Chapter1 Objective1

pacman::p_load(dplyr, readxl, tidyverse, raster, vegan, tigris, sf, sp, plotly, ggrepel, kableExtra, brms, parameters, gt, katex, emmeans, bayestestR, cowplot, ggeffects, patchwork)

## Set seed
set.seed(97)

# Tree PCQ Data
tree_data <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/Field_Data_FL_AL_MS.xlsx",
                        sheet = "Tree_PCQ")
tree_data <- tree_data %>%
  filter(Site %in% c("BRSF", "WSF", "Jay"))

# Soil Data
fuel_data <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/Field_Data_FL_AL_MS.xlsx",
                        sheet = "Fuel_Sampling")
fuel_data <- fuel_data %>%
  filter(Site %in% c("BRSF", "WSF", "Jay"))

Seasonal_Fuel_Sampling <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/01_FuelDynamics/02_Data/02_Fuel_Data/Seasonal_Fuel_Sampling.xlsx",
                                     sheet = "Fuel_Data")
Seasonal_Fuel_Sampling <- Seasonal_Fuel_Sampling %>%
  filter(Site %in% c("BRSF", "WSF", "Jay"))

# Seasonal Sampling Locations
Seasonal_Sampling_Locations <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/01_FuelDynamics/02_Data/02_Fuel_Data/Seasonal_Fuel_Sampling.xlsx",
                                          sheet = "Sites")
Seasonal_Sampling_Locations <- Seasonal_Sampling_Locations %>%
  filter(Site %in% c("BRSF", "WSF", "Jay"))

# Bag Weights
bag_weights <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/01_FuelDynamics/02_Data/02_Fuel_Data/Seasonal_Fuel_Sampling.xlsx",
                                          sheet = "Bag_Avg")

## New names:
## • `` -> `...6`
## • `` -> `...7`
## • `` -> `...8`
## • `` -> `...9`
## • `` -> `...10`
## • `` -> `...11`

# Site Data
CogonSites <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/CogonSites_FL_AL_MS.xlsx")
CogonSites <- CogonSites %>%
  filter(Site %in% c("BRSF", "WSF", "Jay"))

# Only include Florida/Alabama Sites
CogonSites <- CogonSites[CogonSites$Site != "CNF" & CogonSites$Site != "DSNF", ]

Filter All data to only include specified species (Per PLANTS database)

Filter all data to only include species found at 3% of all sites

#Fuel Dynamics ## Combine seasonal fuel data

Net Weight Method

Live

Comb_Live_Data_Net <- Combined_Data_Net %>%
  mutate(
    Live_Bag = as.numeric(Live_Bag),
    Live_Weight_Post = as.numeric(Live_Weight_Post),
    Live_Weight_Initial = as.numeric(Live_Weight_Initial),
    Live_Height = as.numeric(Height),
    Net_Live = as.numeric(Net_Live),
    Status = as.character(Status)  # Status as a character
  )

## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `Live_Height = as.numeric(Height)`.
## Caused by warning:
## ! NAs introduced by coercion

Comb_Live_Data_Net <- Comb_Live_Data_Net %>%
  mutate(biomass = Net_Live)

Comb_Live_Data_Net <- Comb_Live_Data_Net %>%
  filter(biomass >= 0)

Comb_Live_Data_Net <- Comb_Live_Data_Net %>%
  mutate(relative_moisture_content = ifelse(biomass > bioT, ((Live_Weight_Initial - Live_Bag) - Net_Live) / Net_Live * 100, NA))

avg_live_values_Net <- Comb_Live_Data_Net %>%
  group_by(Plot, Season, Status) %>%
  summarize(avg_live_biomass = mean(biomass, na.rm = TRUE),
            avg_live_moisture_content = mean(relative_moisture_content, na.rm = TRUE),
            avg_soil_moisture = mean(Soil_Moisture, na.rm = TRUE),
            avg_height = mean(Live_Height, na.rm = TRUE) / 100,
            .groups = "drop")

Dead

Comb_Dead_Data_Net <- Combined_Data_Net %>%
  mutate(
    Dead_Bag = as.numeric(Dead_Bag),
    Dead_Weight_Post = as.numeric(Dead_Weight_Post),
    Dead_Weight_Initial = as.numeric(Dead_Weight_Initial),
    Net_Dead = as.numeric(Net_Dead),
    Status = as.character(Status)  # Status as a character
  )

Comb_Dead_Data_Net <- Comb_Dead_Data_Net %>%
  mutate(biomass = Net_Dead)

Comb_Dead_Data_Net <- Comb_Dead_Data_Net %>%
  filter(biomass >= 0)

Comb_Dead_Data_Net <- Comb_Dead_Data_Net %>%
  mutate(relative_moisture_content = ifelse(biomass > bioT, ((Dead_Weight_Initial - Dead_Bag) - Net_Dead) / Net_Dead * 100, NA))

avg_dead_values_Net <- Comb_Dead_Data_Net %>%
  group_by(Plot, Season, Status) %>%
  summarize(avg_dead_biomass = mean(biomass, na.rm = TRUE),
            avg_dead_moisture_content = mean(relative_moisture_content, na.rm = TRUE),
            avg_soil_moisture = mean(Soil_Moisture, na.rm = TRUE),
            .groups = "drop")

Litter

Comb_Litter_Data_Net <- Combined_Data_Net %>%
  mutate(
    Litter_Bag = as.numeric(Litter_Bag),
    Litter_Weight_Post = as.numeric(Litter_Weight_Post),
    Litter_Weight_Initial = as.numeric(Litter_Weight_Initial),
    Net_Litter = as.numeric(Net_Litter),
    Status = as.character(Status)  # Status as a character
  )

Comb_Litter_Data_Net <- Comb_Litter_Data_Net %>%
  mutate(biomass = Net_Litter)

Comb_Litter_Data_Net <- Comb_Litter_Data_Net %>%
  filter(biomass >= 0)

Comb_Litter_Data_Net <- Comb_Litter_Data_Net %>%
  mutate(relative_moisture_content = ifelse(biomass > bioT, ((Litter_Weight_Initial - Litter_Bag) - Net_Litter) / Net_Litter * 100, NA))

avg_litter_values_Net <- Comb_Litter_Data_Net %>%
  group_by(Plot, Season, Status) %>%
  summarize(avg_litter_biomass = mean(biomass, na.rm = TRUE),
            avg_litter_moisture_content = mean(relative_moisture_content, na.rm = TRUE),
            avg_soil_moisture = mean(Soil_Moisture, na.rm = TRUE),
            .groups = "drop")

Average Bag Weight Method

Live

Comb_Live_Data_Avg <- Combined_Data_Avg %>%
  mutate(
    Live_Bag = as.numeric(Live_Bag),
    Live_Weight_Post = as.numeric(Live_Weight_Post),
    Live_Weight_Initial = as.numeric(Live_Weight_Initial),
    Live_Height = as.numeric(Height),
    Dry_LiveBag = as.numeric(Dry_LiveBag),
    Status = as.character(Status)  # Status as a character
  )

## Warning: There were 2 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `Live_Height = as.numeric(Height)`.
## Caused by warning:
## ! NAs introduced by coercion
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 1 remaining warning.

Comb_Live_Data_Avg <- Comb_Live_Data_Avg %>%
  mutate(biomass = Live_Weight_Post - Dry_LiveBag)

Comb_Live_Data_Avg <- Comb_Live_Data_Avg %>%
  filter(biomass >= 0)

Comb_Live_Data_Avg <- Comb_Live_Data_Avg %>%
  mutate(relative_moisture_content = ifelse(biomass > bioT, (Live_Weight_Initial - Live_Weight_Post) / biomass * 100, NA))

avg_live_values_Avg <- Comb_Live_Data_Avg %>%
  group_by(Plot, Season, Status) %>%
  summarize(avg_live_biomass = mean(biomass, na.rm = TRUE),
            avg_live_moisture_content = mean(relative_moisture_content, na.rm = TRUE),
            avg_soil_moisture = mean(Soil_Moisture, na.rm = TRUE),
            avg_height = mean(Live_Height, na.rm = TRUE) / 100,
            .groups = "drop")

Dead

Comb_Dead_Data_Avg <- Combined_Data_Avg %>%
  mutate(
    Dead_Bag = as.numeric(Dead_Bag),
    Dead_Weight_Post = as.numeric(Dead_Weight_Post),
    Dead_Weight_Initial = as.numeric(Dead_Weight_Initial),
    Dry_DeadBag = as.numeric(Dry_DeadBag),
    Status = as.character(Status)  # Status as a character
  )

## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `Dry_DeadBag = as.numeric(Dry_DeadBag)`.
## Caused by warning:
## ! NAs introduced by coercion

Comb_Dead_Data_Avg <- Comb_Dead_Data_Avg %>%
  mutate(biomass = Dead_Weight_Post - Dry_DeadBag)

Comb_Dead_Data_Avg <- Comb_Dead_Data_Avg %>%
  filter(biomass >= 0)

Comb_Dead_Data_Avg <- Comb_Dead_Data_Avg %>%
  mutate(relative_moisture_content = ifelse(biomass > bioT, (Dead_Weight_Initial - Dead_Weight_Post) / biomass * 100, NA))

avg_dead_values_Avg <- Comb_Dead_Data_Avg %>%
  group_by(Plot, Season, Status) %>%
  summarize(avg_dead_biomass = mean(biomass, na.rm = TRUE),
            avg_dead_moisture_content = mean(relative_moisture_content, na.rm = TRUE),
            avg_soil_moisture = mean(Soil_Moisture, na.rm = TRUE),
            .groups = "drop")

Litter

Comb_Litter_Data_Avg <- Combined_Data_Avg %>%
  mutate(
    Litter_Bag = as.numeric(Litter_Bag),
    Litter_Weight_Post = as.numeric(Litter_Weight_Post),
    Litter_Weight_Initial = as.numeric(Litter_Weight_Initial),
    Dry_LitterBag = as.numeric(Dry_LitterBag),
    Status = as.character(Status)  # Status as a character
  )

## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `Dry_LitterBag = as.numeric(Dry_LitterBag)`.
## Caused by warning:
## ! NAs introduced by coercion

Comb_Litter_Data_Avg <- Comb_Litter_Data_Avg %>%
  mutate(biomass = Litter_Weight_Post - Dry_LitterBag)

Comb_Litter_Data_Avg <- Comb_Litter_Data_Avg %>%
  filter(biomass >= 0)

Comb_Litter_Data_Avg <- Comb_Litter_Data_Avg %>%
  mutate(relative_moisture_content = ifelse(biomass > bioT, (Litter_Weight_Initial - Litter_Weight_Post) / biomass * 100, NA))

avg_litter_values_Avg <- Comb_Litter_Data_Avg %>%
  group_by(Plot, Season, Status) %>%
  summarize(avg_litter_biomass = mean(biomass, na.rm = TRUE),
            avg_litter_moisture_content = mean(relative_moisture_content, na.rm = TRUE),
            avg_soil_moisture = mean(Soil_Moisture, na.rm = TRUE),
            .groups = "drop")

Fill in gaps within Net method with Avg method.

# Live
avg_live_values_Combined <- avg_live_values_Net %>%
  full_join(avg_live_values_Avg, by = "Plot", suffix = c("_Net", "_Avg")) %>%
  mutate(
    avg_live_biomass = coalesce(avg_live_biomass_Net, avg_live_biomass_Avg),
    avg_live_moisture_content = coalesce(avg_live_moisture_content_Net, avg_live_moisture_content_Avg),
    avg_soil_moisture = coalesce(avg_soil_moisture_Net, avg_soil_moisture_Avg),
    avg_height = coalesce(avg_height_Net, avg_height_Avg),
    Season = coalesce(Season_Net, Season_Avg),
    Status = coalesce(Status_Net, Status_Avg)
  ) %>%
  select(Plot, Season, Status, avg_live_biomass, avg_live_moisture_content, avg_soil_moisture, avg_height)

# Dead
avg_dead_values_Combined <- avg_dead_values_Net %>%
  full_join(avg_dead_values_Avg, by = "Plot", suffix = c("_Net", "_Avg")) %>%
  mutate(
    avg_dead_biomass = coalesce(avg_dead_biomass_Net, avg_dead_biomass_Avg),
    avg_dead_moisture_content = coalesce(avg_dead_moisture_content_Net, avg_dead_moisture_content_Avg),
    avg_soil_moisture = coalesce(avg_soil_moisture_Net, avg_soil_moisture_Avg),
    Season = coalesce(Season_Net, Season_Avg),
    Status = coalesce(Status_Net, Status_Avg)
  ) %>%
  select(Plot, Season, Status, avg_dead_biomass, avg_dead_moisture_content, avg_soil_moisture)

# Litter
avg_litter_values_Combined <- avg_litter_values_Net %>%
  full_join(avg_litter_values_Avg, by = "Plot", suffix = c("_Net", "_Avg")) %>%
  mutate(
    avg_litter_biomass = coalesce(avg_litter_biomass_Net, avg_litter_biomass_Avg),
    avg_litter_moisture_content = coalesce(avg_litter_moisture_content_Net, avg_litter_moisture_content_Avg),
    avg_soil_moisture = coalesce(avg_soil_moisture_Net, avg_soil_moisture_Avg),
    Season = coalesce(Season_Net, Season_Avg),
    Status = coalesce(Status_Net, Status_Avg)
  ) %>%
  select(Plot, Season, Status, avg_litter_biomass, avg_litter_moisture_content, avg_soil_moisture)

Combine summer sampling (CogonSites) locations with winter sampling locations

Merge avg_live_values, avg_dead_values, and avg_litter_values

Average Fuel Values by Invasion Status and Season

There are 10,000 square meters in a hectare. Biomass is from 25 cm by 25 cm quadrats, so we have 0.0625 square meters. Therefore, 10,000/0.0625 = 160,000. So biomass gets multiplied by 160,000 and divided by 1,000,000 to convert from grams to tonnes.

25th, 50th and 75 quantiles of fuel values

Fuel_model_quantiles <- avg_fuel_values %>%
  group_by(Status, Season) %>%
  summarize(avg_live_biomass_25 = quantile(avg_live_biomass, 0.25, na.rm = TRUE) * 0.16,
            avg_live_biomass_50 = quantile(avg_live_biomass, 0.50, na.rm = TRUE) * 0.16,
            avg_live_biomass_75 = quantile(avg_live_biomass, 0.75, na.rm = TRUE) * 0.16,
            avg_dead_biomass_25 = quantile(avg_dead_biomass, 0.25, na.rm = TRUE) * 0.16,
            avg_dead_biomass_50 = quantile(avg_dead_biomass, 0.50, na.rm = TRUE) * 0.16,
            avg_dead_biomass_75 = quantile(avg_dead_biomass, 0.75, na.rm = TRUE) * 0.16,
            avg_litter_biomass_25 = quantile(avg_litter_biomass, 0.25, na.rm = TRUE) * 0.16,
            avg_litter_biomass_50 = quantile(avg_litter_biomass, 0.50, na.rm = TRUE) * 0.16,
            avg_litter_biomass_75 = quantile(avg_litter_biomass, 0.75, na.rm = TRUE) * 0.16,
            avg_live_moisture_content_25 = quantile(avg_live_moisture_content, 0.25, na.rm = TRUE),
            avg_live_moisture_content_50 = quantile(avg_live_moisture_content, 0.50, na.rm = TRUE),
            avg_live_moisture_content_75 = quantile(avg_live_moisture_content, 0.75, na.rm = TRUE),
            avg_dead_moisture_content_25 = quantile(avg_dead_moisture_content, 0.25, na.rm = TRUE),
            avg_dead_moisture_content_50 = quantile(avg_dead_moisture_content, 0.50, na.rm = TRUE),
            avg_dead_moisture_content_75 = quantile(avg_dead_moisture_content, 0.75, na.rm = TRUE),
            avg_litter_moisture_content_25 = quantile(avg_litter_moisture_content, 0.25, na.rm = TRUE),
            avg_litter_moisture_content_50 = quantile(avg_litter_moisture_content, 0.50, na.rm = TRUE),
            avg_litter_moisture_content_75 = quantile(avg_litter_moisture_content, 0.75, na.rm = TRUE),
            avg_soil_moisture_25 = quantile(avg_soil_moisture, 0.25, na.rm = TRUE),
            avg_soil_moisture_50 = quantile(avg_soil_moisture, 0.50, na.rm = TRUE),
            avg_soil_moisture_75 = quantile(avg_soil_moisture, 0.75, na.rm = TRUE),
            avg_height_25 = quantile(avg_height, 0.25, na.rm = TRUE),
            avg_height_50 = quantile(avg_height, 0.50, na.rm = TRUE),
            avg_height_75 = quantile(avg_height, 0.75, na.rm = TRUE),
            .groups = "drop")

# Kable table of quantiles
kable(Fuel_model_quantiles)

Status	Season	avg_live_biomass_25	avg_live_biomass_50	avg_live_biomass_75	avg_dead_biomass_25	avg_dead_biomass_50	avg_dead_biomass_75	avg_litter_biomass_25	avg_litter_biomass_50	avg_litter_biomass_75	avg_live_moisture_content_25	avg_live_moisture_content_50	avg_live_moisture_content_75	avg_dead_moisture_content_25	avg_dead_moisture_content_50	avg_dead_moisture_content_75	avg_litter_moisture_content_25	avg_litter_moisture_content_50	avg_litter_moisture_content_75	avg_soil_moisture_25	avg_soil_moisture_50	avg_soil_moisture_75	avg_height_25	avg_height_50	avg_height_75
Invaded	Green_Up	1.1562667	2.1616000	3.4720000	1.8922667	2.4192000	3.108267	3.486400	4.974400	9.215467	54.66557	117.06158	133.0470	9.195465	10.39843	16.57708	9.487179	11.44906	14.92138	4.833333	5.766667	7.10000	0.5600000	0.7533333	0.9500000
Invaded	Summer	1.7720000	2.4472000	3.7221333	1.2645333	2.3952000	4.480933	2.325600	4.085333	6.754400	133.21727	147.42139	168.2493	13.454489	18.01118	27.29767	11.681481	21.20772	35.50451	6.316667	10.900000	12.95833	0.6633333	0.8050000	1.0100000
Invaded	Winter	0.9458667	1.4976000	2.4898667	1.9476000	3.4101333	6.198267	3.023867	5.620267	7.916800	95.76815	119.49396	151.1411	13.788625	19.72430	36.73561	15.979345	27.86209	47.96388	5.933333	10.916667	13.89167	0.7116667	0.8500000	0.9733333
Non_Invaded	Green_Up	0.3685333	0.5088000	0.7546667	0.3370667	0.7482667	1.361600	3.924267	6.187200	8.342933	51.67528	80.33146	146.1973	9.750584	15.46700	17.59368	7.290356	12.30107	17.27920	3.066667	4.033333	9.30000	0.2333333	0.3333333	0.4366667
Non_Invaded	Summer	0.2821333	0.5946667	1.0218667	0.1384000	0.3152000	0.896000	3.992200	6.060000	7.308933	133.27391	163.91720	191.7656	8.801051	15.42178	29.73250	10.007541	21.21443	47.66848	3.741667	5.500000	11.65833	0.1533333	0.2366667	0.3366667
Non_Invaded	Winter	0.2112000	0.2728000	0.5125333	0.3168000	0.7242667	1.806667	4.612133	6.603733	9.257733	30.64949	85.18529	184.4349	11.679660	16.25337	49.32975	15.910721	42.65335	56.80946	6.233333	9.566667	12.37500	0.1116667	0.2366667	0.3583333

Fuel Table

Fuel and Moisture Quantiles by Invasion Status and Season
Variable	Invaded - Spring	Invaded - Summer	Invaded - Winter	Non Invaded - Spring	Non Invaded - Summer	Non Invaded - Winter
Live Biomass (25%)	1.16	1.77	0.95	0.37	0.28	0.21
Live Biomass (50%)	2.16	2.45	1.50	0.51	0.59	0.27
Live Biomass (75%)	3.47	3.72	2.49	0.75	1.02	0.51
Dead Biomass (25%)	1.89	1.26	1.95	0.34	0.14	0.32
Dead Biomass (50%)	2.42	2.40	3.41	0.75	0.32	0.72
Dead Biomass (75%)	3.11	4.48	6.20	1.36	0.90	1.81
Litter Biomass (25%)	3.49	2.33	3.02	3.92	3.99	4.61
Litter Biomass (50%)	4.97	4.09	5.62	6.19	6.06	6.60
Litter Biomass (75%)	9.22	6.75	7.92	8.34	7.31	9.26
Live Moisture Content (25%)	54.67	133.22	95.77	51.68	133.27	30.65
Live Moisture Content (50%)	117.06	147.42	119.49	80.33	163.92	85.19
Live Moisture Content (75%)	133.05	168.25	151.14	146.20	191.77	184.43
Dead Moisture Content (25%)	9.20	13.45	13.79	9.75	8.80	11.68
Dead Moisture Content (50%)	10.40	18.01	19.72	15.47	15.42	16.25
Dead Moisture Content (75%)	16.58	27.30	36.74	17.59	29.73	49.33
Litter Moisture Content (25%)	9.49	11.68	15.98	7.29	10.01	15.91
Litter Moisture Content (50%)	11.45	21.21	27.86	12.30	21.21	42.65
Litter Moisture Content (75%)	14.92	35.50	47.96	17.28	47.67	56.81
Soil Moisture (25%)	4.83	6.32	5.93	3.07	3.74	6.23
Soil Moisture (50%)	5.77	10.90	10.92	4.03	5.50	9.57
Soil Moisture (75%)	7.10	12.96	13.89	9.30	11.66	12.38
Height (25%)	0.56	0.66	0.71	0.23	0.15	0.11
Height (50%)	0.75	0.80	0.85	0.33	0.24	0.24
Height (75%)	0.95	1.01	0.97	0.44	0.34	0.36

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##   <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
##   <thead>
##     <tr class="gt_heading">
##       <td colspan="7" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Fuel and Moisture Quantiles by Invasion Status and Season</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="Variable">Variable</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Invaded---Spring">Invaded - Spring</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Invaded---Summer">Invaded - Summer</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Invaded---Winter">Invaded - Winter</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Non_Invaded---Spring">Non Invaded - Spring</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Non_Invaded---Summer">Non Invaded - Summer</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Non_Invaded---Winter">Non Invaded - Winter</th>
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##   </thead>
##   <tbody class="gt_table_body">
##     <tr><td headers="Variable" class="gt_row gt_left">Live Biomass (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">1.16</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">1.77</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">0.95</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.37</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.28</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.21</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Live Biomass (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">2.16</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">2.45</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">1.50</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.51</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.59</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.27</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Live Biomass (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">3.47</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">3.72</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">2.49</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.75</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">1.02</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.51</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Dead Biomass (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">1.89</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">1.26</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">1.95</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.34</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.14</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.32</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Dead Biomass (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">2.42</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">2.40</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">3.41</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.75</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.32</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.72</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Dead Biomass (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">3.11</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">4.48</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">6.20</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">1.36</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.90</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">1.81</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Litter Biomass (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">3.49</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">2.33</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">3.02</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">3.92</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">3.99</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">4.61</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Litter Biomass (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">4.97</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">4.09</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">5.62</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">6.19</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">6.06</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">6.60</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Litter Biomass (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">9.22</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">6.75</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">7.92</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">8.34</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">7.31</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">9.26</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Live Moisture Content (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">54.67</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">133.22</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">95.77</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">51.68</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">133.27</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">30.65</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Live Moisture Content (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">117.06</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">147.42</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">119.49</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">80.33</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">163.92</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">85.19</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Live Moisture Content (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">133.05</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">168.25</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">151.14</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">146.20</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">191.77</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">184.43</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Dead Moisture Content (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">9.20</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">13.45</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">13.79</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">9.75</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">8.80</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">11.68</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Dead Moisture Content (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">10.40</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">18.01</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">19.72</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">15.47</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">15.42</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">16.25</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Dead Moisture Content (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">16.58</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">27.30</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">36.74</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">17.59</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">29.73</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">49.33</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Litter Moisture Content (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">9.49</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">11.68</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">15.98</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">7.29</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">10.01</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">15.91</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Litter Moisture Content (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">11.45</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">21.21</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">27.86</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">12.30</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">21.21</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">42.65</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Litter Moisture Content (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">14.92</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">35.50</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">47.96</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">17.28</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">47.67</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">56.81</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Soil Moisture (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">4.83</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">6.32</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">5.93</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">3.07</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">3.74</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">6.23</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Soil Moisture (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">5.77</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">10.90</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">10.92</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">4.03</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">5.50</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">9.57</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Soil Moisture (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">7.10</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">12.96</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">13.89</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">9.30</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">11.66</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">12.38</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Height (25%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">0.56</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">0.66</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">0.71</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.23</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.15</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.11</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Height (50%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">0.75</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">0.80</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">0.85</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.33</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.24</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.24</td></tr>
##     <tr><td headers="Variable" class="gt_row gt_left">Height (75%)</td>
## <td headers="Invaded - Spring" class="gt_row gt_right">0.95</td>
## <td headers="Invaded - Summer" class="gt_row gt_right">1.01</td>
## <td headers="Invaded - Winter" class="gt_row gt_right">0.97</td>
## <td headers="Non_Invaded - Spring" class="gt_row gt_right">0.44</td>
## <td headers="Non_Invaded - Summer" class="gt_row gt_right">0.34</td>
## <td headers="Non_Invaded - Winter" class="gt_row gt_right">0.36</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Objective 1- Cogongrass relationship with fuel dynamics

Data Cleaning

GLMM Live Fuel Biomass

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_live_biomass ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.35      1.36     0.05     4.98 1.00     2198     3697
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                    -20.82     29.43   -99.13    13.10 1.00     3076
## StatusInvaded                 18.99      3.71    12.01    26.34 1.00     6018
## SeasonSpring                  -0.11      0.17    -0.45     0.23 1.00     8077
## SeasonWinter                  -0.23      0.16    -0.54     0.08 1.00     8971
## Latitude                       0.71      0.98    -0.41     3.33 1.00     3071
## StatusInvaded:SeasonSpring    -0.69      0.30    -1.26    -0.07 1.00     8947
## StatusInvaded:SeasonWinter    -0.99      0.28    -1.54    -0.42 1.00     9396
## StatusInvaded:Latitude        -0.57      0.12    -0.81    -0.34 1.00     6079
##                            Tail_ESS
## Intercept                      3661
## StatusInvaded                  6260
## SeasonSpring                   8146
## SeasonWinter                   7788
## Latitude                       3757
## StatusInvaded:SeasonSpring     7917
## StatusInvaded:SeasonWinter     8264
## StatusInvaded:Latitude         6398
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.59      0.08     0.45     0.75 1.00     6119     7080
## nu        2.41      0.65     1.48     3.99 1.00     6391     7219
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    1.959     1.625      2.30
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    1.259     0.765      1.78
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.962     0.512      1.43
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |   pd
## -------------------------------------
## Invaded - Non_Invaded | Summer | 100%
## Invaded - Non_Invaded | Spring | 100%
## Invaded - Non_Invaded | Winter | 100%

Live Biomass Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Live Biomass</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
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##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">−9.97</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">17.75</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−88.91</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">19.08</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.783</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">3,074</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,618</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">0.35</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">0.59</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−0.61</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">2.98</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.808</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">3,070</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,710</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">−0.11</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">0.17</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−0.44</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">0.24</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.744</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">8,056</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">8,134</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right">−0.23</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">0.16</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−0.53</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">0.09</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right">0.928</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">8,941</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">7,759</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right" style="font-weight: bold;">18.94</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right" style="font-weight: bold;">3.71</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">11.86</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">26.15</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">5,974</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">6,228</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.57</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.12</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.81</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−0.34</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">6,034</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">6,384</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.70</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.30</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−1.30</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−0.12</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right" style="font-weight: bold;">0.984</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">8,934</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,893</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.99</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.28</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−1.55</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−0.43</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">9,360</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,232</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Live Biomass

## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

Conditional Effects Live Biomass

GLMM Dead Fuel Biomass

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_dead_biomass ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.83      1.05     0.02     3.78 1.00     2404     4047
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                     -1.81     19.64   -55.21    29.90 1.00     4300
## StatusInvaded                 14.57      7.85    -0.57    30.62 1.00     7032
## SeasonSpring                   0.45      0.28    -0.09     1.01 1.00     8891
## SeasonWinter                   0.39      0.25    -0.08     0.91 1.00     9351
## Latitude                       0.07      0.65    -0.98     1.84 1.00     4345
## StatusInvaded:SeasonSpring    -0.26      0.45    -1.16     0.60 1.00     8228
## StatusInvaded:SeasonWinter     0.79      0.62    -0.46     2.01 1.00     8360
## StatusInvaded:Latitude        -0.42      0.26    -0.94     0.08 1.00     7066
##                            Tail_ESS
## Intercept                      3243
## StatusInvaded                  7336
## SeasonSpring                   8462
## SeasonWinter                   9020
## Latitude                       3242
## StatusInvaded:SeasonSpring     8068
## StatusInvaded:SeasonWinter     8097
## StatusInvaded:Latitude         7205
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.89      0.13     0.65     1.17 1.00     6823     6390
## nu        1.77      0.43     1.14     2.78 1.00     6276     4536
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Warning: There were 21 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

##  Family: student 
##   Links: mu = identity 
## Formula: avg_dead_biomass ~ Status + Season + Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.85      1.04     0.01     3.94 1.01      590      268
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        -3.20     21.57   -69.21    24.72 1.01      550      213
## StatusInvaded     1.88      0.18     1.52     2.24 1.00     1579     1398
## SeasonSpring      0.33      0.21    -0.07     0.73 1.00     1809     2871
## SeasonWinter      0.44      0.23    -0.02     0.91 1.01      804      238
## Latitude          0.12      0.72    -0.81     2.34 1.01      543      213
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.83      0.13     0.61     1.11 1.00     2323     5463
## nu        1.61      0.36     1.09     2.46 1.00     2623     3485
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     2.12      1.52      2.81
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     1.90      1.17      2.65
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     2.97      1.70      4.06
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |   pd
## -------------------------------------
## Invaded - Non_Invaded | Summer | 100%
## Invaded - Non_Invaded | Spring | 100%
## Invaded - Non_Invaded | Winter | 100%

##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     1.88      1.53      2.25
## 
## Results are averaged over the levels of: Season 
## Point estimate displayed: median 
## HPD interval probability: 0.95

##  contrast        estimate lower.HPD upper.HPD
##  Spring - Summer    0.323   -0.0687     0.731
##  Winter - Summer    0.433    0.0069     0.934
##  Winter - Spring    0.103   -0.4635     0.710
## 
## Results are averaged over the levels of: Status 
## Point estimate displayed: median 
## HPD interval probability: 0.95

Dead Biomass Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Dead Biomass</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
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##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
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##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">1.59</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">7.86</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−48.58</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">34.29</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.587</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">4,281</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,239</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−0.04</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">0.26</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−1.15</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">1.61</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.567</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">4,325</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,237</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">0.44</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">0.28</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−0.08</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">1.02</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.949</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">8,856</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">8,414</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right">0.38</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">0.24</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−0.09</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">0.90</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right">0.946</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">9,330</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">9,004</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right" style="font-weight: bold;">14.38</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right" style="font-weight: bold;">7.74</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.96</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">30.12</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right" style="font-weight: bold;">0.971</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,014</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,298</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.41</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.25</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.92</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">0.09</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right" style="font-weight: bold;">0.953</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,048</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,167</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right">−0.25</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">0.44</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−1.18</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">0.59</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right">0.717</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">8,189</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">8,038</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">0.79</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">0.60</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−0.45</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">2.02</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.899</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">8,329</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,073</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Dead Biomass Summary Table- NonI

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Dead Biomass (Non-Interaction Model)</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">2.17</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">8.15</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−55.41</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">29.11</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.608</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">568</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">219</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−0.06</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">0.27</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−0.97</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">1.83</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.593</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">561</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">219</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">0.32</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">0.21</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−0.07</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">0.73</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.947</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">1,811</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">2,851</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">0.43</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.23</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">0.01</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">0.93</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.971</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">796</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">237</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.001</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right" style="font-weight: bold;">1.88</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.18</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">1.53</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">2.25</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">1,542</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">1,405</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Dead Biomass

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

GLMM Litter Fuel Biomass

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_litter_biomass ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     3.03      2.66     0.35    10.24 1.00     3079     4873
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                     49.58     82.64   -44.36   281.96 1.00     3705
## StatusInvaded                 -7.26     14.14   -34.55    20.59 1.00     7664
## SeasonSpring                   1.05      0.96    -0.80     2.97 1.00     8914
## SeasonWinter                   0.89      0.82    -0.73     2.49 1.00     9150
## Latitude                      -1.47      2.76    -9.30     1.65 1.00     3681
## StatusInvaded:SeasonSpring     0.75      1.31    -1.81     3.29 1.00     9052
## StatusInvaded:SeasonWinter     0.55      1.21    -1.87     2.89 1.00     8713
## StatusInvaded:Latitude         0.20      0.47    -0.73     1.11 1.00     7711
##                            Tail_ESS
## Intercept                      3892
## StatusInvaded                  7903
## SeasonSpring                   8540
## SeasonWinter                   8591
## Latitude                       3868
## StatusInvaded:SeasonSpring     8628
## StatusInvaded:SeasonWinter     8324
## StatusInvaded:Latitude         7864
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     2.82      0.31     2.25     3.46 1.00     7382     8317
## nu        5.43      3.20     2.48    13.32 1.00     8045     6919
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Warning: There were 14 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

##  Family: student 
##   Links: mu = identity 
## Formula: avg_litter_biomass ~ Status + Season + Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.99      2.45     0.34     9.55 1.01      910      633
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        46.53     75.71   -43.07   270.30 1.01      694      150
## StatusInvaded    -0.93      0.50    -1.89     0.06 1.00    10593     7878
## SeasonSpring      1.41      0.68     0.06     2.77 1.00     9681     7702
## SeasonWinter      1.16      0.58     0.01     2.31 1.00     9292     8317
## Latitude         -1.37      2.52    -8.78     1.61 1.01      707      150
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     2.82      0.29     2.30     3.43 1.00     2322     7546
## nu        5.58      3.25     2.52    13.40 1.00     1442      917
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -1.235     -2.53    0.0738
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.467     -2.62    1.7205
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.664     -2.63    1.1840
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 96.30%
## Invaded - Non_Invaded | Spring | 66.56%
## Invaded - Non_Invaded | Winter | 75.26%

Litter Biomass Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Litter Biomass</td>
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##     
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##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
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##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">25.71</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">46.84</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−68.65</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">235.08</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.753</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">3,677</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,862</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−0.67</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">1.56</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−7.64</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">2.47</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.693</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">3,652</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,836</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">1.05</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">0.96</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−0.85</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">2.92</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.864</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">8,864</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">8,480</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right">0.88</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">0.82</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−0.70</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">2.51</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right">0.860</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">9,150</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">8,577</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">−7.42</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">14.09</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−34.80</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">20.04</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.698</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,635</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,879</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right">0.21</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">0.47</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−0.70</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">1.13</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right">0.667</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,683</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,839</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right">0.76</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">1.31</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−1.82</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">3.27</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right">0.717</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">9,026</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">8,607</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">0.58</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">1.21</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−1.73</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">3.02</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.685</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">8,704</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,302</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Litter Biomass Summary Table- NonI

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Litter Biomass (Non-Interaction Model)</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
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##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">22.24</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">45.23</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−65.65</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">234.50</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.725</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">655</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">146</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.003</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−0.56</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">1.50</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−7.78</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">2.27</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.662</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">667</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">145</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.003</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">1.40</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.66</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">0.10</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">2.79</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">0.981</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">9,619</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,695</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.001</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">1.16</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.57</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">0.08</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">2.37</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.975</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">9,033</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,316</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.94</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.49</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−1.88</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">0.06</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right" style="font-weight: bold;">0.968</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">10,528</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,760</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Litter Biomass

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

GLMM Live Moisture

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_live_moisture_content ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 133) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)    18.36     19.87     0.47    70.88 1.00     4054     5736
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                    439.72    487.97  -375.74  1597.50 1.00     5416
## StatusInvaded               -199.11    272.27  -726.60   331.62 1.00     7513
## SeasonSpring                 -69.58     19.02  -106.59   -32.14 1.00     7972
## SeasonWinter                 -71.29     29.92  -129.95   -11.72 1.00     5949
## Latitude                      -9.17     16.27   -47.81    18.07 1.00     5440
## StatusInvaded:SeasonSpring    20.50     23.59   -25.92    67.63 1.00     7715
## StatusInvaded:SeasonWinter    41.01     32.62   -23.11   104.90 1.00     6103
## StatusInvaded:Latitude         6.22      9.09   -11.53    23.77 1.00     7539
##                            Tail_ESS
## Intercept                      4202
## StatusInvaded                  7128
## SeasonSpring                   7422
## SeasonWinter                   6524
## Latitude                       4266
## StatusInvaded:SeasonSpring     6713
## StatusInvaded:SeasonWinter     6778
## StatusInvaded:Latitude         7158
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma    44.32      4.36    35.24    52.60 1.00     8337     6570
## nu       15.41     11.57     3.47    46.80 1.00     8193     7380
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Warning: There were 12 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

##  Family: student 
##   Links: mu = identity 
## Formula: avg_live_moisture_content ~ Status + Season + Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 133) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)    17.39     17.78     0.46    66.82 1.00     2770     4125
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept       270.64    402.88  -485.46  1278.00 1.00     3558     2923
## StatusInvaded    -5.31      9.29   -23.47    12.48 1.00    10117     7897
## SeasonSpring    -56.11     10.80   -77.37   -34.70 1.00    10331     8181
## SeasonWinter    -37.99     11.71   -60.83   -14.98 1.00     9105     8497
## Latitude         -3.69     13.45   -37.39    21.62 1.00     3574     2971
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma    45.01      3.90    37.15    52.56 1.00     7949     6071
## nu       17.00     11.51     4.33    48.08 1.00     7622     7014
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

## Warning: Removed 53 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

## Warning: Removed 53 rows containing missing values or values outside the scale range
## (`geom_point()`).

## Warning: Removed 53 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
## Removed 53 rows containing missing values or values outside the scale range
## (`geom_point()`).

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -14.13     -36.3      7.87
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     6.19     -34.3     47.86
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    26.58     -29.5     87.97
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 89.54%
## Invaded - Non_Invaded | Spring | 61.84%
## Invaded - Non_Invaded | Winter | 81.83%

Live Moisture Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Live Moisture</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
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##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">397.76</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">345.71</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−455.62</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">1,450.93</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.877</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">5,412</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">4,196</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−7.77</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">11.54</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−43.08</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">20.53</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.758</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">5,436</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">4,260</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">−69.56</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">18.94</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−106.36</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−32.06</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,929</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,349</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">−71.37</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">29.31</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−129.55</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−11.51</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.991</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">5,891</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">6,494</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.001</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">−198.37</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">272.62</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−727.48</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">328.45</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.768</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,499</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,111</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right">6.20</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">9.10</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−12.02</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">23.24</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right">0.754</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,526</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,141</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right">20.41</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">23.40</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−24.78</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">68.55</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right">0.811</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">7,613</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">6,629</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">41.08</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">32.51</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−25.05</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">102.67</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.894</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">6,031</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">6,726</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.001</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Live Moisture Summary Table- NonI

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Live Moisture (Non-Interaction Model)</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">240.62</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">246.12</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−544.09</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">1,204.92</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.834</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">3,499</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">2,908</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−2.69</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">8.19</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−34.28</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">24.16</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.637</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">3,514</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">2,956</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">−56.15</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">10.59</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−77.49</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−34.86</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">10,297</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,120</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">−37.98</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">11.55</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−61.03</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−15.22</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">8,900</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,455</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">−5.20</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">9.34</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−23.61</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">12.29</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.715</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">10,050</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,819</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Live Moisture

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

GLMM Dead Moisture

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_dead_moisture_content ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 135) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     5.78      4.68     0.65    18.03 1.00     3515     3733
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                      2.63    125.61  -259.09   256.07 1.00     5090
## StatusInvaded                 16.42     44.60   -70.99   105.10 1.00     7396
## SeasonSpring                   0.54      3.29    -6.26     6.78 1.00     6582
## SeasonWinter                   1.61      3.26    -4.98     7.99 1.00     6618
## Latitude                       0.35      4.20    -8.11     9.00 1.00     5058
## StatusInvaded:SeasonSpring    -4.40      3.81   -11.69     3.46 1.00     6612
## StatusInvaded:SeasonWinter     0.37      4.09    -7.52     8.59 1.00     6979
## StatusInvaded:Latitude        -0.44      1.51    -3.44     2.49 1.00     7358
##                            Tail_ESS
## Intercept                      4620
## StatusInvaded                  6787
## SeasonSpring                   6464
## SeasonWinter                   6726
## Latitude                       4593
## StatusInvaded:SeasonSpring     6784
## StatusInvaded:SeasonWinter     7018
## StatusInvaded:Latitude         6773
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     5.95      0.88     4.43     7.88 1.00     9192     8360
## nu        1.24      0.18     1.01     1.67 1.00     6472     4233
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

##  Family: student 
##   Links: mu = identity 
## Formula: avg_dead_moisture_content ~ Status + Season + Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 135) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     5.54      4.06     0.65    16.22 1.00     2876     3199
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        13.40    110.53  -222.23   249.51 1.00     3752     3221
## StatusInvaded     1.59      1.51    -1.37     4.53 1.00    10246     8404
## SeasonSpring     -2.35      1.72    -5.73     1.02 1.00     8057     7617
## SeasonWinter      1.37      1.94    -2.33     5.30 1.00     8112     7452
## Latitude          0.02      3.68    -7.80     7.85 1.00     3765     3182
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     5.97      0.87     4.46     7.87 1.00     7619     7420
## nu        1.24      0.18     1.01     1.66 1.00     5132     3927
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

## Warning: Removed 51 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

## Warning: Removed 51 rows containing missing values or values outside the scale range
## (`geom_point()`).

## Warning: Removed 51 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
## Removed 51 rows containing missing values or values outside the scale range
## (`geom_point()`).

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     3.42     -2.43      9.10
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    -1.09     -5.64      3.69
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     3.65     -1.86      9.54
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 87.62%
## Invaded - Non_Invaded | Spring | 67.59%
## Invaded - Non_Invaded | Winter | 90.38%

Dead Moisture Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Dead Moisture</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
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##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">3.44</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">85.40</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−256.26</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">257.90</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.517</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">5,044</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">4,606</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">0.32</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">2.87</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−8.12</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">9.00</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.547</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">5,013</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">4,580</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">0.65</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">3.19</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−5.94</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">7.00</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.580</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">6,562</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">6,441</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right">1.63</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">3.15</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−4.84</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">8.13</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right">0.699</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">6,604</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">6,705</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">16.12</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">43.48</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−68.99</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">106.37</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.645</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,382</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">6,710</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.002</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right">−0.43</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">1.46</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−3.44</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">2.49</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right">0.615</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,345</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">6,702</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right">1.002</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right">−4.47</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">3.73</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−12.10</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">2.89</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right">0.881</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">6,594</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">6,766</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">0.28</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">3.97</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−7.64</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">8.40</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.528</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">6,968</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">6,996</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Dead Moisture Summary Table- NonI

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Dead Moisture (Non-Interaction Model)</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">11.98</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">76.46</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−214.32</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">254.30</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.568</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">3,736</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,215</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">0.06</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">2.55</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−8.28</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">7.30</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.511</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">3,749</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,177</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">−2.36</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">1.70</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−5.70</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">1.04</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.913</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">8,036</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">7,565</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right">1.30</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">1.90</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−2.36</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">5.25</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right">0.763</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">7,955</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">7,420</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">1.61</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">1.51</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−1.40</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">4.49</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.854</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">10,234</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">8,348</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Dead Moisture

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

GLMM Litter Moisture

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_litter_moisture_content ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     7.74      8.33     0.21    30.70 1.00     3108     4571
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                    -10.53    200.19  -330.59   515.57 1.00     3907
## StatusInvaded                 38.59     81.21  -118.53   201.24 1.00     7185
## SeasonSpring                  -8.65      4.92   -18.61     0.51 1.00     7911
## SeasonWinter                  15.92      6.40     3.33    28.19 1.00     7279
## Latitude                       1.08      6.70   -16.46    11.72 1.00     3876
## StatusInvaded:SeasonSpring    -0.27      6.18   -12.26    12.09 1.00     9223
## StatusInvaded:SeasonWinter    -8.89      8.20   -24.50     7.55 1.00     7549
## StatusInvaded:Latitude        -1.31      2.73    -6.75     3.99 1.00     7170
##                            Tail_ESS
## Intercept                      2855
## StatusInvaded                  7228
## SeasonSpring                   8070
## SeasonWinter                   7143
## Latitude                       2834
## StatusInvaded:SeasonSpring     8569
## StatusInvaded:SeasonWinter     8081
## StatusInvaded:Latitude         7151
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma    14.57      1.88    11.09    18.51 1.00     7323     6902
## nu        2.36      0.65     1.45     3.89 1.00     7336     6817
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Warning: There were 26 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

##  Family: student 
##   Links: mu = identity 
## Formula: avg_litter_moisture_content ~ Status + Season + Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     7.23      7.04     0.21    25.62 1.00     2492     3649
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        -8.46    167.80  -329.55   403.32 1.00     2098     1941
## StatusInvaded    -1.94      2.82    -7.49     3.48 1.00     8865     7124
## SeasonSpring     -8.97      3.51   -16.05    -2.49 1.00     6874     7051
## SeasonWinter     10.33      3.93     2.75    18.15 1.00    10008     8193
## Latitude          1.04      5.60   -12.85    11.74 1.00     2123     1965
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma    14.80      1.85    11.45    18.72 1.00     5550     4750
## nu        2.44      0.67     1.49     4.09 1.00     5472     3861
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.215     -8.52      7.46
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.577     -9.67      8.46
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -9.211    -22.45      4.68
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 52.00%
## Invaded - Non_Invaded | Spring | 55.02%
## Invaded - Non_Invaded | Winter | 90.77%

Litter Moisture Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Litter Moisture</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">−37.99</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">115.05</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−374.56</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">462.90</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.633</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">3,911</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">2,845</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">2.00</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">3.87</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−14.89</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">12.99</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.696</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">3,883</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">2,822</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">−8.46</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">4.91</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−18.24</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">0.76</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">0.967</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,892</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,973</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">15.96</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">6.44</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">3.32</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">28.17</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.992</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,255</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,083</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.001</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">38.17</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">79.91</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−123.29</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">194.84</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.683</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,150</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,203</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right">−1.28</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">2.68</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−6.68</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">4.02</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right">0.684</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,134</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,124</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right">−0.30</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">5.99</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−12.31</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">12.01</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right">0.518</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">9,185</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">8,557</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">−8.96</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">8.12</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−24.35</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">7.64</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.860</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">7,498</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,072</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.001</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Litter Moisture Summary Table- NonI

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Litter Moisture (Non-Interaction Model)</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
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##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">−25.14</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">95.84</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−350.03</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">381.47</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.611</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">2,035</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">1,840</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">1.59</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">3.20</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−11.90</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">12.47</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.686</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">2,058</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">1,848</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">−8.89</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">3.55</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−15.67</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−2.19</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">0.997</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">6,855</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,019</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">10.30</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">3.98</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">2.46</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">17.76</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.997</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">9,996</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,155</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">−1.91</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">2.83</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−7.49</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">3.48</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.755</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">8,698</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,075</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Litter Moisture

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

GLMM Soil Moisture

Model Comparison

##  Family: student 
##   Links: mu = identity 
## Formula: avg_soil_moisture ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.79      2.95     0.10    10.50 1.00     2522     3959
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                    -45.69     70.44  -144.76   146.47 1.00     4128
## StatusInvaded                  8.90     20.90   -31.97    50.06 1.00     6797
## SeasonSpring                  -0.67      1.18    -3.00     1.68 1.00     8291
## SeasonWinter                   2.03      1.02     0.06     4.06 1.00     8838
## Latitude                       1.76      2.35    -4.64     5.10 1.00     4141
## StatusInvaded:SeasonSpring    -2.71      1.63    -5.93     0.48 1.00     7912
## StatusInvaded:SeasonWinter    -1.80      1.56    -4.91     1.23 1.00     8513
## StatusInvaded:Latitude        -0.22      0.69    -1.58     1.13 1.00     6829
##                            Tail_ESS
## Intercept                      2927
## StatusInvaded                  6359
## SeasonSpring                   8389
## SeasonWinter                   7710
## Latitude                       2951
## StatusInvaded:SeasonSpring     7129
## StatusInvaded:SeasonWinter     8338
## StatusInvaded:Latitude         6481
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     3.23      0.34     2.60     3.92 1.00     8409     7910
## nu        2.02      0.37     1.41     2.86 1.00     8534     6186
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Warning: There were 9 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

##  Family: student 
##   Links: mu = identity 
## Formula: avg_soil_moisture ~ Status + Season + Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 186) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.74      2.61     0.10     9.84 1.00     1576      810
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept       -51.16     55.87  -149.72   102.88 1.00     2056      762
## StatusInvaded     1.04      0.64    -0.20     2.32 1.00     8018     6904
## SeasonSpring     -1.98      0.86    -3.63    -0.28 1.00     5224     4878
## SeasonWinter      1.30      0.74    -0.15     2.74 1.00     5651     7091
## Latitude          1.95      1.86    -3.17     5.24 1.00     2074      757
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     3.23      0.33     2.62     3.90 1.00     6320     6028
## nu        2.02      0.36     1.40     2.83 1.00     6259     5679
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    2.196     0.302      4.08
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.503    -3.240      2.15
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.420    -1.911      2.80
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 98.93%
## Invaded - Non_Invaded | Spring | 64.37%
## Invaded - Non_Invaded | Winter | 63.48%

Soil Moisture Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Soil Moisture</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">−59.45</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">34.88</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−163.89</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">112.68</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.855</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">4,094</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">2,923</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">2.22</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">1.17</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−3.44</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">5.79</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.871</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">4,096</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">2,946</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right">−0.66</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">1.17</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−2.94</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">1.73</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right">0.719</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">8,271</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">8,358</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">2.03</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">1.00</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.01</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">3.98</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.978</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">8,807</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,688</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">8.80</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">21.16</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−33.00</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">48.58</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.661</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">6,773</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">6,335</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right">−0.22</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">0.70</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−1.54</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">1.18</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right">0.623</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">6,805</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">6,454</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right" style="font-weight: bold;">−2.71</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right" style="font-weight: bold;">1.60</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−5.85</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">0.54</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right" style="font-weight: bold;">0.952</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,907</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">6,944</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">−1.78</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">1.55</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−4.79</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">1.32</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.873</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">8,455</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,307</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Soil Moisture Summary Table- NonI

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##   <thead>
##     <tr class="gt_heading">
##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Soil Moisture (Non-Interaction Model)</td>
##     </tr>
##     
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##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
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##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
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##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">−60.48</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">32.13</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−156.97</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">90.07</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.865</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">2,025</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">753</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">2.26</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">1.07</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−2.45</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">5.83</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.880</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">2,044</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">741</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">−1.98</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.88</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−3.68</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−0.36</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">0.989</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">5,122</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">4,828</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.001</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right" style="font-weight: bold;">1.30</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.74</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.10</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">2.78</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right" style="font-weight: bold;">0.960</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">5,583</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,074</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right">1.04</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">0.63</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−0.20</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">2.31</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right">0.948</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,846</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">6,866</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Soil Moisture

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

GLMM Veg Height

Model Comparison

## Warning: There were 4 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

##  Family: student 
##   Links: mu = identity 
## Formula: avg_height ~ Status * Season + Status * Latitude + (1 | Site) 
##    Data: merged_sites (Number of observations: 183) 
##   Draws: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
##          total post-warmup draws = 12000
## 
## Multilevel Hyperparameters:
## ~Site (Number of levels: 3) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.26      0.35     0.00     1.30 1.00     1814     3794
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                     -0.40      4.29   -12.05     6.79 1.00     4568
## StatusInvaded                  3.79      0.70     2.39     5.15 1.00     6795
## SeasonSpring                   0.09      0.04     0.01     0.18 1.00     8091
## SeasonWinter                  -0.02      0.04    -0.10     0.06 1.00     7083
## Latitude                       0.02      0.14    -0.22     0.41 1.00     4576
## StatusInvaded:SeasonSpring    -0.16      0.06    -0.27    -0.04 1.00     8127
## StatusInvaded:SeasonWinter     0.01      0.06    -0.11     0.12 1.00     7169
## StatusInvaded:Latitude        -0.11      0.02    -0.15    -0.06 1.00     6857
##                            Tail_ESS
## Intercept                      3412
## StatusInvaded                  7126
## SeasonSpring                   7987
## SeasonWinter                   7611
## Latitude                       3382
## StatusInvaded:SeasonSpring     8600
## StatusInvaded:SeasonWinter     7706
## StatusInvaded:Latitude         7206
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.14      0.01     0.11     0.16 1.00     7445     7522
## nu        4.95      2.19     2.55    10.41 1.00     7683     6328
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## Using 10 posterior draws for ppc type 'dens_overlay' by default.

## Warning: Removed 3 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_point()`).

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.587     0.521     0.652
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.427     0.333     0.523
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.594     0.498     0.685
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |   pd
## -------------------------------------
## Invaded - Non_Invaded | Summer | 100%
## Invaded - Non_Invaded | Spring | 100%
## Invaded - Non_Invaded | Winter | 100%

Veg Height Summary Table

## Warning: Dropping 'draws_df' class as required metadata was removed.

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##       <td colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Posterior Estimates for Vegetation Height</td>
##     </tr>
##     
##     <tr class="gt_col_headings">
##       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Estimate">Estimate</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Est.-Error">Est. Error</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Lower)">95% HPDI (Lower)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="a95%-HPDI-(Upper)">95% HPDI (Upper)</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Pd">Pd</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Bulk-ESS">Bulk ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Tail-ESS">Tail ESS</th>
##       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="R-hat">R-hat</th>
##     </tr>
##   </thead>
##   <tbody class="gt_table_body">
##     <tr><th id="stub_1_1" scope="row" class="gt_row gt_left gt_stub">(Intercept)</th>
## <td headers="stub_1_1 Estimate" class="gt_row gt_right">0.50</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">1.76</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−11.12</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">7.64</td>
## <td headers="stub_1_1 Pd" class="gt_row gt_right">0.615</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">4,520</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,355</td>
## <td headers="stub_1_1 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_2" scope="row" class="gt_row gt_left gt_stub">Latitude</th>
## <td headers="stub_1_2 Estimate" class="gt_row gt_right">−0.01</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">0.06</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−0.24</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">0.38</td>
## <td headers="stub_1_2 Pd" class="gt_row gt_right">0.564</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">4,530</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,323</td>
## <td headers="stub_1_2 R-hat" class="gt_row gt_right">1.001</td></tr>
##     <tr><th id="stub_1_3" scope="row" class="gt_row gt_left gt_stub">Season-Spring</th>
## <td headers="stub_1_3 Estimate" class="gt_row gt_right" style="font-weight: bold;">0.09</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.04</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">0.01</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">0.18</td>
## <td headers="stub_1_3 Pd" class="gt_row gt_right" style="font-weight: bold;">0.985</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">8,065</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,907</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_4" scope="row" class="gt_row gt_left gt_stub">Season-Winter</th>
## <td headers="stub_1_4 Estimate" class="gt_row gt_right">−0.02</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">0.04</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−0.10</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">0.06</td>
## <td headers="stub_1_4 Pd" class="gt_row gt_right">0.695</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">7,039</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">7,562</td>
## <td headers="stub_1_4 R-hat" class="gt_row gt_right">1.000</td></tr>
##     <tr><th id="stub_1_5" scope="row" class="gt_row gt_left gt_stub">Status-Invaded</th>
## <td headers="stub_1_5 Estimate" class="gt_row gt_right" style="font-weight: bold;">3.79</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.70</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">2.34</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">5.09</td>
## <td headers="stub_1_5 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">6,755</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,136</td>
## <td headers="stub_1_5 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_6" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Latitude</th>
## <td headers="stub_1_6 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.11</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.02</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.15</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−0.06</td>
## <td headers="stub_1_6 Pd" class="gt_row gt_right" style="font-weight: bold;">1.000</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">6,816</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,195</td>
## <td headers="stub_1_6 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_7" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Spring</th>
## <td headers="stub_1_7 Estimate" class="gt_row gt_right" style="font-weight: bold;">−0.16</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right" style="font-weight: bold;">0.06</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−0.27</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−0.04</td>
## <td headers="stub_1_7 Pd" class="gt_row gt_right" style="font-weight: bold;">0.997</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">8,076</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,534</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right" style="font-weight: bold;">1.000</td></tr>
##     <tr><th id="stub_1_8" scope="row" class="gt_row gt_left gt_stub">Status-Invaded x Season-Winter</th>
## <td headers="stub_1_8 Estimate" class="gt_row gt_right">0.01</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">0.06</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−0.11</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">0.12</td>
## <td headers="stub_1_8 Pd" class="gt_row gt_right">0.550</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">7,115</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">7,681</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">1.000</td></tr>
##   </tbody>
##   
##   
## </table>
## </div>

Conditional Effects Veg Height

## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_ribbon()`).

## You are calculating adjusted predictions on the population-level (i.e.
##   `type = "fixed"`) for a *generalized* linear mixed model.
##   This may produce biased estimates due to Jensen's inequality. Consider
##   setting `bias_correction = TRUE` to correct for this bias.
##   See also the documentation of the `bias_correction` argument.
## Note: uncertainty of error terms are not taken into account. Consider
##   setting `interval` to "prediction". This will call `posterior_predict()`
##   instead of `posterior_epred()`.
## Scale for colour is already present.
## Adding another scale for colour, which will replace the existing scale.Ignoring unknown labels:
## • linetype : "Latitude"
## • shape : "Latitude"

## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.

## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## No shared levels found between `names(values)` of the manual scale and the
## data's colour values.

Merge Plot

## Warning: Removed 3 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

## Warning: Removed 3 rows containing missing values or values outside the scale range
## (`geom_point()`).

## Warning: Removed 3 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
## Removed 3 rows containing missing values or values outside the scale range
## (`geom_point()`).