This vignette gives an example of
how to take raw data and format it for use in mvgam
. This
is not an exhaustive example, as data can be recorded and stored in a
variety of ways, which requires different approaches to wrangle the data
into the necessary format for mvgam
. For full details on
the basic mvgam
functionality, please see the
introductory vignette.
Manipulating the data into a ‘long’ format is necessary for modelling
in mvgam
. By ‘long’ format, we mean that each
series x time
observation needs to have its own entry in
the dataframe
or list
object that we wish to
use as data for modelling. A simple example can be viewed by simulating
data using the sim_mvgam
function. See
?sim_mvgam
for more details
series
as a factor
variableNotice how we have four different time series in these simulated
data, and we have identified the series-level indicator as a
factor
variable.
It is important that the number of levels matches the number of
unique series in the data to ensure indexing across series works
properly in the underlying modelling functions. Several of the main
workhorse functions in the package (including mvgam()
and
get_mvgam_priors()
) will give an error if this is not the
case, but it may be worth checking anyway:
Note that you can technically supply data that does not have a
series
indicator, and the package will generally assume
that you are only using a single time series. There are exceptions to
this, for example if you have grouped data and would like to estimate
hierarchical dependencies (see an example of hierarchical process error
correlations in the ?AR
documentation) or if you would like
to set up a Joint Species Distribution Model (JSDM) using a Zero-Mean
Multivariate Gaussian distribution for the latent residuals (see
examples in the ?ZMVN
documentation).
You may also have notices that we do not spread the
numeric / integer
-classed outcome variable into different
columns. Rather, there is only a single column for the outcome variable,
labelled y
in these simulated data (though the outcome does
not have to be labelled y
). This is another important
requirement in mvgam
, but it shouldn’t be too unfamiliar to
R
users who frequently use modelling packages such as
lme4
, mgcv
, brms
or the many
other regression modelling packages out there. The advantage of this
format is that it is now very easy to specify effects that vary among
time series:
Depending on the observation families you plan to use when building
models, there may be some restrictions that need to be satisfied within
the outcome variable. For example, a Beta regression can only handle
proportional data, so values >= 1
or
<= 0
are not allowed. Likewise, a Poisson regression can
only handle non-negative integers. Most regression functions in
R
will assume the user knows all of this and so will not
issue any warnings or errors if you choose the wrong distribution, but
often this ends up leading to some unhelpful error from an optimizer
that is difficult to interpret and diagnose. mvgam
will
attempt to provide some errors if you do something that is simply not
allowed. For example, we can simulate data from a zero-centred Gaussian
distribution (ensuring that some of our values will be
< 1
) and attempt a Beta regression in mvgam
using the betar
family:
gauss_dat <- data.frame(outcome = rnorm(10),
series = factor('series1',
levels = 'series1'),
time = 1:10)
gauss_dat
A call to gam
using the mgcv
package leads
to a model that actually fits (though it does give an unhelpful warning
message):
But the same call to mvgam
gives us something more
useful:
Please see ?mvgam_families
for more information on the
types of responses that the package can handle and their
restrictions
time
variableThe other requirement for most models that can be fit in
mvgam
is a numeric / integer
-classed variable
labelled time
. This ensures the modelling software knows
how to arrange the time series when building models. This setup still
allows us to formulate multivariate time series models. If you plan to
use any of the autoregressive dynamic trend functions available in
mvgam
(see ?mvgam_trends
for details of
available dynamic processes), you will need to ensure your time series
are entered with a fixed sampling interval (i.e. the time between
timesteps 1 and 2 should be the same as the time between timesteps 2 and
3, etc…). But note that you can have missing observations for some (or
all) series. mvgam
will check this for you, but again it is
useful to ensure you have no missing timepoint x series combinations in
your data. You can generally do this with a simple dplyr
call:
# A function to ensure all timepoints within a sequence are identical
all_times_avail = function(time, min_time, max_time){
identical(as.numeric(sort(time)),
as.numeric(seq.int(from = min_time, to = max_time)))
}
# Get min and max times from the data
min_time <- min(simdat$data_train$time)
max_time <- max(simdat$data_train$time)
# Check that all times are recorded for each series
data.frame(series = simdat$data_train$series,
time = simdat$data_train$time) %>%
dplyr::group_by(series) %>%
dplyr::summarise(all_there = all_times_avail(time,
min_time,
max_time)) -> checked_times
if(any(checked_times$all_there == FALSE)){
warning("One or more series in is missing observations for one or more timepoints")
} else {
cat('All series have observations at all timepoints :)')
}
Note that models which use dynamic components will assume that
smaller values of time
are older
(i.e. time = 1
came before time = 2
,
etc…)
Most mvgam
dynamic trend models expect time
to be measured in discrete, evenly-spaced intervals (i.e. one
measurement per week, or one per year, for example; though missing
values are allowed). But please note that irregularly sampled time
intervals are allowed, in which case the CAR()
trend model
(continuous time autoregressive) is appropriate. You can see an example
of this kind of model in the Examples section in
?CAR
. You can also use trend_model = 'None'
(the default in mvgam()
) and instead use a Gaussian Process
to model temporal variation for irregularly-sampled time series. See the
?brms::gp
for details. But to reiterate the point from
above, if you do not have time series data (or don’t want to estimate
latent temporal dynamics) but you would like to estimate correlated
latent residuals among multivariate outcomes, you can set up models that
use trend_model = ZMVN(...)
without the need for a
time
variable (see ?ZMVN
for details).
get_mvgam_priors
The get_mvgam_priors
function is designed to return
information about the parameters in a model whose prior distributions
can be modified by the user. But in doing so, it will perform a series
of checks to ensure the data are formatted properly. It can therefore be
very useful to new users for ensuring there isn’t anything strange going
on in the data setup. For example, we can replicate the steps taken
above (to check factor levels and timepoint x series combinations) with
a single call to get_mvgam_priors
. Here we first simulate
some data in which some of the timepoints in the time
variable are not included in the data:
bad_times <- data.frame(time = seq(1, 16, by = 2),
series = factor('series_1'),
outcome = rnorm(8))
bad_times
Next we call get_mvgam_priors
by simply specifying an
intercept-only model, which is enough to trigger all the checks:
This error is useful as it tells us where the problem is. There are
many ways to fill in missing timepoints, so the correct way will have to
be left up to the user. But if you don’t have any covariates, it should
be pretty easy using expand.grid
:
bad_times %>%
dplyr::right_join(expand.grid(time = seq(min(bad_times$time),
max(bad_times$time)),
series = factor(unique(bad_times$series),
levels = levels(bad_times$series)))) %>%
dplyr::arrange(time) -> good_times
good_times
Now the call to get_mvgam_priors
, using our filled in
data, should work:
This function should also pick up on misaligned factor levels for the
series
variable. We can check this by again simulating,
this time adding an additional factor level that is not included in the
data:
bad_levels <- data.frame(time = 1:8,
series = factor('series_1',
levels = c('series_1',
'series_2')),
outcome = rnorm(8))
levels(bad_levels$series)
Another call to get_mvgam_priors
brings up a useful
error:
Following the message’s advice tells us there is a level for
series_2
in the series
variable, but there are
no observations for this series in the data:
Re-assigning the levels fixes the issue:
NA
sCovariates can be used in models just as you would when using
mgcv
(see ?formula.gam
for details of the
formula syntax). But although the outcome variable can have
NA
s, covariates cannot. Most regression software will
silently drop any raws in the model matrix that have NA
s,
which is not helpful when debugging. Both the mvgam
and
get_mvgam_priors
functions will run some simple checks for
you, and hopefully will return useful errors if it finds in missing
values:
miss_dat <- data.frame(outcome = rnorm(10),
cov = c(NA, rnorm(9)),
series = factor('series1',
levels = 'series1'),
time = 1:10)
miss_dat
Just like with the mgcv
package, mvgam
can
also accept data as a list
object. This is useful if you
want to set up linear
functional predictors or even distributed lag predictors. The checks
run by mvgam
should still work on these data. Here we
change the cov
predictor to be a matrix
:
miss_dat <- list(outcome = rnorm(10),
series = factor('series1',
levels = 'series1'),
time = 1:10)
miss_dat$cov <- matrix(rnorm(50), ncol = 5, nrow = 10)
miss_dat$cov[2,3] <- NA
A call to mvgam
returns the same error:
plot_mvgam_series
Plotting the data is a useful way to ensure everything looks ok, once
you’ve gone throug the above checks on factor levels and timepoint x
series combinations. The plot_mvgam_series
function will
take supplied data and plot either a series of line plots (if you choose
series = 'all'
) or a set of plots to describe the
distribution for a single time series. For example, to plot all of the
time series in our data, and highlight a single series in each plot, we
can use:
Or we can look more closely at the distribution for the first time series:
If you have split your data into training and testing folds (i.e. for forecast evaluation), you can include the test data in your plots:
To give one example of how data can be reformatted for
mvgam
modelling, we will use observations from the National
Ecological Observatory Network (NEON) tick drag cloth samples.
Ixodes scapularis is a widespread tick species capable of
transmitting a diversity of parasites to animals and humans, many of
which are zoonotic. Due to the medical and ecological importance of this
tick species, a common goal is to understand factors that influence
their abundances. The NEON field team carries out standardised long-term monitoring of tick abundances as well as other
important indicators of ecological change. Nymphal abundance of
I. scapularis is routinely recorded across NEON plots using a
field sampling method called drag cloth sampling, which is a common
method for sampling ticks in the landscape. Field researchers sample
ticks by dragging a large cloth behind themselves through terrain that
is suspected of harboring ticks, usually working in a grid-like pattern.
The sites have been sampled since 2014, resulting in a rich dataset of
nymph abundance time series. These tick time series show strong
seasonality and incorporate many of the challenging features associated
with ecological data including overdispersion, high proportions of
missingness and irregular sampling in time, making them useful for
exploring the utility of dynamic GAMs.
We begin by loading NEON tick data for the years 2014 - 2021, which
were downloaded from NEON and prepared as described in Clark & Wells 2022. You can read a bit about the
data using the call ?all_neon_tick_data
For this exercise, we will use the epiWeek
variable as
an index of seasonality, and we will only work with observations from a
few sampling plots (labelled in the plotID
column):
plotIDs <- c('SCBI_013','SCBI_002',
'SERC_001','SERC_005',
'SERC_006','SERC_012',
'BLAN_012','BLAN_005')
Now we can select the target species we want (I.
scapularis), filter to the correct plot IDs and convert the
epiWeek
variable from character
to
numeric
:
model_dat <- all_neon_tick_data %>%
dplyr::ungroup() %>%
dplyr::mutate(target = ixodes_scapularis) %>%
dplyr::filter(plotID %in% plotIDs) %>%
dplyr::select(Year, epiWeek, plotID, target) %>%
dplyr::mutate(epiWeek = as.numeric(epiWeek))
Now is the tricky part: we need to fill in missing observations with
NA
s. The tick data are sparse in that field observers do
not go out and sample in each possible epiWeek
. So there
are many particular weeks in which observations are not included in the
data. But we can use expand.grid
again to take care of
this:
model_dat %>%
# Create all possible combos of plotID, Year and epiWeek;
# missing outcomes will be filled in as NA
dplyr::full_join(expand.grid(plotID = unique(model_dat$plotID),
Year = unique(model_dat$Year),
epiWeek = seq(1, 52))) %>%
# left_join back to original data so plotID and siteID will
# match up, in case you need the siteID for anything else later on
dplyr::left_join(all_neon_tick_data %>%
dplyr::select(siteID, plotID) %>%
dplyr::distinct()) -> model_dat
Create the series
variable needed for mvgam
modelling:
model_dat %>%
dplyr::mutate(series = plotID,
y = target) %>%
dplyr::mutate(siteID = factor(siteID),
series = factor(series)) %>%
dplyr::select(-target, -plotID) %>%
dplyr::arrange(Year, epiWeek, series) -> model_dat
Now create the time
variable, which needs to track
Year
and epiWeek
for each unique series. The
n
function from dplyr
is often useful if
generating a time
index for grouped dataframes:
model_dat %>%
dplyr::ungroup() %>%
dplyr::group_by(series) %>%
dplyr::arrange(Year, epiWeek) %>%
dplyr::mutate(time = seq(1, dplyr::n())) %>%
dplyr::ungroup() -> model_dat
Check factor levels for the series
:
This looks good, as does a more rigorous check using
get_mvgam_priors
:
We can also set up a model in mvgam
but use
run_model = FALSE
to further ensure all of the necessary
steps for creating the modelling code and objects will run. It is
recommended that you use the cmdstanr
backend if possible,
as the auto-formatting options available in this package are very useful
for checking the package-generated Stan
code for any
inefficiencies that can be fixed to lead to sampling performance
improvements:
testmod <- mvgam(y ~ s(epiWeek, by = series, bs = 'cc') +
s(series, bs = 're'),
trend_model = 'AR1',
data = model_dat,
backend = 'cmdstanr',
run_model = FALSE)
This call runs without issue, and the resulting object now contains the model code and data objects that are needed to initiate sampling:
I’m actively seeking PhD students and other researchers to work in
the areas of ecological forecasting, multivariate model evaluation and
development of mvgam
. Please reach out if you are
interested (n.clark’at’uq.edu.au)