	1982-1999 –> 2000-2010	6.2893329	15806.422
Atlantic	(26.5,26.75]	2000-2010 –> 2011-2019	6.7325953	10800.414
Atlantic	(26.75,27]	1982-1999 –> 2000-2010	3.7832631	20868.896
Atlantic	(26.75,27]	2000-2010 –> 2011-2019	4.5475486	16345.796
Atlantic	(27,27.25]	1982-1999 –> 2000-2010	3.8782461	17902.215
Atlantic	(27,27.25]	2000-2010 –> 2011-2019	4.3033088	13829.429
Atlantic	(27.25,27.5]	1982-1999 –> 2000-2010	4.5742725	20547.523
Atlantic	(27.25,27.5]	2000-2010 –> 2011-2019	5.3485496	14989.669
Atlantic	(27.5,27.75]	1982-1999 –> 2000-2010	4.9952746	28321.296
Atlantic	(27.5,27.75]	2000-2010 –> 2011-2019	5.7021120	21218.105
Atlantic	(27.75,27.85]	1982-1999 –> 2000-2010	3.5944319	8737.894
Atlantic	(27.75,27.85]	2000-2010 –> 2011-2019	3.7780980	6355.180
Atlantic	(27.85,27.95]	1982-1999 –> 2000-2010	5.9444247	10785.724
Atlantic	(27.85,27.95]	2000-2010 –> 2011-2019	6.6970689	8157.493
Atlantic	(27.95,28.05]	1982-1999 –> 2000-2010	8.7858377	15606.154
Atlantic	(27.95,28.05]	2000-2010 –> 2011-2019	8.4506366	10720.748
Atlantic	(28.05,28.1]	1982-1999 –> 2000-2010	1.9889244	4913.343
Atlantic	(28.05,28.1]	2000-2010 –> 2011-2019	2.1647037	3731.946
Atlantic	(28.1,28.15]	1982-1999 –> 2000-2010	1.4661833	4534.141
Atlantic	(28.1,28.15]	2000-2010 –> 2011-2019	1.6772251	3571.553
Atlantic	(28.15,28.2]	1982-1999 –> 2000-2010	1.1096501	5819.256
Atlantic	(28.15,28.2]	2000-2010 –> 2011-2019	1.3712367	4779.000
Atlantic	(28.2, Inf]	1982-1999 –> 2000-2010	0.7163786	4339.572
Atlantic	(28.2, Inf]	2000-2010 –> 2011-2019	0.8427383	4478.841
Indo-Pacific	(-Inf,26]	1982-1999 –> 2000-2010	14.0424420	78718.385
Indo-Pacific	(-Inf,26]	2000-2010 –> 2011-2019	13.5043159	53955.587
Indo-Pacific	(26,26.5]	1982-1999 –> 2000-2010	9.2080015	72708.484
Indo-Pacific	(26,26.5]	2000-2010 –> 2011-2019	9.5330494	50322.889
Indo-Pacific	(26.5,26.75]	1982-1999 –> 2000-2010	7.8683285	56544.121
Indo-Pacific	(26.5,26.75]	2000-2010 –> 2011-2019	8.2586531	39614.384
Indo-Pacific	(26.75,27]	1982-1999 –> 2000-2010	7.9850791	66843.097
Indo-Pacific	(26.75,27]	2000-2010 –> 2011-2019	8.9294511	47866.848
Indo-Pacific	(27,27.25]	1982-1999 –> 2000-2010	7.7180410	78822.136
Indo-Pacific	(27,27.25]	2000-2010 –> 2011-2019	9.0932919	58071.948
Indo-Pacific	(27.25,27.5]	1982-1999 –> 2000-2010	6.5531240	66475.502
Indo-Pacific	(27.25,27.5]	2000-2010 –> 2011-2019	7.5953628	49253.403
Indo-Pacific	(27.5,27.75]	1982-1999 –> 2000-2010	5.5929162	62508.724
Indo-Pacific	(27.5,27.75]	2000-2010 –> 2011-2019	7.2513721	48108.148
Indo-Pacific	(27.75,27.85]	1982-1999 –> 2000-2010	4.6090397	22321.529
Indo-Pacific	(27.75,27.85]	2000-2010 –> 2011-2019	5.7715506	17720.372
Indo-Pacific	(27.85,27.95]	1982-1999 –> 2000-2010	4.9321656	29243.892
Indo-Pacific	(27.85,27.95]	2000-2010 –> 2011-2019	5.9114793	22239.705
Indo-Pacific	(27.95,28.05]	1982-1999 –> 2000-2010	4.1134818	23777.553
Indo-Pacific	(27.95,28.05]	2000-2010 –> 2011-2019	4.6129843	17210.175
Indo-Pacific	(28.05,28.1]	1982-1999 –> 2000-2010	3.5025659	15726.008
Indo-Pacific	(28.05,28.1]	2000-2010 –> 2011-2019	3.8954610	11196.441
Indo-Pacific	(28.1, Inf]	1982-1999 –> 2000-2010	2.6271154	109513.225
Indo-Pacific	(28.1, Inf]	2000-2010 –> 2011-2019	2.9544303	80796.754

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

rm(max_rmse)

6.3 Predictor counts

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

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

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

	aou	nitrate	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1999 --> 2000-2010
(-Inf,26]	5	1	4	5	3	2	2
(26,26.5]	5	3	2	4	1	4	4
(26.5,26.75]	5	1	4	4	2	5	2
(26.75,27]	5	1	4	4	1	5	3
(27,27.25]	5	2	3	4	3	5	2
(27.25,27.5]	5	4	1	3	3	5	2
(27.5,27.75]	5	1	4	3	4	3	1
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	3	5	2	3	3
(28.05,28.1]	5	0	5	5	2	3	2
(28.1,28.15]	5	1	4	5	3	4	1
(28.15,28.2]	5	5	0	4	2	3	3
(28.2, Inf]	5	5	0	3	4	3	1
total	70.00	28.00	42.00	57.00	37.00	52.00	28.00
Atlantic - 2000-2010 --> 2011-2019
(-Inf,26]	5	0	4	5	3	3	2
(26,26.5]	5	3	2	4	1	4	4
(26.5,26.75]	5	1	4	4	2	5	2
(26.75,27]	5	1	4	4	2	5	2
(27,27.25]	5	2	2	4	4	5	1
(27.25,27.5]	5	5	0	3	2	5	2
(27.5,27.75]	5	2	3	3	5	4	0
(27.75,27.85]	5	2	3	3	5	4	0
(27.85,27.95]	5	0	5	5	2	3	2
(27.95,28.05]	5	2	3	5	2	3	3
(28.05,28.1]	5	1	4	5	3	3	2
(28.1,28.15]	5	1	4	5	3	3	2
(28.15,28.2]	5	5	0	4	2	3	3
(28.2, Inf]	5	5	0	3	4	3	1
total	70.00	30.00	38.00	57.00	40.00	53.00	26.00
Indo-Pacific - 1982-1999 --> 2000-2010
(-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 - 2000-2010 --> 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	2	3	5	3	4	2
(27.85,27.95]	4	5	0	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	55.00	21.00	37.00	55.00	24.00	51.00	31.00

6.4 RMSE alternatives

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

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

Past versions of aic_vs_rmse_all_models-1.png

Version	Author	Date
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
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