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Spatial structural models

James T. Thorson

Source: vignettes/web_only/spatial_structural_model.Rmd
spatial_structural_model.Rmd

tinyVAST provides an expressive interface to specify structural interactions among variables using arrow or arrow-and-lag notation from structural equation models and dynamic structural equation models, respectively. Here, we replicate the original analysis from (Thorson et al. 2025)

Load data 

# Load data
data(alaska_sponge_coral_fish)
combined_samples = alaska_sponge_coral_fish$combined_samples

# Define the spatial mesh
mesh = fm_mesh_2d( 
  loc = combined_samples[,c('X','Y')],
  cutoff = 10 # Value from original paper
  #cutoff = 25 # Lower resolution to speed up vignette
)

Fit model

We then define a separate intercept for each group and year, and a log-area offset

# Define formula
Formula = Count ~ 0 + interaction(Group4,Year) + offset(log(AreaSwept))

We also specify the AIC-selected structural model from the original paper, which includes habitat-effects for camera-measured coral and sponge densities on camera-measured fish densities, separate habitat-effects for coral/sponge on trawl-measured fish densities, and proportional variation in fish density between camera and trawl measurements.

# Define arrow-and-lag notation
space_term = "
  # Habitat effects on drop-camera measurements
  Coral -> Flat, b1
  Sponge -> Flat, b2
  Coral -> Rock, b3
  Sponge -> Rock, b4
  
  # Habitat effects on trawl measurements
  Coral -> Flat_trawl, d1
  Sponge -> Flat_trawl, d2
  Coral -> Rock_trawl, d3
  Sponge -> Rock_trawl, d4

  # Fix these at 1 
  # (Proportional change in density between gears)
  Flat -> Flat_trawl, NA, 1
  Rock -> Rock_trawl, NA, 1
"

We also estimate separate measurement-error parameters for each of six variables

# Specify distribution for each variable
Family = list(
  Coral = tweedie(),
  Sponge = tweedie(),
  Rock = tweedie(),
  Flat = tweedie(),
  Rock_trawl = tweedie(),
  Flat_trawl = tweedie()
)

We then run the model without standard errors to speed up the vignette:

# Specify estimation settings
control = tinyVASTcontrol( 
  profile = c("alpha_j"),
  getsd = FALSE # To speed up vignette
)

# Fit model
myfit = tinyVAST(
  data = combined_samples,
  formula = Formula,
  space_term = space_term,
  family = Family,
  space_columns = c("X", "Y"),
  variable_column = "Group4",
  variables = c("Coral", "Sponge", "Rock", "Flat", "Rock_trawl", "Flat_trawl"),
  distribution_column = "Group4",
  spatial_domain = mesh,
  control = control
)

Visualize structural linkages

Finally, we use igraph to allow detailed control when plotting the estimated structural linkages among variables:

# Function to relabel variables
Switch = function(x){
  switch( x, "Coral"="C", "Sponge"="S", "Rock"="R", 
          "Flat"="F", "Rock_trawl"="R2", "Flat_trawl"="F2" )
}

# Extract objects
out = summary( myfit )
variables = as.character(myfit$internal$variables)
var_labels = sapply( variables, FUN=Switch )
label = round(out$Estimate,2)

# Define location for plotting variables
layout = cbind( 
  x=c(2,2,1,3,1,3), 
  y=c(2,3,1,1,4,4)
)
rownames(layout) = c( "Coral", "Sponge", "Rock", 
                      "Flat", "Rock_trawl", "Flat_trawl" )

# Define locations for plotting arrows
df <- data.frame(
  from = sapply(out$from,FUN=Switch),
  to = sapply(out$to,FUN=Switch),
  label = label,
  x = NA,
  y = NA
)

# Only show one-headed arrows
df = subset( df, from!=to )

# Define location for labels of one-headed arrows
df$x = c( 0.5, 0.5, -0.5, -0.5, 0.5, 0.5, -0.5, -0.5, 1, -1 )
df$y = c( -0.66, -0.22, -0.66, -0.33, 0.33, 0.66, 0.33, 0.66, 0, 0 )

# Make graph
pg = graph_from_data_frame(
  d = df[,1:3],
  directed=TRUE,
  vertices=data.frame(var_labels)
)

# Make plot
par( mar=c(0,0,0,0) )
plot.igraph(
  pg,
  vertex.shape="rectangle",
  vertex.size=0,
  vertex.size2=0,
  vertex.label.cex=2,
  vertex.color="grey",
  vertex.label.color="black",
  edge.label.color="black",
  edge.label.cex=1,
  layout=layout[as.character(variables),],
  xlim=1.2*c(-1,1),
  ylim=1.2*c(-1,1),
  edge.label.dist=0.8,
  edge.label.x=df$x,
  edge.label.y=df$y
)

Runtime for this vignette: 7.16 mins

Works cited

Thorson, James T., Sean C. Anderson, Pamela Goddard, and Christopher N. Rooper. 2025. “tinyVAST: R Package With an Expressive Interface to Specify Lagged and Simultaneous Effects in Multivariate Spatio-Temporal Models.” Global Ecology and Biogeography 34 (4): e70035. https://doi.org/10.1111/geb.70035.