Building Worlds
We are going to start by building a simulated version of our study system. While it is often tempting to jump straight into working with real data, the models we are using here are quite complex. It can be challenging, therefore, to intuitively grasp whether something has gone wrong in our modelling, or whether there is something missing in our understanding of the data. By building simulated datasets where we have full control over how the data were generated, we give the models nowhere to hide!
There is an art to constructing good simulations for model testing. We want to make our simulated world’s realistic enough to give a flavour of the real data, but not so complex that we can’t track down problems if they arise. When working with spatio-temporal questions, things become very complicated very quickly!
Using Our Package
We have designed the ascot package to give you a lot of flexibility for simulating and sampling from realistic spatio-temporal scenarios. In other vignettes, we explore this flexibility but here we will make some quick decisions that give a flavour of the available options.
The Temporal Pattern
We start by thinking about the pattern through time. In many
realistic ecological and environmental datasets we expect there to be
periodic patterns in the data corresponding to cycles within days,
weeks, seasons or years. The define_pattern_t function
allows you to generate these cycles at multiple scales (weeks, seasons
and years) and to tune the amplitude and noise associated with these
patterns. We discuss in more detail in the
temporal_simulations vignette. Here, we generate one
month’s worth of data which have oscillations of amplitude 1 at the
weekly scale.
# Determine duration of time series
time_df <- set_timeline(1, "month")
# Set time series pattern
time_series <- define_pattern_t(time_df,
weekly_amplitude = 1,
weekly_noise = 0)
#> Warning: One quarter or less of data, ignoring arguments for seasonal and annual
#> patterns
# Visualise
ggplot(time_series, aes(x = date, y = pattern)) +
geom_point() +
geom_line() +
theme_bw()
Spatial Pattern
Similarly, in most real-world processes we expect there to be spatial
autocorrelation, that is to say, places closer together in space are
likely to be more similar to each other than places further apart. This
can happen for numerous reasons, from simple diffusion to complex
aggregation behaviours. Our next job, therefore, is to define how
spatial locations will relate to each other. Here we create a 20 by 20
grid with moderate autocorrelation. More information on generating
spatial fields can be found in the spatial_simulations
vignette.
# Generate Field
spatial_field <- define_pattern_s(20, 20, autocorr = TRUE, range = 5)
# Visualise
ggplot(spatial_field, aes(x = x, y = y, fill = value)) +
geom_raster() +
theme_bw()Combining Patterns
We now want to combine the two patterns we have made so that our
locations in space change through time. Conceptually, we treat our
spatial pattern as a starting point and then allow each location to move
through time according to the temporal pattern. We can make the
relationship between space and time as outlined in the GAMs workshop. An
easy way of doing this is through the pattern_adherence
argument in the function simulate_spacetime. Here, we set
this to 0, the simplest form of combining the two. We refer to this as
the truth as it will represent the true process we are
interested in inferring when we start modelling.
# Simulate from spatial and temporal patterns
truth <- simulate_spacetime(temporal_pattern = time_series,
field = spatial_field,
pattern_adherence = 0)