Chapter1 Objective1

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

## 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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## </style>
##   <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>
##     </tr>
##   </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; sigma = identity; nu = 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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##     
##     <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="Probability-&gt;-0">Probability &gt; 0</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 Probability > 0" class="gt_row gt_right">0.217</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 Probability > 0" 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 Probability > 0" class="gt_row gt_right">0.256</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 Probability > 0" class="gt_row gt_right">0.071</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 Probability > 0" 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 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.000</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 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.016</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 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.000</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; sigma = identity; nu = 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).

## 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%

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>
##       <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>
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##       <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">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 Probability > 0" 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 Probability > 0" class="gt_row gt_right">0.433</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 Probability > 0" 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 Probability > 0" 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">14.38</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">7.74</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−0.96</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">30.12</td>
## <td headers="stub_1_5 Probability > 0" class="gt_row gt_right">0.971</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,014</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,298</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">−0.41</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">0.25</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−0.92</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">0.09</td>
## <td headers="stub_1_6 Probability > 0" class="gt_row gt_right">0.047</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,048</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,167</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">−0.25</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 Probability > 0" class="gt_row gt_right">0.283</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 Probability > 0" 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>

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; sigma = identity; nu = 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)     3.09      2.70     0.39    10.38 1.00     3516     4822
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                     49.74     81.12   -46.46   284.54 1.00     4111
## StatusInvaded                 -7.04     14.32   -34.74    21.50 1.00     8061
## SeasonSpring                   1.06      0.95    -0.80     2.92 1.00     8466
## SeasonWinter                   0.90      0.81    -0.70     2.51 1.00     9764
## Latitude                      -1.48      2.71    -9.30     1.72 1.00     4108
## StatusInvaded:SeasonSpring     0.75      1.29    -1.77     3.26 1.00     8490
## StatusInvaded:SeasonWinter     0.54      1.19    -1.82     2.86 1.00     9413
## StatusInvaded:Latitude         0.20      0.48    -0.76     1.12 1.00     8087
##                            Tail_ESS
## Intercept                      4109
## StatusInvaded                  7977
## SeasonSpring                   8298
## SeasonWinter                   8562
## Latitude                       3990
## StatusInvaded:SeasonSpring     7965
## StatusInvaded:SeasonWinter     8763
## StatusInvaded:Latitude         7849
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     2.82      0.31     2.25     3.45 1.00     8194     8257
## nu        5.41      3.14     2.44    13.39 1.00     8908     7153
## 
## 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     -2.50    0.0962
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.483     -2.61    1.7396
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.683     -2.54    1.2493
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 96.61%
## Invaded - Non_Invaded | Spring | 66.54%
## Invaded - Non_Invaded | Winter | 76.13%

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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##     
##     <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="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>
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##       <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">25.82</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">47.39</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−70.89</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">230.99</td>
## <td headers="stub_1_1 Probability > 0" class="gt_row gt_right">0.752</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">4,091</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">4,094</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">−0.68</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">1.59</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−7.66</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">2.43</td>
## <td headers="stub_1_2 Probability > 0" class="gt_row gt_right">0.305</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">4,088</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,974</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">0.95</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−0.82</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">2.90</td>
## <td headers="stub_1_3 Probability > 0" class="gt_row gt_right">0.867</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">8,373</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">8,266</td>
## <td headers="stub_1_3 R-hat" class="gt_row gt_right">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">0.91</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">0.80</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−0.69</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">2.52</td>
## <td headers="stub_1_4 Probability > 0" class="gt_row gt_right">0.867</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">9,752</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">8,462</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">−7.19</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">14.25</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−35.25</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">20.94</td>
## <td headers="stub_1_5 Probability > 0" class="gt_row gt_right">0.309</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">8,023</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,931</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">0.20</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">−0.76</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">1.12</td>
## <td headers="stub_1_6 Probability > 0" class="gt_row gt_right">0.661</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">8,059</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,832</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">1.29</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−1.87</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">3.16</td>
## <td headers="stub_1_7 Probability > 0" class="gt_row gt_right">0.722</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">8,472</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">7,936</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">0.55</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">1.17</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−1.79</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">2.87</td>
## <td headers="stub_1_8 Probability > 0" class="gt_row gt_right">0.683</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">9,391</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,752</td>
## <td headers="stub_1_8 R-hat" class="gt_row gt_right">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; sigma = identity; nu = 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)    18.01     19.50     0.55    71.09 1.00     3948     4886
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                    433.79    499.14  -403.55  1578.93 1.00     5087
## StatusInvaded               -199.30    274.95  -752.37   341.47 1.00     6626
## SeasonSpring                 -69.80     19.19  -107.37   -32.30 1.00     7538
## SeasonWinter                 -71.45     29.71  -130.36   -13.04 1.00     7034
## Latitude                      -8.97     16.66   -47.33    19.05 1.00     5107
## StatusInvaded:SeasonSpring    20.86     23.46   -24.86    67.41 1.00     7222
## StatusInvaded:SeasonWinter    41.14     32.47   -22.28   105.09 1.00     6825
## StatusInvaded:Latitude         6.22      9.18   -11.87    24.59 1.00     6656
##                            Tail_ESS
## Intercept                      3856
## StatusInvaded                  6702
## SeasonSpring                   7755
## SeasonWinter                   6525
## Latitude                       3855
## StatusInvaded:SeasonSpring     7874
## StatusInvaded:SeasonWinter     6648
## StatusInvaded:Latitude         6694
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma    44.27      4.31    35.39    52.38 1.00     8059     7138
## nu       15.08     11.25     3.48    45.22 1.00     7825     7890
## 
## 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()`).

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -14.27     -36.3      7.74
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     6.48     -33.3     47.75
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    26.72     -34.5     84.52
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 89.82%
## Invaded - Non_Invaded | Spring | 62.41%
## Invaded - Non_Invaded | Winter | 81.81%

Live 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 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="Probability-&gt;-0">Probability &gt; 0</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">395.57</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">343.58</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−466.03</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">1,503.68</td>
## <td headers="stub_1_1 Probability > 0" class="gt_row gt_right">0.875</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">5,071</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,835</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">−7.69</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">11.45</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−44.51</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">21.11</td>
## <td headers="stub_1_2 Probability > 0" class="gt_row gt_right">0.245</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">5,091</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,833</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;">−69.91</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right" style="font-weight: bold;">19.02</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−107.84</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−32.96</td>
## <td headers="stub_1_3 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.000</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,570</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,712</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;">−71.46</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">29.33</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">−129.40</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">−12.23</td>
## <td headers="stub_1_4 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.009</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,000</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">6,396</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">−196.86</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">269.85</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−736.64</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">354.97</td>
## <td headers="stub_1_5 Probability > 0" class="gt_row gt_right">0.229</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">6,606</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">6,671</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">6.13</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">8.99</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−12.56</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">23.81</td>
## <td headers="stub_1_6 Probability > 0" class="gt_row gt_right">0.756</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">6,637</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">6,665</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">20.84</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">23.20</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−26.37</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">65.63</td>
## <td headers="stub_1_7 Probability > 0" class="gt_row gt_right">0.816</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">7,183</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">7,844</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">40.77</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">32.28</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−22.49</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">104.82</td>
## <td headers="stub_1_8 Probability > 0" class="gt_row gt_right">0.899</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">6,768</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">6,525</td>
## <td headers="stub_1_8 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; sigma = identity; nu = 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)     5.91      4.92     0.58    18.38 1.00     3536     3249
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                      4.35    131.14  -260.33   279.90 1.00     5096
## StatusInvaded                 16.50     44.60   -70.62   103.68 1.00     7461
## SeasonSpring                   0.55      3.27    -6.21     6.63 1.00     6142
## SeasonWinter                   1.59      3.24    -4.98     7.82 1.00     6224
## Latitude                       0.29      4.38    -8.89     9.11 1.00     5113
## StatusInvaded:SeasonSpring    -4.38      3.79   -11.72     3.26 1.00     6257
## StatusInvaded:SeasonWinter     0.34      4.05    -7.47     8.75 1.00     6427
## StatusInvaded:Latitude        -0.44      1.51    -3.40     2.50 1.00     7479
##                            Tail_ESS
## Intercept                      4855
## StatusInvaded                  7474
## SeasonSpring                   5763
## SeasonWinter                   6372
## Latitude                       4820
## StatusInvaded:SeasonSpring     6640
## StatusInvaded:SeasonWinter     6175
## StatusInvaded:Latitude         7400
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     5.94      0.88     4.45     7.88 1.00     8235     8195
## nu        1.24      0.18     1.01     1.67 1.00     6108     4641
## 
## 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()`).

Estimated marginal means

## Season = Summer:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     3.39     -2.64      8.91
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    -1.07     -5.62      3.61
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded     3.66     -1.99      9.33
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 87.80%
## Invaded - Non_Invaded | Spring | 68.14%
## Invaded - Non_Invaded | Winter | 89.90%

Dead 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 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>
##       <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="Probability-&gt;-0">Probability &gt; 0</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">2.81</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">86.30</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−268.64</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">269.15</td>
## <td headers="stub_1_1 Probability > 0" class="gt_row gt_right">0.513</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">5,080</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">4,809</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">0.34</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">2.90</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−8.79</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">9.17</td>
## <td headers="stub_1_2 Probability > 0" class="gt_row gt_right">0.548</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">5,097</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">4,775</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">3.08</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−6.01</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">6.80</td>
## <td headers="stub_1_3 Probability > 0" class="gt_row gt_right">0.583</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">6,113</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">5,724</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">1.65</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right">3.10</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right">−4.54</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right">8.24</td>
## <td headers="stub_1_4 Probability > 0" class="gt_row gt_right">0.701</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">6,174</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">6,360</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">16.38</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">43.87</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−68.01</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">105.31</td>
## <td headers="stub_1_5 Probability > 0" class="gt_row gt_right">0.642</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,439</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,428</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">−0.43</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">1.49</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−3.42</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">2.46</td>
## <td headers="stub_1_6 Probability > 0" class="gt_row gt_right">0.389</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,437</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,388</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">−4.43</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">3.66</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−12.01</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">2.91</td>
## <td headers="stub_1_7 Probability > 0" class="gt_row gt_right">0.120</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">6,234</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">6,631</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">0.26</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">3.94</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−7.87</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">8.21</td>
## <td headers="stub_1_8 Probability > 0" class="gt_row gt_right">0.528</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">6,387</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">6,125</td>
## <td headers="stub_1_8 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; sigma = identity; nu = 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)     7.99      9.05     0.22    31.63 1.00     2989     4235
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                     -7.75    218.01  -336.89   574.54 1.00     4632
## StatusInvaded                 40.41     79.91  -114.34   196.97 1.00     8000
## SeasonSpring                  -8.71      4.91   -18.57     0.50 1.00     7079
## SeasonWinter                  15.82      6.27     3.43    28.10 1.00     7192
## Latitude                       0.99      7.30   -18.34    11.95 1.00     4620
## StatusInvaded:SeasonSpring    -0.21      6.12   -11.99    11.98 1.00     8329
## StatusInvaded:SeasonWinter    -8.79      7.99   -24.50     7.03 1.00     7937
## StatusInvaded:Latitude        -1.37      2.69    -6.65     3.82 1.00     7940
##                            Tail_ESS
## Intercept                      3132
## StatusInvaded                  7120
## SeasonSpring                   6918
## SeasonWinter                   8307
## Latitude                       3058
## StatusInvaded:SeasonSpring     7398
## StatusInvaded:SeasonWinter     7987
## StatusInvaded:Latitude         7288
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma    14.58      1.87    11.18    18.45 1.00     7733     7510
## nu        2.36      0.64     1.45     3.92 1.00     7669     6283
## 
## 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   -0.353     -8.37      7.52
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.562    -10.33      7.87
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -9.208    -22.38      3.88
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 53.29%
## Invaded - Non_Invaded | Spring | 54.78%
## Invaded - Non_Invaded | Winter | 91.28%

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="Probability-&gt;-0">Probability &gt; 0</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">−39.23</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">117.19</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−403.38</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">452.50</td>
## <td headers="stub_1_1 Probability > 0" class="gt_row gt_right">0.370</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">4,602</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,126</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">2.03</td>
## <td headers="stub_1_2 Est. Error" class="gt_row gt_right">3.93</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−14.73</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">13.97</td>
## <td headers="stub_1_2 Probability > 0" class="gt_row gt_right">0.690</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">4,589</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,052</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">−8.66</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">4.92</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−18.18</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">0.81</td>
## <td headers="stub_1_3 Probability > 0" class="gt_row gt_right">0.033</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">7,000</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">6,902</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;">15.76</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">6.26</td>
## <td headers="stub_1_4 95% HPDI (Lower)" class="gt_row gt_right" style="font-weight: bold;">3.37</td>
## <td headers="stub_1_4 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">28.03</td>
## <td headers="stub_1_4 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.996</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,160</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,262</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">38.61</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">78.93</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−111.44</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">199.41</td>
## <td headers="stub_1_5 Probability > 0" class="gt_row gt_right">0.694</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,987</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,101</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">−1.32</td>
## <td headers="stub_1_6 Est. Error" class="gt_row gt_right">2.64</td>
## <td headers="stub_1_6 95% HPDI (Lower)" class="gt_row gt_right">−6.78</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">3.67</td>
## <td headers="stub_1_6 Probability > 0" class="gt_row gt_right">0.304</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,927</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,268</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">−0.24</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">6.04</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−11.61</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">12.26</td>
## <td headers="stub_1_7 Probability > 0" class="gt_row gt_right">0.485</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">8,286</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">7,379</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">−8.74</td>
## <td headers="stub_1_8 Est. Error" class="gt_row gt_right">8.07</td>
## <td headers="stub_1_8 95% HPDI (Lower)" class="gt_row gt_right">−24.55</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">6.90</td>
## <td headers="stub_1_8 Probability > 0" class="gt_row gt_right">0.136</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">7,888</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">7,940</td>
## <td headers="stub_1_8 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; sigma = identity; nu = 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)     2.78      3.03     0.08    11.00 1.00     2784     4069
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                    -46.86     71.46  -154.45   138.95 1.00     4709
## StatusInvaded                  8.40     21.05   -31.85    50.06 1.00     7480
## SeasonSpring                  -0.67      1.19    -3.03     1.62 1.00     7929
## SeasonWinter                   2.05      1.00     0.12     4.08 1.00     9227
## Latitude                       1.80      2.38    -4.44     5.38 1.00     4726
## StatusInvaded:SeasonSpring    -2.70      1.64    -5.87     0.57 1.00     7562
## StatusInvaded:SeasonWinter    -1.83      1.55    -4.91     1.19 1.00     9252
## StatusInvaded:Latitude        -0.21      0.70    -1.60     1.12 1.00     7523
##                            Tail_ESS
## Intercept                      3141
## StatusInvaded                  7305
## SeasonSpring                   8099
## SeasonWinter                   8862
## Latitude                       3219
## StatusInvaded:SeasonSpring     8088
## StatusInvaded:SeasonWinter     8449
## StatusInvaded:Latitude         7334
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     3.22      0.34     2.60     3.93 1.00    10366     8353
## nu        2.02      0.37     1.41     2.85 1.00     9631     7022
## 
## 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    2.192     0.226      4.06
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded   -0.482    -3.233      2.20
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.387    -2.013      2.75
## 
## Point estimate displayed: median 
## HPD interval probability: 0.95

## Probability of Direction
## 
## contrast              | Season |     pd
## ---------------------------------------
## Invaded - Non_Invaded | Summer | 98.90%
## Invaded - Non_Invaded | Spring | 64.12%
## Invaded - Non_Invaded | Winter | 62.75%

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="Probability-&gt;-0">Probability &gt; 0</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">−59.61</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">34.32</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−171.91</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">112.60</td>
## <td headers="stub_1_1 Probability > 0" class="gt_row gt_right">0.143</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">4,704</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,149</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">1.15</td>
## <td headers="stub_1_2 95% HPDI (Lower)" class="gt_row gt_right">−3.52</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">5.98</td>
## <td headers="stub_1_2 Probability > 0" class="gt_row gt_right">0.873</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">4,722</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,233</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">−0.67</td>
## <td headers="stub_1_3 Est. Error" class="gt_row gt_right">1.19</td>
## <td headers="stub_1_3 95% HPDI (Lower)" class="gt_row gt_right">−2.99</td>
## <td headers="stub_1_3 95% HPDI (Upper)" class="gt_row gt_right">1.65</td>
## <td headers="stub_1_3 Probability > 0" class="gt_row gt_right">0.286</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right">7,894</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right">8,076</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;">2.05</td>
## <td headers="stub_1_4 Est. Error" class="gt_row gt_right" style="font-weight: bold;">1.01</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;">4.01</td>
## <td headers="stub_1_4 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.981</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">9,167</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,807</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">8.22</td>
## <td headers="stub_1_5 Est. Error" class="gt_row gt_right">21.14</td>
## <td headers="stub_1_5 95% HPDI (Lower)" class="gt_row gt_right">−32.85</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right">48.62</td>
## <td headers="stub_1_5 Probability > 0" class="gt_row gt_right">0.647</td>
## <td headers="stub_1_5 Bulk ESS" class="gt_row gt_right">7,467</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right">7,284</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">−0.20</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">−1.58</td>
## <td headers="stub_1_6 95% HPDI (Upper)" class="gt_row gt_right">1.13</td>
## <td headers="stub_1_6 Probability > 0" class="gt_row gt_right">0.388</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right">7,510</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right">7,299</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">−2.73</td>
## <td headers="stub_1_7 Est. Error" class="gt_row gt_right">1.64</td>
## <td headers="stub_1_7 95% HPDI (Lower)" class="gt_row gt_right">−5.89</td>
## <td headers="stub_1_7 95% HPDI (Upper)" class="gt_row gt_right">0.53</td>
## <td headers="stub_1_7 Probability > 0" class="gt_row gt_right">0.050</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right">7,545</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right">8,062</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">−1.82</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">−4.77</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">1.33</td>
## <td headers="stub_1_8 Probability > 0" class="gt_row gt_right">0.119</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">9,214</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,430</td>
## <td headers="stub_1_8 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 2 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; sigma = identity; nu = 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      0.39     0.00     1.35 1.00     1937     3705
## 
## Regression Coefficients:
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                     -0.38      4.32   -12.54     6.59 1.00     3899
## StatusInvaded                  3.78      0.70     2.40     5.13 1.00     7102
## SeasonSpring                   0.09      0.04     0.01     0.18 1.00     7827
## SeasonWinter                  -0.02      0.04    -0.10     0.06 1.00     8134
## Latitude                       0.02      0.14    -0.21     0.43 1.00     3956
## StatusInvaded:SeasonSpring    -0.16      0.06    -0.28    -0.04 1.00     7826
## StatusInvaded:SeasonWinter     0.01      0.06    -0.11     0.12 1.00     8332
## StatusInvaded:Latitude        -0.11      0.02    -0.15    -0.06 1.00     7137
##                            Tail_ESS
## Intercept                      3085
## StatusInvaded                  7647
## SeasonSpring                   8490
## SeasonWinter                   8297
## Latitude                       3142
## StatusInvaded:SeasonSpring     7690
## StatusInvaded:SeasonWinter     8424
## StatusInvaded:Latitude         7569
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.14      0.01     0.11     0.17 1.00     6825     7024
## nu        5.01      2.44     2.56    10.70 1.00     7342     6768
## 
## 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    0.588     0.524     0.654
## 
## Season = Spring:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.427     0.330     0.523
## 
## Season = Winter:
##  contrast              estimate lower.HPD upper.HPD
##  Invaded - Non_Invaded    0.594     0.500     0.689
## 
## 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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## </style>
##   <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 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="Probability-&gt;-0">Probability &gt; 0</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">0.56</td>
## <td headers="stub_1_1 Est. Error" class="gt_row gt_right">1.70</td>
## <td headers="stub_1_1 95% HPDI (Lower)" class="gt_row gt_right">−10.75</td>
## <td headers="stub_1_1 95% HPDI (Upper)" class="gt_row gt_right">8.12</td>
## <td headers="stub_1_1 Probability > 0" class="gt_row gt_right">0.628</td>
## <td headers="stub_1_1 Bulk ESS" class="gt_row gt_right">3,906</td>
## <td headers="stub_1_1 Tail ESS" class="gt_row gt_right">3,077</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">−0.26</td>
## <td headers="stub_1_2 95% HPDI (Upper)" class="gt_row gt_right">0.37</td>
## <td headers="stub_1_2 Probability > 0" class="gt_row gt_right">0.420</td>
## <td headers="stub_1_2 Bulk ESS" class="gt_row gt_right">3,967</td>
## <td headers="stub_1_2 Tail ESS" class="gt_row gt_right">3,134</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;">0.17</td>
## <td headers="stub_1_3 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.987</td>
## <td headers="stub_1_3 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,732</td>
## <td headers="stub_1_3 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">8,404</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">−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 Probability > 0" class="gt_row gt_right">0.309</td>
## <td headers="stub_1_4 Bulk ESS" class="gt_row gt_right">8,105</td>
## <td headers="stub_1_4 Tail ESS" class="gt_row gt_right">8,272</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;">3.78</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;">2.33</td>
## <td headers="stub_1_5 95% HPDI (Upper)" class="gt_row gt_right" style="font-weight: bold;">5.04</td>
## <td headers="stub_1_5 Probability > 0" 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;">7,094</td>
## <td headers="stub_1_5 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,607</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 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.000</td>
## <td headers="stub_1_6 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,128</td>
## <td headers="stub_1_6 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,519</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;">−0.28</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 Probability > 0" class="gt_row gt_right" style="font-weight: bold;">0.004</td>
## <td headers="stub_1_7 Bulk ESS" class="gt_row gt_right" style="font-weight: bold;">7,798</td>
## <td headers="stub_1_7 Tail ESS" class="gt_row gt_right" style="font-weight: bold;">7,619</td>
## <td headers="stub_1_7 R-hat" class="gt_row gt_right" style="font-weight: bold;">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">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">−0.10</td>
## <td headers="stub_1_8 95% HPDI (Upper)" class="gt_row gt_right">0.12</td>
## <td headers="stub_1_8 Probability > 0" class="gt_row gt_right">0.547</td>
## <td headers="stub_1_8 Bulk ESS" class="gt_row gt_right">8,284</td>
## <td headers="stub_1_8 Tail ESS" class="gt_row gt_right">8,396</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 in max(ids, na.rm = TRUE): no non-missing arguments to max; returning
## -Inf