eMLR - model fitting

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Last updated: 2021-03-23

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---

1 Required data

Required are:

• cleaned and prepared GLODAPv2_2020 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)

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

# remove helper objects
rm(i_gamma_slab,
   i_era,
   i_basin,
   GLODAP_basin_era,
   GLODAP_basin_era_slab,
   lm_full)

3 Apply predictor threshold

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

• Minimum: 2
  
• Maximum: 5

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:

• 112

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.

# prepare nested data frame

GLODAP %>%
  # filter(basin %in% unique(GLODAP$basin)[1],
  #        era %in% unique(GLODAP$era)[c(1,2)],
  #        gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>%
  filter_all(any_vars(is.na(.)))

GLODAP_nested <- GLODAP %>% 
  # filter(basin %in% unique(GLODAP$basin)[1],
  #        era %in% unique(GLODAP$era)[c(1,2)],
  #        gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>%
  group_by(gamma_slab, era, basin) %>% 
  nest()

# expand with model definitions

GLODAP_nested_lm <- expand_grid(
  GLODAP_nested,
  lm_all
)

# fit models and extract tidy model output

GLODAP_nested_lm_fit <- GLODAP_nested_lm %>% 
  mutate(
    fit = map2(.x = data, .y = model, 
               ~ lm(as.formula(.y), data = .x)),
    tidied = map(fit, tidy),
    glanced = map(fit, glance),
    augmented = map(fit, augment),
    vif = map(fit, ols_vif_tol)
  )

# print(object.size(GLODAP_nested), units = "MB")
# print(object.size(GLODAP_nested_lm), units = "MB")
# print(object.size(GLODAP_nested_lm_fit), units = "MB")

5 Tidy models

# extract glanced model output (model diagnostics, such as AIC)
GLODAP_glanced <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, tidied, augmented, vif)) %>%
  unnest(glanced) %>% 
  rename(n_predictors = n)

# extract tidy model output (model coefficients)
GLODAP_tidy <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, glanced, augmented, vif)) %>%
  unnest(tidied)

# extract augmented model output (fitted values and residuals)
GLODAP_augmented <- GLODAP_nested_lm_fit %>% 
  select(-c(data, fit, tidied, glanced, vif)) %>% 
  unnest(augmented) 

# print(object.size(GLODAP_augmented), units = "MB")

# extract VIC from output
GLODAP_glanced_vif <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, tidied, augmented, glanced)) %>%
  unnest(vif)

# calculte max vif per model
GLODAP_glanced_vif_max <- GLODAP_glanced_vif %>% 
  group_by(era, basin, gamma_slab, model, n) %>% 
  summarise(vif_max = max(VIF)) %>% 
  ungroup()

# calculate RMSE from augmented output
GLODAP_glanced_rmse <- GLODAP_augmented %>%
  group_by(gamma_slab, era, basin, model) %>%
  summarise(rmse = sqrt(c(crossprod(.resid)) / length(.resid))) %>%
  ungroup()

# add RMSE and vif_max to glanced output
GLODAP_glanced <- full_join(GLODAP_glanced, GLODAP_glanced_rmse)
GLODAP_glanced <- full_join(GLODAP_glanced, GLODAP_glanced_vif_max)
rm(GLODAP_glanced_rmse)
rm(GLODAP_glanced_vif_max)


# extract input data
GLODAP_data <- GLODAP_nested_lm_fit %>%
  select(-c(fit, tidied, glanced, augmented, vif)) %>%
  unnest(data)

# append input data with augmented data
GLODAP_augmented <- bind_cols(
  GLODAP_data,
  GLODAP_augmented %>% select(.fitted, .resid)
)

rm(GLODAP, GLODAP_nested, GLODAP_nested_lm, GLODAP_nested_lm_fit, lm_all,
   GLODAP_data)

6 Prepare coeffcients

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

6.1 VIF threshold

To avoid multicollinearity among predictors, models were excluded with a VIF above:

• 50

After removing models affected by multicollinearity, the targeted number of MLRs (10) was undercut in following fitting units:

GLODAP_glanced_clean <- GLODAP_glanced %>% 
  filter(vif_max <= params_local$vif_max)

GLODAP_glanced_clean %>% 
  group_by(era, basin, gamma_slab) %>% 
  count() %>% 
  filter(n < params_local$MLR_number)

# A tibble: 0 x 4
# Groups:   era, basin, gamma_slab [0]
# … with 4 variables: era <chr>, basin <chr>, gamma_slab <chr>, n <int>

6.2 Predictor selection

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

• 10

The criterion used to select the best models was:

• rmse

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

# calculate RMSE sum for adjacent eras
lm_all_eras <- GLODAP_glanced_clean  %>%
  select(basin, gamma_slab, model, era, AIC, BIC, rmse) %>% 
  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),
         bic_sum = BIC + lag(BIC)
         ) %>% 
  ungroup() %>% 
  select(-c(era)) %>% 
  drop_na()

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

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

if (params_local$MLR_criterion == "bic") {
  lm_best_eras <- lm_all_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = bic_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
}

if (params_local$MLR_criterion == "rmse") {
  lm_best_eras <- lm_all_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = rmse_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
}


# print table
lm_best_eras %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	gamma_slab	model	AIC	BIC	rmse	eras	rmse_sum	aic_sum	bic_sum
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	541.5135	558.0996	6.819284	1981-1999 –> 2000-2012	13.389675	1149.786	1183.870
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	541.6622	558.2484	6.825706	1981-1999 –> 2000-2012	13.380448	1149.505	1183.590
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	542.4170	559.0032	6.858393	1981-1999 –> 2000-2012	13.380721	1149.368	1183.452
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	557.6573	574.2434	7.552892	1981-1999 –> 2000-2012	14.027452	1163.285	1197.370
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + phosphate	544.0160	558.2327	7.016407	1981-1999 –> 2000-2012	13.828051	1156.779	1185.994
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + phosphate_star	543.9312	558.1479	7.012641	1981-1999 –> 2000-2012	13.782018	1155.574	1184.789
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	545.5342	562.1203	6.995043	1981-1999 –> 2000-2012	13.557524	1153.589	1187.674
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	545.4069	561.9930	6.989410	1981-1999 –> 2000-2012	13.523425	1152.680	1186.764
Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	543.7304	557.9471	7.003736	1981-1999 –> 2000-2012	13.708870	1153.657	1182.872
Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	545.0304	561.6165	6.972774	1981-1999 –> 2000-2012	13.462469	1151.078	1185.163
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + nitrate + phosphate	4585.2802	4612.6887	6.005254	1981-1999 –> 2000-2012	11.004060	7910.063	7963.298
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	4587.2749	4619.2515	6.005231	1981-1999 –> 2000-2012	10.965680	7905.630	7967.738
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + phosphate	4589.6041	4612.4445	6.031981	1981-1999 –> 2000-2012	11.032359	7912.731	7957.093
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate	4591.0840	4618.4925	6.029779	1981-1999 –> 2000-2012	10.991944	7907.818	7961.053
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate	4579.6203	4607.0287	5.981432	1981-1999 –> 2000-2012	10.964134	7900.873	7954.108
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4581.0351	4613.0117	5.978974	1981-1999 –> 2000-2012	10.927818	7896.828	7958.936
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate	4530.1645	4557.5730	5.777262	1981-1999 –> 2000-2012	10.752781	7849.839	7903.074
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	4549.2019	4576.6103	5.855016	1981-1999 –> 2000-2012	10.860078	7875.353	7928.588
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	4528.2461	4560.2226	5.761386	1981-1999 –> 2000-2012	10.708235	7843.598	7905.706
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4545.6162	4577.5927	5.832095	1981-1999 –> 2000-2012	10.808514	7867.488	7929.596
Atlantic	(26.5,26.75]	cstar_tref ~ aou + phosphate	7280.1190	7300.1057	6.737843	1981-1999 –> 2000-2012	11.689101	12395.557	12434.505
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate	7273.2540	7298.2374	6.710574	1981-1999 –> 2000-2012	11.631845	12380.413	12429.099
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate_star	7176.7298	7201.7132	6.420711	1981-1999 –> 2000-2012	11.531689	12347.887	12396.573
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	7168.1000	7198.0801	6.389565	1981-1999 –> 2000-2012	11.468280	12330.543	12388.966
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + phosphate_star	6824.2032	6849.1866	5.464449	1981-1999 –> 2000-2012	9.781254	11709.624	11758.310
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	6825.7180	6855.6981	5.463236	1981-1999 –> 2000-2012	9.745260	11699.450	11757.874
Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate_star	6830.4451	6855.4285	5.480074	1981-1999 –> 2000-2012	9.829384	11728.558	11777.244
Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	6831.9861	6861.9662	5.478924	1981-1999 –> 2000-2012	9.801109	11721.514	11779.937
Atlantic	(26.5,26.75]	cstar_tref ~ temp + phosphate_star	7029.5114	7049.4981	6.008035	1981-1999 –> 2000-2012	11.533574	12330.627	12369.576
Atlantic	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate_star	6923.8865	6948.8699	5.719401	1981-1999 –> 2000-2012	10.501222	11982.408	12031.094
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate_star	7922.9279	7953.8038	5.463307	1981-1999 –> 2000-2012	10.307623	13922.424	13982.740
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	7873.0340	7909.0559	5.352735	1981-1999 –> 2000-2012	10.188968	13871.193	13941.563
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + phosphate_star	7924.7383	7955.6142	5.467206	1981-1999 –> 2000-2012	10.296194	13917.902	13978.219
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7874.2407	7910.2626	5.355280	1981-1999 –> 2000-2012	10.173003	13864.738	13935.107
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	7887.1559	7918.0318	5.386845	1981-1999 –> 2000-2012	10.308775	13918.410	13978.726
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + phosphate_star	7938.0864	7963.8163	5.500368	1981-1999 –> 2000-2012	10.380212	13950.182	14000.446
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	7903.9794	7934.8553	5.422670	1981-1999 –> 2000-2012	10.301665	13917.727	13978.043
Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + phosphate_star	7941.4218	7967.1517	5.507601	1981-1999 –> 2000-2012	10.359431	13942.014	13992.278
Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	7900.8391	7931.7150	5.415965	1981-1999 –> 2000-2012	10.260975	13900.621	13960.937
Atlantic	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	7903.1589	7934.0348	5.420918	1981-1999 –> 2000-2012	10.300207	13917.027	13977.344
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate_star	15011.0398	15045.7591	5.449261	1981-1999 –> 2000-2012	10.876349	28459.714	28528.500
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14878.0604	14918.5663	5.298654	1981-1999 –> 2000-2012	10.533373	28172.828	28253.079
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	14912.2089	14952.7147	5.336358	1981-1999 –> 2000-2012	10.543939	28184.522	28264.773
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + phosphate + phosphate_star	15019.3928	15054.1121	5.458721	1981-1999 –> 2000-2012	10.887007	28469.020	28537.807
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	14882.6168	14923.1227	5.303669	1981-1999 –> 2000-2012	10.536845	28176.111	28256.362
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate_star	15002.6044	15037.3238	5.439725	1981-1999 –> 2000-2012	10.720205	28332.973	28401.759
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate_star	14950.7168	14985.4361	5.381432	1981-1999 –> 2000-2012	10.743588	28347.393	28416.180
Atlantic	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	15008.3589	15043.0782	5.446229	1981-1999 –> 2000-2012	10.790290	28390.433	28459.219
Atlantic	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	14956.2894	14991.0088	5.387662	1981-1999 –> 2000-2012	10.749291	28352.541	28421.327
Atlantic	(27,27.25]	cstar_tref ~ temp + silicate + phosphate_star	15142.3082	15171.2410	5.602159	1981-1999 –> 2000-2012	10.971485	28542.757	28600.079
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	16361.1537	16396.8270	4.378766	1981-1999 –> 2000-2012	8.973725	31127.972	31198.604
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate_star	16327.2984	16362.9717	4.352588	1981-1999 –> 2000-2012	8.966973	31115.261	31185.893
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	16328.4438	16370.0626	4.351930	1981-1999 –> 2000-2012	8.961897	31113.606	31196.010
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	16333.1999	16368.8732	4.357140	1981-1999 –> 2000-2012	8.965408	31114.514	31185.146
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + phosphate	16527.6289	16557.3566	4.511397	1981-1999 –> 2000-2012	9.191043	31383.980	31442.840
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + phosphate_star	16535.8193	16565.5471	4.517946	1981-1999 –> 2000-2012	9.225744	31422.232	31481.092
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate	16513.8099	16549.4832	4.498774	1981-1999 –> 2000-2012	9.137906	31328.580	31399.212
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	16503.4768	16539.1501	4.490548	1981-1999 –> 2000-2012	9.144750	31334.502	31405.134
Atlantic	(27.25,27.5]	cstar_tref ~ temp + phosphate + phosphate_star	16526.9176	16556.6454	4.510828	1981-1999 –> 2000-2012	9.210878	31405.074	31463.934
Atlantic	(27.25,27.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	16501.2212	16536.8945	4.488755	1981-1999 –> 2000-2012	9.136841	31325.656	31396.288
Atlantic	(27.5,27.75]	cstar_tref ~ aou + silicate + phosphate	18994.0514	19024.4308	4.630024	1981-1999 –> 2000-2012	9.420829	33991.950	34051.469
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	18896.6158	18933.0711	4.558996	1981-1999 –> 2000-2012	9.222206	33761.001	33832.425
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate	19002.6156	19039.0710	4.634751	1981-1999 –> 2000-2012	9.281935	33849.719	33921.143
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	18684.0566	18726.5879	4.409426	1981-1999 –> 2000-2012	8.907118	33369.022	33452.349
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18717.6217	18760.1529	4.432496	1981-1999 –> 2000-2012	8.960338	33436.126	33519.453
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	19046.6271	19083.0825	4.666574	1981-1999 –> 2000-2012	9.361582	33945.127	34016.551
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18693.0194	18735.5507	4.415574	1981-1999 –> 2000-2012	8.929671	33396.261	33479.588
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate	18757.2236	18793.6790	4.461258	1981-1999 –> 2000-2012	8.992424	33477.411	33548.835
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	18799.8208	18836.2762	4.490902	1981-1999 –> 2000-2012	9.054859	33556.206	33627.630
Atlantic	(27.5,27.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	18770.3123	18806.7677	4.470346	1981-1999 –> 2000-2012	9.019685	33510.593	33582.017
Atlantic	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate	12782.9811	12811.3263	4.777937	1981-1999 –> 2000-2012	9.676214	20366.677	20420.712
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate_star	12783.7641	12817.7782	4.776580	1981-1999 –> 2000-2012	9.618939	20340.550	20405.392
Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate	13041.0795	13069.4246	5.074785	1981-1999 –> 2000-2012	10.231603	20754.292	20808.327
Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	12694.0777	12728.0919	4.677575	1981-1999 –> 2000-2012	9.475138	20227.461	20292.304
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	12691.0004	12730.6836	4.672032	1981-1999 –> 2000-2012	9.472561	20227.940	20303.590
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate	13013.7744	13047.7885	5.040173	1981-1999 –> 2000-2012	10.134923	20698.496	20763.338
Atlantic	(27.75,27.85]	cstar_tref ~ silicate + phosphate + phosphate_star	12856.0077	12884.3529	4.860121	1981-1999 –> 2000-2012	9.828479	20475.474	20529.510
Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate_star	12697.7113	12731.7255	4.681546	1981-1999 –> 2000-2012	9.513044	20248.843	20313.685
Atlantic	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate	13024.3875	13052.7326	5.055041	1981-1999 –> 2000-2012	10.180090	20722.039	20776.075
Atlantic	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	12698.0402	12732.0544	4.681905	1981-1999 –> 2000-2012	9.514221	20249.598	20314.440
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate	27229.6152	27267.9976	5.208312	1981-1999 –> 2000-2012	9.746422	43235.602	43309.453
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate_star	26665.1014	26703.4838	4.887097	1981-1999 –> 2000-2012	9.189249	42379.764	42453.614
Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate	27541.3464	27573.3317	5.395869	1981-1999 –> 2000-2012	10.035114	43665.588	43727.130
Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	27018.6249	27057.0072	5.085857	1981-1999 –> 2000-2012	9.533971	42915.326	42989.176
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	26606.6884	26651.4678	4.853917	1981-1999 –> 2000-2012	9.124089	42282.642	42368.801
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	26573.3393	26618.1187	4.835697	1981-1999 –> 2000-2012	9.097351	42238.398	42324.557
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate	26732.1745	26770.5569	4.924200	1981-1999 –> 2000-2012	9.212746	42429.554	42503.404
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	26599.1374	26643.9168	4.849785	1981-1999 –> 2000-2012	9.118427	42273.135	42359.293
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate_star	27567.8031	27606.1855	5.410771	1981-1999 –> 2000-2012	10.012195	43649.384	43723.235
Atlantic	(27.85,27.95]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	27659.8981	27698.2804	5.467255	1981-1999 –> 2000-2012	10.094824	43772.392	43846.242
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate_star	30527.1173	30559.4363	6.050656	1981-1999 –> 2000-2012	10.394134	50709.989	50773.100
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate	30435.5839	30474.3666	5.991251	1981-1999 –> 2000-2012	10.159147	50332.184	50407.918
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate_star	30096.2813	30135.0641	5.780608	1981-1999 –> 2000-2012	9.733038	49622.060	49697.793
Atlantic	(27.95,28.05]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	30488.6455	30527.4283	6.024880	1981-1999 –> 2000-2012	10.306154	50572.745	50648.479
Atlantic	(27.95,28.05]	cstar_tref ~ sal + phosphate + phosphate_star	30486.7486	30519.0675	6.024945	1981-1999 –> 2000-2012	10.333830	50613.758	50676.869
Atlantic	(27.95,28.05]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	30190.5511	30229.3339	5.838377	1981-1999 –> 2000-2012	9.862510	49841.928	49917.662
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate	30514.1112	30552.8940	6.041086	1981-1999 –> 2000-2012	10.342571	50631.113	50706.847
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate_star	30455.1557	30493.9384	6.003633	1981-1999 –> 2000-2012	10.277672	50527.438	50603.172
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate + phosphate_star	30469.8013	30508.5840	6.012915	1981-1999 –> 2000-2012	10.292630	50551.357	50627.090
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate	30510.9840	30549.7667	6.039093	1981-1999 –> 2000-2012	10.213184	50417.960	50493.694
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate	23410.1840	23441.1079	6.320355	1981-1999 –> 2000-2012	10.303676	37010.900	37070.794
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate_star	23331.4390	23362.3629	6.251340	1981-1999 –> 2000-2012	10.257774	36960.227	37020.121
Atlantic	(28.05,28.1]	cstar_tref ~ sal + nitrate + phosphate_star	23352.2419	23383.1659	6.269499	1981-1999 –> 2000-2012	10.272657	36977.061	37036.955
Atlantic	(28.05,28.1]	cstar_tref ~ sal + phosphate + phosphate_star	23335.2471	23366.1711	6.254660	1981-1999 –> 2000-2012	10.253590	36954.939	37014.833
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate	23411.7941	23448.9028	6.320011	1981-1999 –> 2000-2012	10.288187	36996.027	37067.900
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate_star	23279.4496	23316.5583	6.204458	1981-1999 –> 2000-2012	10.070388	36737.025	36808.898
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate_star	23283.5776	23320.6864	6.208030	1981-1999 –> 2000-2012	10.073172	36740.164	36812.037
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + phosphate + phosphate_star	23294.2061	23331.3148	6.217237	1981-1999 –> 2000-2012	10.083520	36752.225	36824.098
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + phosphate_star	23351.3166	23382.2406	6.268690	1981-1999 –> 2000-2012	10.134974	36807.336	36867.230
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	23326.7736	23363.8823	6.245533	1981-1999 –> 2000-2012	10.111703	36784.650	36856.523
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate_star	18077.4254	18106.8802	7.104136	1981-1999 –> 2000-2012	10.753668	27400.287	27456.980
Atlantic	(28.1,28.15]	cstar_tref ~ sal + nitrate + phosphate_star	18063.6684	18093.1232	7.085878	1981-1999 –> 2000-2012	10.737938	27388.905	27445.599
Atlantic	(28.1,28.15]	cstar_tref ~ sal + phosphate	18877.7996	18901.3634	8.254561	1981-1999 –> 2000-2012	12.903279	29029.179	29074.534
Atlantic	(28.1,28.15]	cstar_tref ~ sal + phosphate_star	18162.4145	18185.9784	7.220679	1981-1999 –> 2000-2012	10.919516	27529.331	27574.686
Atlantic	(28.1,28.15]	cstar_tref ~ sal + silicate + phosphate_star	18104.2120	18133.6667	7.139821	1981-1999 –> 2000-2012	10.819907	27455.686	27512.380
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate_star	17858.2374	17887.6922	6.818754	1981-1999 –> 2000-2012	10.320564	27039.291	27095.985
Atlantic	(28.1,28.15]	cstar_tref ~ temp + nitrate + phosphate_star	17861.6815	17891.1362	6.823148	1981-1999 –> 2000-2012	10.327404	27045.132	27101.825
Atlantic	(28.1,28.15]	cstar_tref ~ temp + phosphate	18863.1870	18886.7508	8.232029	1981-1999 –> 2000-2012	12.902942	29030.913	29076.268
Atlantic	(28.1,28.15]	cstar_tref ~ temp + phosphate_star	17875.0884	17898.6522	6.842841	1981-1999 –> 2000-2012	10.380776	27089.366	27134.721
Atlantic	(28.1,28.15]	cstar_tref ~ temp + silicate + phosphate_star	17841.6127	17871.0675	6.797582	1981-1999 –> 2000-2012	10.256757	26980.625	27037.319
Atlantic	(28.15,28.2]	cstar_tref ~ nitrate + phosphate_star	6923.3903	6943.5665	4.944360	1981-1999 –> 2000-2012	10.592408	10434.467	10471.926
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + phosphate_star	6543.3631	6568.5833	4.185260	1981-1999 –> 2000-2012	8.128556	9656.905	9703.729
Atlantic	(28.15,28.2]	cstar_tref ~ sal + phosphate	6986.0687	7006.2449	5.081437	1981-1999 –> 2000-2012	9.350749	10185.944	10223.403
Atlantic	(28.15,28.2]	cstar_tref ~ sal + phosphate_star	6947.1096	6967.2858	4.995793	1981-1999 –> 2000-2012	9.102033	10103.678	10141.137
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + phosphate_star	6385.7489	6410.9690	3.907125	1981-1999 –> 2000-2012	7.443192	9378.081	9424.905
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + phosphate_star	6303.9209	6329.1410	3.770095	1981-1999 –> 2000-2012	7.328177	9303.155	9349.979
Atlantic	(28.15,28.2]	cstar_tref ~ temp + nitrate + phosphate_star	6323.3941	6348.6143	3.802263	1981-1999 –> 2000-2012	7.360907	9322.804	9369.628
Atlantic	(28.15,28.2]	cstar_tref ~ temp + phosphate	6984.5804	7004.7565	5.078138	1981-1999 –> 2000-2012	9.344030	10183.564	10221.023
Atlantic	(28.15,28.2]	cstar_tref ~ temp + phosphate_star	6387.1022	6407.2783	3.912846	1981-1999 –> 2000-2012	7.471511	9384.519	9421.978
Atlantic	(28.15,28.2]	cstar_tref ~ temp + silicate + phosphate_star	6354.3150	6379.5352	3.853906	1981-1999 –> 2000-2012	7.405985	9351.671	9398.495
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate_star	14235.1447	14270.5928	3.308754	1981-1999 –> 2000-2012	6.533074	20312.130	20377.972
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14209.0833	14250.4395	3.291724	1981-1999 –> 2000-2012	6.384071	20190.192	20267.008
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate_star	14388.3991	14423.8472	3.403328	1981-1999 –> 2000-2012	6.630674	20467.581	20533.423
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + phosphate + phosphate_star	14233.6361	14269.0842	3.307836	1981-1999 –> 2000-2012	6.521566	20302.917	20368.758
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + phosphate	14647.1153	14676.6554	3.570470	1981-1999 –> 2000-2012	6.892374	20791.930	20846.798
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + phosphate_star	14584.5586	14614.0987	3.529632	1981-1999 –> 2000-2012	6.868139	20741.049	20795.917
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate	14642.0734	14677.5215	3.565849	1981-1999 –> 2000-2012	6.709055	20659.387	20725.229
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate_star	14586.5572	14622.0053	3.529631	1981-1999 –> 2000-2012	6.653180	20589.179	20655.021
Atlantic	(28.2, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	14770.3276	14805.7757	3.650949	1981-1999 –> 2000-2012	6.937059	20891.770	20957.612
Atlantic	(28.2, Inf]	cstar_tref ~ temp + phosphate + phosphate_star	14600.8733	14630.4134	3.540237	1981-1999 –> 2000-2012	6.874845	20754.627	20809.495
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate	29095.2337	29133.7074	6.117150	1981-1999 –> 2000-2012	17.606841	41560.848	41631.636
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	28943.6385	28988.5244	6.013685	1981-1999 –> 2000-2012	17.291446	41351.192	41433.779
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	28958.5889	29003.4748	6.023679	1981-1999 –> 2000-2012	17.309105	41368.335	41450.922
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	29095.0849	29139.9709	6.115690	1981-1999 –> 2000-2012	17.558014	41549.372	41631.959
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate	29946.7760	29985.2496	6.723912	1981-1999 –> 2000-2012	18.388298	42461.071	42531.859
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	29512.8670	29557.7530	6.406142	1981-1999 –> 2000-2012	17.674730	41917.796	42000.383
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	29570.1072	29614.9931	6.446997	1981-1999 –> 2000-2012	17.729238	41978.943	42061.529
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	29885.7426	29930.6285	6.677005	1981-1999 –> 2000-2012	18.065402	42324.790	42407.377
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	29596.2584	29641.1444	6.465749	1981-1999 –> 2000-2012	17.752842	42006.481	42089.068
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate_star	29929.5163	29967.9899	6.711035	1981-1999 –> 2000-2012	18.133970	42376.332	42447.121
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	18436.9484	18479.2112	4.746014	1981-1999 –> 2000-2012	12.041189	30147.673	30228.074
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate_star	18797.6394	18833.8647	5.032406	1981-1999 –> 2000-2012	12.508019	30590.267	30659.183
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18593.7248	18635.9877	4.867753	1981-1999 –> 2000-2012	12.141106	30294.162	30374.563
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	18444.1249	18486.3877	4.751520	1981-1999 –> 2000-2012	12.052876	30157.758	30238.159
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate_star	18653.7644	18689.9897	4.916786	1981-1999 –> 2000-2012	12.359619	30431.301	30500.217
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	18584.0621	18626.3249	4.860161	1981-1999 –> 2000-2012	12.190428	30311.266	30391.668
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	18796.9580	18833.1832	5.031852	1981-1999 –> 2000-2012	12.507721	30589.703	30658.619
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + phosphate_star	18812.5595	18842.7472	5.046181	1981-1999 –> 2000-2012	12.523214	30603.839	30661.269
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18595.6937	18637.9565	4.869302	1981-1999 –> 2000-2012	12.145540	30297.493	30377.894
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	18611.8738	18648.0990	4.883624	1981-1999 –> 2000-2012	12.216295	30338.204	30407.119
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate_star	20474.7673	20511.2968	5.603427	1981-1999 –> 2000-2012	11.476024	31719.255	31788.626
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate_star	20225.3357	20261.8652	5.392855	1981-1999 –> 2000-2012	11.139278	31393.328	31462.699
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	20155.7215	20198.3393	5.333873	1981-1999 –> 2000-2012	11.080177	31325.640	31406.573
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	20692.9577	20729.4873	5.794355	1981-1999 –> 2000-2012	11.628846	31914.517	31983.888
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	20579.4919	20616.0215	5.694268	1981-1999 –> 2000-2012	11.462198	31760.641	31830.012
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	20557.7409	20600.3587	5.673538	1981-1999 –> 2000-2012	11.441342	31740.813	31821.746
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	20586.3750	20622.9046	5.700290	1981-1999 –> 2000-2012	11.476498	31772.575	31841.946
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate_star	20634.6745	20665.1158	5.744491	1981-1999 –> 2000-2012	11.720734	31938.780	31996.590
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	20562.2747	20604.8925	5.677489	1981-1999 –> 2000-2012	11.453682	31750.465	31831.398
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	20588.2831	20624.8127	5.701961	1981-1999 –> 2000-2012	11.677752	31894.122	31963.494
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate	30805.5485	30838.0558	5.525748	1981-1999 –> 2000-2012	12.062720	50422.610	50485.106
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate_star	31136.8380	31175.8469	5.713715	1981-1999 –> 2000-2012	12.237122	50743.544	50818.539
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	31127.8081	31166.8169	5.708476	1981-1999 –> 2000-2012	12.112232	50624.404	50699.399
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	31000.1913	31039.2001	5.634950	1981-1999 –> 2000-2012	12.133985	50584.634	50659.629
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate_star	30638.8936	30677.9025	5.431883	1981-1999 –> 2000-2012	11.806722	50108.570	50183.565
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	30741.6068	30780.6156	5.488857	1981-1999 –> 2000-2012	11.955486	50296.317	50371.311
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + phosphate_star	30813.3469	30845.8543	5.530128	1981-1999 –> 2000-2012	12.048541	50413.498	50475.994
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	30422.6230	30461.6318	5.313847	1981-1999 –> 2000-2012	11.616915	49824.954	49899.949
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + phosphate + phosphate_star	31107.1596	31139.6669	5.697673	1981-1999 –> 2000-2012	12.317022	50798.709	50861.204
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	30705.8773	30744.8862	5.468971	1981-1999 –> 2000-2012	11.926962	50252.637	50327.632
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	39820.9872	39861.7416	4.973992	1981-1999 –> 2000-2012	11.204445	63877.553	63955.605
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	40229.7292	40270.4836	5.130808	1981-1999 –> 2000-2012	11.282635	64192.288	64270.340
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	39718.1468	39758.9012	4.935297	1981-1999 –> 2000-2012	11.138510	63742.278	63820.331
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate_star	40314.2828	40355.0372	5.163860	1981-1999 –> 2000-2012	11.892256	64939.970	65018.023
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	39625.5058	39673.0526	4.899953	1981-1999 –> 2000-2012	11.108316	63657.780	63748.842
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	39695.8732	39743.4200	4.926208	1981-1999 –> 2000-2012	11.018168	63588.047	63679.108
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate_star	40284.3180	40325.0724	5.152123	1981-1999 –> 2000-2012	11.635182	64635.064	64713.117
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate_star	40358.5407	40399.2951	5.181245	1981-1999 –> 2000-2012	11.503526	64523.404	64601.457
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	40268.8346	40309.5890	5.146068	1981-1999 –> 2000-2012	11.339142	64280.858	64358.911
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	40318.2130	40358.9674	5.165402	1981-1999 –> 2000-2012	11.473226	64466.132	64544.184
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	40534.9464	40576.0219	4.473004	1981-1999 –> 2000-2012	10.360168	65831.696	65910.477
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	41213.8994	41254.9750	4.697046	1981-1999 –> 2000-2012	10.225501	66012.624	66091.405
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	40145.7933	40193.7148	4.348815	1981-1999 –> 2000-2012	9.905672	64987.112	65079.024
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	40167.1345	40215.0560	4.355501	1981-1999 –> 2000-2012	9.877168	64958.127	65050.038
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	40119.9000	40167.8214	4.340717	1981-1999 –> 2000-2012	9.890125	64950.593	65042.504
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	40787.3462	40828.4217	4.555015	1981-1999 –> 2000-2012	10.126312	65647.225	65726.006
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	41096.3379	41137.4134	4.657465	1981-1999 –> 2000-2012	10.216485	65938.741	66017.522
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	40981.7984	41022.8740	4.619222	1981-1999 –> 2000-2012	10.147025	65779.589	65858.370
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	41072.1824	41113.2579	4.649374	1981-1999 –> 2000-2012	10.202235	65905.803	65984.584
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + silicate + phosphate_star	41438.2195	41472.4491	4.774195	1981-1999 –> 2000-2012	10.345496	66296.105	66361.756
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate	43727.8027	43769.5377	4.056597	1981-1999 –> 2000-2012	9.043735	69664.864	69744.774
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate_star	43784.3949	43826.1299	4.071430	1981-1999 –> 2000-2012	9.167507	69906.601	69986.511
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	42985.3841	43034.0749	3.866447	1981-1999 –> 2000-2012	8.943747	69077.961	69171.191
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	42957.4603	43006.1512	3.859491	1981-1999 –> 2000-2012	8.975346	69114.854	69208.083
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	43793.1964	43834.9314	4.073741	1981-1999 –> 2000-2012	9.188211	69946.269	70026.180
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	42981.0918	43029.7827	3.865377	1981-1999 –> 2000-2012	8.955427	69095.157	69188.387
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	43079.7515	43121.4865	3.890551	1981-1999 –> 2000-2012	9.065278	69333.180	69413.091
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + phosphate	43975.0925	44009.8717	4.122342	1981-1999 –> 2000-2012	9.116335	69921.922	69988.514
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	43813.2579	43854.9929	4.079015	1981-1999 –> 2000-2012	9.156970	69904.940	69984.851
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	43816.5545	43858.2895	4.079883	1981-1999 –> 2000-2012	9.170246	69929.147	70009.058
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate	21639.5234	21677.3011	3.591007	1981-1999 –> 2000-2012	7.849360	33300.612	33372.087
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate_star	21616.0859	21653.8637	3.580526	1981-1999 –> 2000-2012	7.857194	33294.608	33366.084
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	21464.4076	21508.4817	3.512553	1981-1999 –> 2000-2012	7.787125	33142.939	33226.327
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	21448.5838	21492.6579	3.505627	1981-1999 –> 2000-2012	7.795359	33141.495	33224.883
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + phosphate + phosphate_star	21613.1033	21650.8811	3.579194	1981-1999 –> 2000-2012	7.861231	33296.722	33368.197
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	21462.4959	21506.5700	3.511715	1981-1999 –> 2000-2012	7.790870	33145.379	33228.767
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate	21638.8226	21670.3041	3.591589	1981-1999 –> 2000-2012	7.861943	33309.342	33368.905
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate_star	21480.1961	21517.9738	3.520354	1981-1999 –> 2000-2012	7.804176	33165.507	33236.982
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	21458.0065	21495.7843	3.510625	1981-1999 –> 2000-2012	7.817584	33165.197	33236.673
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	21477.7098	21515.4876	3.519263	1981-1999 –> 2000-2012	7.807521	33167.225	33238.701
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate	29266.7761	29306.6306	3.197002	1981-1999 –> 2000-2012	7.587926	46020.387	46096.051
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	29096.8592	29143.3561	3.148875	1981-1999 –> 2000-2012	7.538748	45851.087	45939.362
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	29119.6902	29166.1871	3.155224	1981-1999 –> 2000-2012	7.557500	45890.214	45978.489
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	29096.2470	29142.7439	3.148705	1981-1999 –> 2000-2012	7.527586	45835.994	45924.269
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	29121.9665	29168.4635	3.155858	1981-1999 –> 2000-2012	7.561501	45896.907	45985.182
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate	29303.7004	29336.9125	3.208000	1981-1999 –> 2000-2012	7.598980	46055.385	46118.439
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate	29097.6220	29137.4765	3.149642	1981-1999 –> 2000-2012	7.539911	45850.371	45926.035
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate_star	29122.7050	29162.5595	3.156620	1981-1999 –> 2000-2012	7.559600	45892.151	45967.816
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	29095.4119	29135.2664	3.149028	1981-1999 –> 2000-2012	7.529858	45835.728	45911.393
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	29125.7151	29165.5696	3.157459	1981-1999 –> 2000-2012	7.564024	45899.864	45975.528
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	48716.4501	48766.6258	3.069814	1981-1999 –> 2000-2012	7.478351	81203.413	81299.995
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate	48790.0518	48833.0596	3.081945	1981-1999 –> 2000-2012	7.499453	81297.758	81380.542
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	48317.5599	48367.7356	3.006597	1981-1999 –> 2000-2012	7.387010	80732.920	80829.502
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	48544.7818	48594.9575	3.042447	1981-1999 –> 2000-2012	7.462566	81061.100	81157.681
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	48480.7402	48530.9159	3.032300	1981-1999 –> 2000-2012	7.447739	80985.206	81081.788
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	48541.1817	48591.3574	3.041875	1981-1999 –> 2000-2012	7.465863	81067.287	81163.869
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	48543.4371	48586.4448	3.042551	1981-1999 –> 2000-2012	7.479852	81101.160	81183.944
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate	48739.7354	48782.7431	3.073866	1981-1999 –> 2000-2012	7.510367	81295.440	81378.224
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	48315.9017	48366.0774	3.006337	1981-1999 –> 2000-2012	7.433978	80851.241	80947.823
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	48471.4099	48514.4176	3.031140	1981-1999 –> 2000-2012	7.488108	81078.609	81161.394
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	38556.1306	38604.8034	2.924481	1981-1999 –> 2000-2012	7.141866	60657.944	60750.433
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	38656.1907	38697.9102	2.943843	1981-1999 –> 2000-2012	7.163355	60759.900	60839.176
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	39000.0053	39048.6780	3.009630	1981-1999 –> 2000-2012	7.147199	60954.160	61046.649
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate	39145.9202	39187.6397	3.038551	1981-1999 –> 2000-2012	7.176897	61099.526	61178.803
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	38531.7536	38580.4264	2.919875	1981-1999 –> 2000-2012	7.045849	60464.220	60556.709
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	38704.3830	38753.0557	2.952649	1981-1999 –> 2000-2012	7.122019	60717.708	60810.197
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	38864.8391	38913.5118	2.983441	1981-1999 –> 2000-2012	7.183082	60934.069	61026.558
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	38674.9279	38723.6007	2.947031	1981-1999 –> 2000-2012	7.123956	60702.243	60794.732
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	38677.2036	38725.8763	2.947465	1981-1999 –> 2000-2012	7.131716	60718.062	60810.551
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	38898.7142	38940.4337	2.990370	1981-1999 –> 2000-2012	7.186059	60958.669	61037.945
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	51371.3395	51421.6547	3.344206	1981-1999 –> 2000-2012	7.281587	92981.681	93080.414
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	51915.4793	51965.7946	3.438564	1981-1999 –> 2000-2012	7.438711	93761.660	93860.393
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	52114.7110	52165.0262	3.473775	1981-1999 –> 2000-2012	7.423311	93771.020	93869.753
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	51630.5661	51680.8814	3.388831	1981-1999 –> 2000-2012	7.400386	93519.216	93617.949
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	51906.3011	51956.6163	3.436951	1981-1999 –> 2000-2012	7.454779	93818.248	93916.981
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + phosphate	51620.4122	51663.5396	3.387418	1981-1999 –> 2000-2012	7.329891	93248.029	93332.657
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	50910.7514	50961.0666	3.266363	1981-1999 –> 2000-2012	7.195305	92489.098	92587.831
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	51720.4008	51770.7161	3.404434	1981-1999 –> 2000-2012	7.403818	93563.737	93662.470
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	51843.3475	51886.4749	3.426255	1981-1999 –> 2000-2012	7.442338	93746.817	93831.445
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	51414.8685	51465.1837	3.351658	1981-1999 –> 2000-2012	7.364347	93307.730	93406.463

6.3 Target variable coefficients

A data frame to map the target variable is prepared.

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

eras_backward <- GLODAP_glanced %>%
  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 <- full_join(
  lm_best_eras %>% select(basin, gamma_slab, model, eras),
  eras_era)

lm_best <- left_join(
  lm_best,
  GLODAP_tidy %>% select(basin, gamma_slab, era, model, term, estimate))

rm(eras_era, eras_forward, eras_backward)

6.4 Cant coeffcients

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

# subtract coefficients of adjacent era  
lm_best_cant <- lm_best %>%
  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 to wide format
lm_best_cant <- lm_best_cant %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

6.5 Write files

# create table of target varaible coefficients in wide format
lm_best_target <- lm_best %>% 
  pivot_wider(names_from = "term",
              names_prefix = "coeff_",
              values_from = "estimate",
              values_fill = 0
              )


lm_best_target %>%
  write_csv(paste(path_version_data,
                  "lm_best_target.csv",
                  sep = ""))

lm_best_cant %>%
  write_csv(paste(path_version_data,
                  "lm_best_cant.csv",
                  sep = ""))

7 Model diagnotics

7.1 Selection criterion vs predictors

The selection criterion (rmse) was plotted against the number of predictors (limited to 2 - 5).

7.1.1 All models

GLODAP_glanced %>%
  ggplot(aes(as.factor(n_predictors),
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = c(0,10)) +
  geom_boxplot() +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1") +
  ylim(c(0,NA)) +
  labs(x="Number of predictors")

Past versions of eMLR_predictor_model_quality_all-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
f3a708f	jens-daniel-mueller	2020-12-17

7.1.2 Best models

left_join(lm_best_target %>% select(basin, gamma_slab, era, model),
          GLODAP_glanced) %>%
  ggplot(aes("",
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = c(0, 10)) +
  geom_boxplot() +
  facet_grid(gamma_slab ~ era) +
  scale_color_brewer(palette = "Set1") +
  ylim(c(0, NA)) +
  labs(x = "Number of predictors pooled")

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
f3a708f	jens-daniel-mueller	2020-12-17

7.2 RMSE correlation between eras

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

7.2.1 All models

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

lm_all_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)) +
  geom_abline(slope = 1,
              col = 'red') +
  facet_grid(eras ~ basin)

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
e4ca289	jens-daniel-mueller	2020-12-16
158fe26	jens-daniel-mueller	2020-12-15
7a9a4cb	jens-daniel-mueller	2020-12-15
61b263c	jens-daniel-mueller	2020-12-15
984697e	jens-daniel-mueller	2020-12-12
3ebff89	jens-daniel-mueller	2020-12-12
ba112d3	jens-daniel-mueller	2020-12-11
24a632f	jens-daniel-mueller	2020-12-07
6a8004b	jens-daniel-mueller	2020-12-07
70bf1a5	jens-daniel-mueller	2020-12-07
7555355	jens-daniel-mueller	2020-12-07
143d6fa	jens-daniel-mueller	2020-12-07
090e4d5	jens-daniel-mueller	2020-12-02
7c25f7a	jens-daniel-mueller	2020-12-02
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

rm(max_rmse)

7.2.2 Best models

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

lm_best_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)) +
  geom_abline(slope = 1,
              col = 'red') +
  facet_grid(eras ~ basin)

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
a84ff3c	jens-daniel-mueller	2020-12-17

rm(max_rmse)

7.3 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_cant %>% 
  pivot_longer(starts_with("delta_coeff_"),
               names_to = "term",
               names_prefix = "delta_coeff_",
               values_to = "delta_coeff") %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(basin, eras, gamma_slab) %>% 
  count(term) %>% 
  ungroup() %>% 
  pivot_wider(values_from = n, names_from = term)

# 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 - 1981-1999 --> 2000-2012
(-Inf,26]	6	9	7	7	4	4	10
(26,26.5]	10	6	8	2	6	5	6
(26.5,26.75]	6	2	2	8	2	5	6
(26.75,27]	4	4	1	10	5	6	10
(27,27.25]	3	2	3	10	6	8	10
(27.25,27.5]	7	NA	6	7	4	4	10
(27.5,27.75]	7	NA	8	5	6	8	8
(27.75,27.85]	4	NA	7	6	5	10	5
(27.85,27.95]	5	NA	7	6	8	10	6
(27.95,28.05]	5	1	6	7	10	5	4
(28.05,28.1]	4	2	4	8	10	1	6
(28.1,28.15]	2	2	2	8	5	2	5
(28.15,28.2]	2	2	2	8	4	1	6
(28.2, Inf]	6	2	4	8	4	4	10
total	71.00	—	67.00	100.00	79.00	73.00	102.00
Indo-Pacific - 1981-1999 --> 2000-2012
(-Inf,26]	7	5	4	5	10	6	10
(26,26.5]	3	4	3	10	10	4	10
(26.5,26.75]	3	8	2	10	4	5	10
(26.75,27]	4	4	4	9	3	7	6
(27,27.25]	4	3	2	10	7	9	7
(27.25,27.5]	3	2	4	9	6	9	9
(27.5,27.75]	5	1	5	8	7	6	10
(27.75,27.85]	5	2	5	8	6	6	10
(27.85,27.95]	6	2	6	6	5	8	10
(27.95,28.05]	7	4	7	4	7	7	10
(28.05,28.1]	8	4	8	3	8	8	8
(28.1, Inf]	6	9	7	6	5	5	10
total	61.00	48.00	57.00	88.00	78.00	80.00	110.00

7.4 RMSE alternatives

7.4.1 AIC

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

lm_all_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
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17

lm_best_eras %>% 
  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
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17

7.4.2 BIC

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

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

Past versions of BIC_vs_rmse_all_models-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

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

Past versions of BIC_vs_rmse_selected_models-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

7.4.3 AIC vs BIC

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

lm_all_eras %>% 
  ggplot(aes(AIC, BIC, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Past versions of BIC_vs_AIC_all_models-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

lm_best_eras %>% 
  ggplot(aes(AIC, BIC, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Past versions of BIC_vs_AIC_selected_models-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

7.5 RMSE vs VIF

GLODAP_glanced %>% 
  ggplot(aes(rmse, log10(vif_max))) +
  geom_hline(yintercept = 1) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(gamma_slab~basin)

Past versions of rmse_vs_VIF_all_models-1.png

Version	Author	Date
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

7.6 Residual patterns

7.6.1 Fitted vs actual models

Plotted are fitted vs actual target variable values, here: rparams_local$MLR_target`

GLODAP_augmented_best <- left_join(
  lm_best_target %>% select(basin, gamma_slab, era, model),
  GLODAP_augmented
)

# calculate equal axis limits and binwidth
axis_lims <- GLODAP_augmented %>%
  summarise(
    max_value = max(
      c(max(.fitted, max(!!sym(params_local$MLR_target))))
      ),
    min_value = min(
      c(min(.fitted, min(!!sym(params_local$MLR_target))))
    )
  )

i_binwidth <- 1
# binwidth_value <- (axis_lims$max_value - axis_lims$min_value) / 40
axis_lims <- c(axis_lims$min_value, axis_lims$max_value)

GLODAP_augmented %>%
  ggplot(aes(cstar_tref, .fitted)) +
  geom_bin2d(binwidth = i_binwidth) +
  scale_fill_viridis_c() +
  geom_abline(slope = 1,
              col = 'red') +
  coord_equal(xlim = axis_lims,
              ylim = axis_lims) +
  labs(title = "All models")

Past versions of fitted_vs_actual_all-1.png

Version	Author	Date
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

GLODAP_augmented_best %>%
  ggplot(aes(cstar_tref, .fitted)) +
  geom_bin2d(binwidth = i_binwidth) +
  scale_fill_viridis_c() +
  geom_abline(slope = 1,
              col = 'red') +
  coord_equal(xlim = axis_lims,
              ylim = axis_lims) +
  labs(title = "Selected models")

Past versions of fitted_vs_actual_best-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

rm(binwidth_value, axis_lims)

7.6.2 Pooled

In the following, we present residual patterns vs latitude across all domains.

i_ylim <- c(-30,30)

GLODAP_augmented_best %>%
  ggplot(aes(lat, .resid)) +
  geom_bin2d(binwidth = i_binwidth) +
  geom_hline(yintercept = 0, col = "white") +
  scale_fill_viridis_c() +
  labs(
    title = paste(
      "Target variable:",
      params_local$MLR_target,
      "| Selected models",
      "| All domains"
    )
  )

Past versions of residual_patterns_full_range-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

Due to the few large residuals, we limit the y axis range for the plots below.

GLODAP_augmented_best %>%
  ggplot(aes(lat, .resid)) +
  geom_bin2d(binwidth = i_binwidth) +
  geom_hline(yintercept = 0, col = "white") +
  scale_fill_viridis_c() +
  coord_cartesian(ylim = i_ylim) +
  labs(
    title = paste(
      "Target variable:",
      params_local$MLR_target,
      "| Selected models",
      "| All domains"
    )
  )

Past versions of residual_patterns_y_range_limit-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

7.6.3 By model domain

In the following, we present residual patterns vs latitude for separate model domains, ie basins, density slabs and eras.

p_residuals <- function(df){
    ggplot(data = df, aes(lat, .resid)) +
      geom_bin2d(binwidth = i_binwidth) +
      geom_hline(yintercept = 0, col = "black") +
      scale_fill_viridis_c() +
      facet_grid(gamma_slab ~ era) +
      coord_cartesian(ylim = i_ylim) +
      labs(
        title = paste(
          "Target variable:",
          params_local$MLR_target,
          "| selected best models | basin:",
          unique(df$basin)
        )
      )
}

GLODAP_augmented_best %>% 
  group_split(basin) %>% 
  map(p_residuals)

[[1]]

Past versions of residual_patterns_by_model_domain-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
a1ba577	jens-daniel-mueller	2021-02-24
071743d	jens-daniel-mueller	2021-02-24

[[2]]

Past versions of residual_patterns_by_model_domain-2.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
a1ba577	jens-daniel-mueller	2021-02-24

7.6.4 Latitudinal mean

GLODAP_augmented_best <- GLODAP_augmented_best %>%
  mutate(lat_grid = as.numeric(as.character(cut(
    lat,
    seq(-90, 90, 10),
    seq(-85, 85, 10)
  ))))

lat_residual <- GLODAP_augmented_best %>%
  group_by(basin, gamma_slab, era, lat_grid) %>% 
  summarise(.resid_mean = mean(.resid)) %>% 
  ungroup()

lat_residual %>%
  ggplot(aes(lat_grid, .resid_mean, col=era)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0, col = "black") +
  facet_grid(gamma_slab ~ basin)

Past versions of latitudinal_residual-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
fec3558	jens-daniel-mueller	2021-02-24

7.6.5 Latitudinal offset

# calculate residual offset for adjacent eras
lat_residual_offset <- lat_residual  %>%
  select(basin, gamma_slab, era, lat_grid, .resid_mean) %>% 
  arrange(era) %>% 
  group_by(basin, gamma_slab, lat_grid) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         .resid_mean_offset = .resid_mean - lag(.resid_mean)
         ) %>% 
  ungroup() %>% 
  select(-era) %>% 
  drop_na() %>% 
  filter(eras != paste(unique(lat_residual$era)[1],
                       unique(lat_residual$era)[3],
                       sep = " --> "))

lat_residual_offset %>%
  ggplot(aes(lat_grid, .resid_mean_offset, col=eras)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0, col = "black") +
  facet_grid(gamma_slab ~ basin)

Past versions of latitudinal_residual_offset-1.png

Version	Author	Date
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
fec3558	jens-daniel-mueller	2021-02-24

8 VIF

GLODAP_glanced %>% 
  ggplot(aes(as.factor(n), log10(vif_max))) + 
  geom_hline(yintercept = log10(params_local$vif_max)) +
  geom_violin() +
  facet_grid(gamma_slab~basin)

Past versions of vif_distribution_n_predictors-1.png

Version	Author	Date
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
330dcd0	jens-daniel-mueller	2021-03-20

GLODAP_glanced_vif %>% 
  ggplot(aes(Variables, log10(VIF))) + 
  geom_hline(yintercept = log10(params_local$vif_max)) +
  geom_violin() +
  # geom_point(shape = 21) +
  facet_grid(gamma_slab~basin) +
  coord_flip()

Past versions of vif_distribution_type_predictor-1.png

Version	Author	Date
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
330dcd0	jens-daniel-mueller	2021-03-20

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_0.7.2      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_3.3.2   
[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         utf8_1.1.4               R6_2.5.0                
[10] nortest_1.0-4            DBI_1.1.0                colorspace_1.4-1        
[13] withr_2.3.0              gridExtra_2.3            tidyselect_1.1.0        
[16] curl_4.3                 compiler_4.0.3           git2r_0.27.1            
[19] cli_2.1.0                rvest_0.3.6              xml2_1.3.2              
[22] sass_0.2.0               labeling_0.4.2           scales_1.1.1            
[25] checkmate_2.0.0          goftest_1.2-2            digest_0.6.27           
[28] foreign_0.8-80           rmarkdown_2.5            rio_0.5.16              
[31] pkgconfig_2.0.3          htmltools_0.5.0          highr_0.8               
[34] dbplyr_1.4.4             rlang_0.4.9              readxl_1.3.1            
[37] rstudioapi_0.13          farver_2.0.3             generics_0.0.2          
[40] jsonlite_1.7.1           zip_2.1.1                car_3.0-10              
[43] magrittr_1.5             Matrix_1.2-18            Rcpp_1.0.5              
[46] munsell_0.5.0            fansi_0.4.1              abind_1.4-5             
[49] lifecycle_0.2.0          stringi_1.5.3            whisker_0.4             
[52] yaml_2.2.1               carData_3.0-4            plyr_1.8.6              
[55] grid_4.0.3               blob_1.2.1               parallel_4.0.3          
[58] promises_1.1.1           crayon_1.3.4             lattice_0.20-41         
[61] haven_2.3.1              hms_0.5.3                pillar_1.4.7            
[64] reprex_0.3.0             glue_1.4.2               evaluate_0.14           
[67] RcppArmadillo_0.10.1.2.0 data.table_1.13.2        modelr_0.1.8            
[70] vctrs_0.3.5              httpuv_1.5.4             cellranger_1.1.0        
[73] gtable_0.3.0             reshape_0.8.8            assertthat_0.2.1        
[76] xfun_0.18                openxlsx_4.2.3           RcppEigen_0.3.3.7.0     
[79] later_1.1.0.1            viridisLite_0.3.0        ellipsis_0.3.1          
[82] here_0.1