Type:	Package
Title:	Multivariate Spatio-Temporal Models using Structural Equations
Version:	1.2.0
Date:	2025-07-19
Description:	Fits a wide variety of multivariate spatio-temporal models with simultaneous and lagged interactions among variables (including vector autoregressive spatio-temporal ('VAST') dynamics) for areal, continuous, or network spatial domains. It includes time-variable, space-variable, and space-time-variable interactions using dynamic structural equation models ('DSEM') as expressive interface, and the 'mgcv' package to specify splines via the formula interface. See Thorson et al. (2024) <doi:10.48550/arXiv.2401.10193> for more details.
License:	GPL-3
Depends:	R (≥ 4.1.0)
Imports:	corpcor, fmesher, igraph, Matrix (≥ 1.3.0), methods, utils, mgcv, sem, sf, sfnetworks, TMB (≥ 1.9.17), units, checkmate, abind, sdmTMB, dsem (≥ 1.6.0), insight, cv
Suggests:	ggplot2, knitr, lattice, mvtnorm, pdp, rmarkdown, rnaturalearth, rnaturalearthdata, testthat, tweedie, viridisLite, visreg, plyr, DHARMa, glmmTMB, tibble,
LinkingTo:	RcppEigen, TMB
VignetteBuilder:	knitr
Config/testthat/edition:	3
Config/testthat/parallel:	true
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.2
URL:	https://vast-lib.github.io/tinyVAST/
BugReports:	https://github.com/vast-lib/tinyVAST/issues
NeedsCompilation:	yes
Packaged:	2025-07-19 22:54:21 UTC; James.Thorson
Author:	James T. Thorson [aut, cre], Sean C. Anderson [aut]
Maintainer:	James T. Thorson <James.Thorson@noaa.gov>
Repository:	CRAN
Date/Publication:	2025-07-19 23:40:03 UTC

Additional families

Description

Additional families compatible with tinyVAST().

Usage

delta_lognormal(link1, link2 = "log", type = c("standard", "poisson-link"))

delta_gamma(link1, link2 = "log", type = c("standard", "poisson-link"))

Arguments

Value

A list with elements common to standard R family objects including family, link, linkfun, and linkinv. Delta/hurdle model families also have elements delta (logical) and type (standard vs. Poisson-link).

References

Poisson-link delta families:

Thorson, J.T. 2018. Three problems with the conventional delta-model for biomass sampling data, and a computationally efficient alternative. Canadian Journal of Fisheries and Aquatic Sciences, 75(9), 1369-1382. doi:10.1139/cjfas-2017-0266

Poisson-link delta families:

Thorson, J.T. 2018. Three problems with the conventional delta-model for biomass sampling data, and a computationally efficient alternative. Canadian Journal of Fisheries and Aquatic Sciences, 75(9), 1369-1382. doi:10.1139/cjfas-2017-0266

Get response

Description

S3 generic from package cv, used for crossvalidation

Usage

## S3 method for class 'tinyVAST'
GetResponse(model, ...)

Arguments

Add predictions to data-list

Description

Given user-provided newdata, expand the object tmb_data to include predictions corresponding to those new observations

Usage

add_predictions(object, newdata, remove_origdata = FALSE)

Arguments

Value

the object fit$tmb_inputs$tmb_data representing data used during fitting, but with updated values for slots associated with predictions, where this updated object can be recompiled by TMB to provide predictions

Survey domain for the eastern and northern Bering Sea surveys

Description

Shapefile defining the spatial domain for the eastern and northern Bering Sea bottom trawl surveys.

Usage

data(bering_sea)

Survey catch-rates at age for Alaska pollock in the Eastern and Northern Bering Sea

Description

Data used to demonstrate and test model-based age expansion, using density= dependence corrected survey catch rates after first=stage expansion from the bottom trawl survey for ages 1-15, conducted by by the Alaska Fisheries Science Center, including annual surveys in the eastern Bering Sea 1982-2019 and 2021-2023, as well as the northern Bering Sea in 1982/85/88/91 and 2010/17/18/19/21/22/23.

Usage

data(bering_sea_pollock_ages)

Estimated proportion-at-age for Alaska pollock using VAST

Description

Estimated proporrtion-at-age for Alaska pollock using the package VAST, for comparison with output using tinyVAST.

Usage

data(bering_sea_pollock_vast)

Calculate conditional AIC

Description

Calculates the conditional Akaike Information criterion (cAIC).

Usage

cAIC(object)

Arguments

Details

cAIC is designed to optimize the expected out-of-sample predictive performance for new data that share the same random effects as the in-sample (fitted) data, e.g., spatial interpolation. In this sense, it should be a fast approximation to optimizing the model structure based on k-fold cross-validation.

By contrast, AIC() calculates the marginal Akaike Information Criterion, which is designed to optimize expected predictive performance for new data that have new random effects, e.g., extrapolation, or inference about generative parameters.

Both cAIC and EDF are calculated using Eq. 6 of Zheng, Cadigan, and Thorson (2024).

For models that include profiled fixed effects, these profiles are turned off.

Value

cAIC value

References

Zheng, N., Cadigan, N., & Thorson, J. T. (2024). A note on numerical evaluation of conditional Akaike information for nonlinear mixed-effects models (arXiv:2411.14185). arXiv. doi:10.48550/arXiv.2411.14185

Examples

data( red_snapper )
red_snapper = droplevels(subset(red_snapper, Data_type=="Biomass_KG"))

# Define mesh
mesh = fmesher::fm_mesh_2d( red_snapper[,c('Lon','Lat')],
                           cutoff = 1 )

# define formula with a catchability covariate for gear
formula = Response_variable ~ factor(Year) + offset(log(AreaSwept_km2))

# make variable column
red_snapper$var = "logdens"
# fit using tinyVAST
fit = tinyVAST( data = red_snapper,
                formula = formula,
                space_term = "logdens <-> logdens, sd_space",
                space_columns = c("Lon",'Lat'),
                spatial_domain = mesh,
                family = tweedie(link="log"),
                variable_column = "var",
                control = tinyVASTcontrol( getsd = FALSE,
                                           profile = "alpha_j" ) )

cAIC(fit) # conditional AIC
AIC(fit) # marginal AIC

Classify variables path

Description

classify_variables is copied from sem:::classifyVariables

Usage

classify_variables(model)

Arguments

Details

Copied from package sem under licence GPL (>= 2) with permission from John Fox

Value

Tagged-list defining exogenous and endogenous variables

Condition and density example

Description

Data used to demonstrate and test a bivariate model for morphometric condition (i.e., residuals in a weight-at-length relationship) and density for fishes, using the same example as was provided as a wiki example for VAST. Data are from doi:10.3354/meps13213

Usage

data(condition_and_density)

Conditional simulation from a GMRF

Description

Generates samples from a Gaussian Markov random field (GMRF) conditional upon fixed values for some elements.

Usage

conditional_gmrf(
  Q,
  observed_idx,
  x_obs,
  n_sims = 1,
  what = c("simulate", "predict")
)

Arguments

Value

A matrix with n_sims columns and a row for every row of Q not in observed_idx, with simulations for those rows

Calculate deviance explained

Description

deviance_explained fits a null model, calculates the deviance relative to a saturated model for both the original and the null model, and uses these to calculate the proportion of deviance explained.

This implementation conditions upon the maximum likelihood estimate of fixed effects and the empirical Bayes ("plug-in") prediction of random effects. It can be described as "conditional deviance explained". A state-space model that estimates measurement error variance approaching zero (i.e., collapses to a process-error-only model) will have a conditional deviance explained that approaches 1.0

Usage

deviance_explained(x, null_formula, null_delta_formula = ~1)

Arguments

Value

the proportion of conditional deviance explained.

Get data

Description

S3 generic from package insight, used for crossvalidation

Usage

## S3 method for class 'tinyVAST'
get_data(x, ...)

Arguments

Integration for target variable

Description

Calculates an estimator for a derived quantity by summing across multiple predictions. This can be used to approximate an integral when estimating area-expanded abundance, abundance-weighting a covariate to calculate distribution shifts, and/or weighting one model variable by another.

Usage

integrate_output(
  object,
  newdata,
  area,
  type = rep(1, nrow(newdata)),
  weighting_index,
  covariate,
  getsd = TRUE,
  bias.correct = TRUE,
  apply.epsilon = FALSE,
  intern = FALSE
)

Arguments

Details

Analysts will often want to calculate some value by combining the predicted response at multiple locations, and potentially from multiple variables in a multivariate analysis. This arises in a univariate model, e.g., when calculating the integral under a predicted density function, which is approximated using a midpoint or Monte Carlo approximation by calculating the linear predictors at each location newdata, applying the inverse-link-trainsformation, and calling this predicted response mu_g. Total abundance is then be approximated by multiplying mu_g by the area associated with each midpoint or Monte Carlo approximation point (supplied by argument area), and summing across these area-expanded values.

In more complicated cases, an analyst can then use covariate to calculate the weighted average of a covariate for each midpoint location. For example, if the covariate is positional coordinates or depth/elevation, then type=2 measures shifts in the average habitat utilization with respect to that covariate. Alternatively, an analyst fitting a multivariate model might weight one variable based on another using weighting_index, e.g., to calculate abundance-weighted average condition, or predator-expanded stomach contents.

In practice, spatial integration in a multivariate model requires two passes through the rows of newdata when calculating a total value. In the following, we write equations using C++ indexing conventions such that indexing starts with 0, to match the way that integrate_output expects indices to be supplied. Given inverse-link-transformed predictor \mu_g , function argument type as type_g function argument area as a_g , function argument covariate as x_g , function argument weighting_index as ⁠\eqn{ h_g }⁠ function argument weighting_index as ⁠\eqn{ h_g }⁠ the first pass calculates:

\nu_g = \mu_g a_g

where the total value from this first pass is calculated as:

\nu^* = \sum_{g=0}^{G-1} \nu_g

The second pass then applies a further weighting, which depends upon type_g , and potentially upon x_g and h_g .

If type_g = 0 then \phi_g = 0

If type_g = 1 then \phi_g = \nu_g

If type_g = 2 then \phi_g = x_g \frac{\nu_g}{\nu^*}

If type_g = 3 then \phi_g = \frac{\nu_{h_g}}{\nu^*} \mu_g

If type_g = 4 then \phi_g = \nu_{h_g} \mu_g

Finally, the total value from this second pass is calculated as:

\phi^* = \sum_{g=0}^{G-1} \phi_g

and \phi^* is outputted by integrate_output, along with a standard error and potentially using the epsilon bias-correction estimator to correct for skewness and retransformation bias.

Standard bias-correction using bias.correct=TRUE can be slow, and in some cases it might be faster to do apply.epsilon=TRUE and intern=TRUE. However, that option is somewhat experimental, and a user might want to confirm that the two options give identical results. Similarly, using bias.correct=TRUE will still calculate the standard-error, whereas using apply.epsilon=TRUE and intern=TRUE will not.

Value

A vector containing the plug-in estimate, standard error, the epsilon bias-corrected estimate if available, and the standard error for the bias-corrected estimator. Depending upon settings, one or more of these will be NA values, and the function can be repeatedly called to get multiple estimators and/or statistics.

Extract the (marginal) log-likelihood of a tinyVAST model

Description

Extract the (marginal) log-likelihood of a tinyVAST model

Usage

## S3 method for class 'tinyVAST'
logLik(object, ...)

Arguments

Value

object of class logLik with attributes

Make a RAM (Reticular Action Model)

Description

make_dsem_ram converts SEM arrow notation to ram describing SEM parameters

Usage

make_dsem_ram(
  dsem,
  times,
  variables,
  covs = NULL,
  quiet = FALSE,
  remove_na = TRUE
)

Arguments

Details

RAM specification using arrow-and-lag notation

Each line of the RAM specification for make_dsem_ram consists of four (unquoted) entries, separated by commas:

1. Arrow specification:

This is a simple formula, of the form A -> B or, equivalently, B <- A for a regression coefficient (i.e., a single-headed or directional arrow); A <-> A for a variance or A <-> B for a covariance (i.e., a double-headed or bidirectional arrow). Here, A and B are variable names in the model. If a name does not correspond to an observed variable, then it is assumed to be a latent variable. Spaces can appear freely in an arrow specification, and there can be any number of hyphens in the arrows, including zero: Thus, e.g., A->B, A --> B, and A>B are all legitimate and equivalent.

2. Lag (using positive values):

An integer specifying whether the linkage is simultaneous (lag=0) or lagged (e.g., X -> Y, 1, XtoY indicates that X in time T affects Y in time T+1), where only one-headed arrows can be lagged. Using positive values to indicate lags then matches the notational convention used in package dynlm.

3. Parameter name:

The name of the regression coefficient, variance, or covariance specified by the arrow. Assigning the same name to two or more arrows results in an equality constraint. Specifying the parameter name as NA produces a fixed parameter.

4. Value:

start value for a free parameter or value of a fixed parameter. If given as NA (or simply omitted), the model is provide a default starting value.

Lines may end in a comment following #. The function extends code copied from package sem under licence GPL (>= 2) with permission from John Fox.

Simultaneous autoregressive process for simultaneous and lagged effects

This text then specifies linkages in a multivariate time-series model for variables \mathbf X with dimensions T \times C for T times and C variables. make_dsem_ram then parses this text to build a path matrix \mathbf P with dimensions TC \times TC, where \rho_{k_2,k_1} represents the impact of x_{t_1,c_1} on x_{t_2,c_2}, where k_1=T c_1+t_1 and k_2=T c_2+t_2. This path matrix defines a simultaneous equation

\mathrm{vec}(\mathbf X) = \mathbf P \mathrm{vec}(\mathbf X) + \mathrm{vec}(\mathbf \Delta)

where \mathbf \Delta is a matrix of exogenous errors with covariance \mathbf{V = \Gamma \Gamma}^t, where \mathbf \Gamma is the Cholesky of exogenous covariance. This simultaneous autoregressive (SAR) process then results in \mathbf X having covariance:

\mathrm{Cov}(\mathbf X) = \mathbf{(I - P)}^{-1} \mathbf{\Gamma \Gamma}^t \mathbf{((I - P)}^{-1})^t

Usefully, it is also easy to compute the inverse-covariance (precision) matrix \mathbf{Q = V}^{-1}:

\mathbf{Q} = (\mathbf{\Gamma}^{-1} \mathbf{(I - P)})^t \mathbf{\Gamma}^{-1} \mathbf{(I - P)}

Example: univariate and first-order autoregressive model

This simultaneous autoregressive (SAR) process across variables and times allows the user to specify both simultaneous effects (effects among variables within year T) and lagged effects (effects among variables among years T). As one example, consider a univariate and first-order autoregressive process where T=4. with independent errors. This is specified by passing dsem = X -> X, 1, rho; X <-> X, 0, sigma to make_dsem_ram. This is then parsed to a RAM:

Rows of this RAM where heads=1 are then interpreted to construct the path matrix \mathbf P:

\deqn{ \mathbf P = \begin{bmatrix}
    0 & 0 & 0 & 0 \
    \rho & 0 & 0 & 0 \
    0 & \rho & 0 & 0 \
    0 & 0 & \rho & 0\
    \end{bmatrix} }

While rows where heads=2 are interpreted to construct the Cholesky of exogenous covariance \mathbf \Gamma:

\deqn{ \mathbf \Gamma = \begin{bmatrix}
    \sigma & 0 & 0 & 0 \
    0 & \sigma & 0 & 0 \
    0 & 0 & \sigma & 0 \
    0 & 0 & 0 & \sigma\
    \end{bmatrix} }

with two estimated parameters \mathbf \beta = (\rho, \sigma) . This then results in covariance:

\deqn{ \mathrm{Cov}(\mathbf X) = \sigma^2 \begin{bmatrix}
    1 & \rho^1 & \rho^2 & \rho^3 \
    \rho^1 & 1 & \rho^1 & \rho^2 \
    \rho^2 & \rho^1 & 1 & \rho^1 \
    \rho^3 & \rho^2 & \rho^1 & 1\
    \end{bmatrix} }

Similarly, the arrow-and-lag notation can be used to specify a SAR representing a conventional structural equation model (SEM), cross-lagged (a.k.a. vector autoregressive) models (VAR), dynamic factor analysis (DFA), or many other time-series models.

Value

A reticular action module (RAM) describing dependencies

Examples

# Univariate AR1
dsem = "
  X -> X, 1, rho
  X <-> X, 0, sigma
"
make_dsem_ram( dsem=dsem, variables="X", times=1:4 )

# Univariate AR2
dsem = "
  X -> X, 1, rho1
  X -> X, 2, rho2
  X <-> X, 0, sigma
"
make_dsem_ram( dsem=dsem, variables="X", times=1:4 )

# Bivariate VAR
dsem = "
  X -> X, 1, XtoX
  X -> Y, 1, XtoY
  Y -> X, 1, YtoX
  Y -> Y, 1, YtoY
  X <-> X, 0, sdX
  Y <-> Y, 0, sdY
"
make_dsem_ram( dsem=dsem, variables=c("X","Y"), times=1:4 )

# Dynamic factor analysis with one factor and two manifest variables
# (specifies a random-walk for the factor, and miniscule residual SD)
dsem = "
  factor -> X, 0, loadings1
  factor -> Y, 0, loadings2
  factor -> factor, 1, NA, 1
  X <-> X, 0, NA, 0           # No additional variance
  Y <-> Y, 0, NA, 0           # No additional variance
"
make_dsem_ram( dsem=dsem, variables=c("X","Y","factor"), times=1:4 )

# ARIMA(1,1,0)
dsem = "
  factor -> factor, 1, rho1 # AR1 component
  X -> X, 1, NA, 1          # Integrated component
  factor -> X, 0, NA, 1
  X <-> X, 0, NA, 0         # No additional variance
"
make_dsem_ram( dsem=dsem, variables=c("X","factor"), times=1:4 )

# ARIMA(0,0,1)
dsem = "
  factor -> X, 0, NA, 1
  factor -> X, 1, rho1     # MA1 component
  X <-> X, 0, NA, 0        # No additional variance
"
make_dsem_ram( dsem=dsem, variables=c("X","factor"), times=1:4 )

Make a RAM (Reticular Action Model)

Description

make_eof_ram converts SEM arrow notation to ram describing SEM parameters

Usage

make_eof_ram(
  times,
  variables,
  n_eof,
  remove_na = TRUE,
  standard_deviations = "unequal"
)

Arguments

Value

A reticular action module (RAM) describing dependencies

Examples

# Two EOFs for two variables
make_eof_ram( times = 2010:2020, variables = c("pollock","cod"), n_eof=2 )

Make a RAM (Reticular Action Model) from a SEM (structural equation model)

Description

make_sem_ram converts SEM arrow notation to ram describing SEM parameters

Usage

make_sem_ram(sem, variables, quiet = FALSE, covs = variables)

Arguments

Value

An S3-class "sem_ram" containing:

model

Output from specifyEquations or specifyModel that defines paths and parameters

ram

reticular action module (RAM) describing dependencies

Parse path

Description

parse_path is copied from sem::parse.path

Usage

parse_path(path)

Arguments

Details

Copied from package sem under licence GPL (>= 2) with permission from John Fox

Value

Tagged-list defining variables and direction for a specified path coefficient

Predict using vector autoregressive spatio-temporal model

Description

Predicts values given new covariates using a tinyVAST model

Usage

## S3 method for class 'tinyVAST'
predict(
  object,
  newdata,
  remove_origdata = FALSE,
  what = c("mu_g", "p_g", "palpha_g", "pgamma_g", "pepsilon_g", "pomega_g", "pdelta_g",
    "pxi_g", "p2_g", "palpha2_g", "pgamma2_g", "pepsilon2_g", "pomega2_g", "pdelta2_g",
    "pxi2_g"),
  se.fit = FALSE,
  bias.correct = FALSE,
  ...
)

Arguments

Value

Either a vector with the prediction for each row of newdata, or a named list with the prediction and standard error (when se.fit = TRUE).

print summary of tinyVAST model

Description

print summary of tinyVAST model

Usage

## S3 method for class 'tinyVAST'
print(x, ...)

Arguments

Value

invisibly returns a named list of key model outputs and summary statements

Project tinyVAST to future times (EXPERIMENTAL)

Description

Projects a fitted model forward in time.

Usage

project(
  object,
  extra_times,
  newdata,
  what = "mu_g",
  future_var = TRUE,
  past_var = FALSE,
  parm_var = FALSE
)

Arguments

Value

A vector of values corresponding to rows in newdata

Examples

# Convert to long-form
set.seed(123)
n_obs = 100
rho = 0.9
sigma_x = 0.2
sigma_y = 0.1
x = rnorm(n_obs, mean=0, sd = sigma_x)
for(i in 2:length(x)) x[i] = rho * x[i-1] + x[i]
y = x + rnorm( length(x), mean = 0, sd = sigma_y )
data = data.frame( "val" = y, "var" = "y", "time" = seq_along(y) )

# Define AR2 time_term
time_term = "
  y -> y, 1, rho1
  y -> y, 2, rho2
  y <-> y, 0, sd
"

# fit model
mytiny = tinyVAST(
  time_term = time_term,
  data = data,
  times = unique(data$t),
  variables = "y",
  formula = val ~ 1,
  control = tinyVASTcontrol( getJointPrecision = TRUE )
)

# Deterministic projection
extra_times = length(x) + 1:100
n_sims = 10
newdata = data.frame( "time" = c(seq_along(x),extra_times), "var" = "y" )
Y = project(
  mytiny,
  newdata = newdata,
  extra_times = extra_times,
  future_var = FALSE
)
plot( x = seq_along(Y),
      y = Y,
      type = "l", lty = "solid", col = "black" )

# Stochastic projection with future process errors
## Not run: 
extra_times = length(x) + 1:100
n_sims = 10
newdata = data.frame( "time" = c(seq_along(x),extra_times), "var" = "y" )
Y = NULL
for(i in seq_len(n_sims) ){
  tmp = project(
    mytiny,
    newdata = newdata,
    extra_times = extra_times,
    future_var = TRUE,
    past_var = TRUE,
    parm_var = TRUE
  )
  Y = cbind(Y, tmp)
}
matplot( x = row(Y),
         y = Y,
         type = "l", lty = "solid", col = "black" )

## End(Not run)

Presence/absence, count, and biomass data for red snapper

Description

Data used to demonstrate and test analysis using multiple data types

Usage

data(red_snapper)

Shapefile for red snapper analysis

Description

Spatial extent used for red snapper analysis, derived from Chap-7 of doi:10.1201/9781003410294

Usage

data(red_snapper_shapefile)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

sdmTMB

lognormal, nbinom1, nbinom2, tweedie

Reload a previously fitted model

Description

reload_model allows a user to save a fitted model, reload it in a new R terminal, and then relink the DLLs so that it functions as expected.

Usage

reload_model(x, check_gradient = TRUE)

Arguments

Value

Output from tinyVAST with DLLs relinked

Calculate deviance or response residuals for tinyVAST

Description

Calculate residuals

Usage

## S3 method for class 'tinyVAST'
residuals(object, type = c("deviance", "response"), ...)

Arguments

Value

a vector residuals, associated with each row of data supplied during fitting

Multivariate Normal Random Deviates using Sparse Precision

Description

This function provides a random number generator for the multivariate normal distribution with mean equal to mu and sparse precision matrix prec.

Usage

rmvnorm_prec(prec, n = 1, mu = rep(0, nrow(prec)))

Arguments

Value

a matrix with dimension length(mu) by n, containing realized draws from the specified mean and precision

Rotate factors to match Principal-Components Analysis

Description

Rotate lower-triangle loadings matrix to order factors from largest to smallest variance.

Usage

rotate_pca(
  L_tf,
  x_sf = matrix(0, nrow = 0, ncol = ncol(L_tf)),
  order = c("none", "increasing", "decreasing")
)

Arguments

Value

List containing the rotated loadings L_tf, the inverse-rotated response matrix x_sf, and the rotation H

North Pacific salmon returns

Description

Data used to demonstrate and test multivariate second-order autoregressive models using a simultaneous autoregressive (SAR) process across regions. Data are from doi:10.1002/mcf2.10023

Usage

data(salmon_returns)

Sample from predictive distribution of a variable

Description

sample_variable samples from the joint distribution of random and fixed effects to approximate the predictive distribution for a variable

Using sample_fixed=TRUE (the default) in sample_variable propagates variance in both fixed and random effects, while using sample_fixed=FALSE does not. Sampling fixed effects will sometimes cause numerical under- or overflow (i.e., output values of NA) in cases when variance parameters are estimated imprecisely. In these cases, the multivariate normal approximation being used is a poor representation of the tail probabilities, and results in some samples with implausibly high (or negative) variances, such that the associated random effects then have implausibly high magnitude.

Usage

sample_variable(
  object,
  newdata = NULL,
  variable_name = "mu_i",
  n_samples = 100,
  sample_fixed = TRUE,
  seed = 123456
)

Arguments

Value

A matrix with a row for each data supplied during fitting, and n_samples columns, where each column in a vector of samples for a requested quantity given sampled uncertainty in fixed and/or random effects

Examples

 set.seed(101)
 x = runif(n = 100, min = 0, max = 2*pi)
 y = 1 + sin(x) + 0.1 * rnorm(100)

 # Do fit with getJointPrecision=TRUE
 fit = tinyVAST( formula = y ~ s(x),
                 data = data.frame(x=x,y=y) )

 # samples from distribution for the mean
 # excluding fixed effects due to CRAN checks
 samples = sample_variable(fit, sample_fixed = FALSE)

Arctic September sea ice concentrations

Description

Data used to demonstrate and test empirical orthogonal function generalized linear latent variable model (EOF-GLLVM)

Usage

data(sea_ice)

Construct projection matrix for stream network

Description

Make sparse matrix to project from stream-network nodes to user-supplied points

Usage

sfnetwork_evaluator(stream, loc, tolerance = 0.01)

Arguments

Value

the sparse interpolation matrix, with rows for each row of data supplied during fitting and columns for each spatial random effect.

Make mesh for stream network

Description

make an object representing spatial information required to specify a stream-network spatial domain, similar in usage to link[fmesher]{fm_mesh_2d} for a 2-dimensional continuous domain

Usage

sfnetwork_mesh(stream)

Arguments

Value

An object (list) of class sfnetwork_mesh. Elements include:

N

The number of random effects used to represent the network

table

a table containing a description of parent nodes (from), childen nodes (to), and the distance separating them

stream

copy of the stream network object passed as argument

Simulate new data from a fitted model

Description

simulate.tinyVAST is an S3 method for producing a matrix of simulations from a fitted model. It can be used with the DHARMa package among other uses. Code is modified from the version in sdmTMB

Usage

## S3 method for class 'tinyVAST'
simulate(
  object,
  nsim = 1L,
  seed = sample.int(1e+06, 1L),
  type = c("mle-eb", "mle-mvn"),
  ...
)

Arguments

Value

A matrix with row for each row of data in the fitted model and nsim columns, containing new samples from the fitted model.

Examples

set.seed(101)
x = seq(0, 2*pi, length=100)
y = sin(x) + 0.1*rnorm(length(x))
fit = tinyVAST( data=data.frame(x=x,y=y), formula = y ~ s(x) )
sims = simulate(fit, nsim=100, type="mle-mvn")

if(requireNamespace("DHARMa")){
  # simulate new data conditional on fixed effects
  # and sampling random effects from their predictive distribution
  y_iz = simulate(fit, nsim=500, type="mle-mvn")

  # Visualize using DHARMa
  res = DHARMa::createDHARMa( simulatedResponse = y_iz,
                      observedResponse = y,
                      fittedPredictedResponse = fitted(fit) )
  plot(res)
}

Simulate GMRF for stream network

Description

Simulate values from a GMRF using a tail-down (flow-unconnected) exponential model on a stream network

Usage

simulate_sfnetwork(sfnetwork_mesh, theta, n = 1, what = c("samples", "Q"))

Arguments

Value

a matrix of simulated values for a Gaussian Markov random field arising from a stream-network spatial domain, with row for each spatial random effect and n columns, using the sparse precision matrix defined in Charsley et al. (2023)

References

Charsley, A. R., Gruss, A., Thorson, J. T., Rudd, M. B., Crow, S. K., David, B., Williams, E. K., & Hoyle, S. D. (2023). Catchment-scale stream network spatio-temporal models, applied to the freshwater stages of a diadromous fish species, longfin eel (Anguilla dieffenbachii). Fisheries Research, 259, 106583. doi:10.1016/j.fishres.2022.106583

summarize tinyVAST

Description

summarize parameters from a fitted tinyVAST

Usage

## S3 method for class 'tinyVAST'
summary(
  object,
  what = c("space_term", "time_term", "spacetime_term", "fixed"),
  predictor = c("one", "two"),
  ...
)

Arguments

Details

tinyVAST includes three components:

Space-variable interaction

a separable Gaussian Markov random field (GMRF) constructed from a structural equation model (SEM) and a spatial variable

Space-variable-time interaction

a separable GMRF constructed from a a dynamic SEM (a nonseparable time-variable interaction) and a spatial variable

Additive variation

a generalized additive model (GAM), representing exogenous covariates

Each of these are summarized and interpreted differently, and summary.tinyVAST facilitates this.

Regarding the DSEM componennt, tinyVAST includes an "arrow and lag" notation, which specifies the set of path coefficients and exogenous variance parameters to be estimated. Function tinyVAST then estimates the maximum likelihood value for those coefficients and parameters by maximizing the log-marginal likelihood.

However, many users will want to associate individual parameters and standard errors with the path coefficients that were specified using the "arrow and lag" notation. This task is complicated in models where some path coefficients or variance parameters are specified to share a single value a priori, or were assigned a name of NA and hence assumed to have a fixed value a priori (such that these coefficients or parameters have an assigned value but no standard error). The summary function therefore compiles the MLE for coefficients (including duplicating values for any path coefficients that assigned the same value) and standard error estimates, and outputs those in a table that associates them with the user-supplied path and parameter names. It also outputs the z-score and a p-value arising from a two-sided Wald test (i.e. comparing the estimate divided by standard error against a standard normal distribution).

Value

A data-frame containing the estimate (and standard errors, two-sided Wald-test z-value, and associated p-value if the standard errors are available) for model parameters, including the fixed-effects specified via formula, or the path coefficients for the spatial SEM specified via space_term, the dynamic SEM specified via time_term, or the spatial dynamic SEM specified via spacetime_term

Extract covariance

Description

Extract the covariance resulting from a specified path structure and estimated parameters for a SEM or DSEM term in tinyVAST

Usage

term_covariance(
  object,
  what = c("space_term", "time_term", "spacetime_term"),
  pred = c("one", "two"),
  n_times = NULL
)

Arguments

Details

tinyVAST constructs the covariance from specified path structure and estimated parameters

Value

The covariance matrix among variables

Examples

# Extract covariance for spatial factor analysis (too slow for CRAN)

# Simulate settings
set.seed(101)
theta_xy = 0.4
n_x = n_y = 10
n_c = 3           # Number of species
n_f = 1           # Number of factors
rho = 0.8
resid_sd = 0.5

# Simulate GMRFs
R_s = exp(-theta_xy * abs(outer(1:n_x, 1:n_y, FUN="-")) )
R_ss = kronecker(X=R_s, Y=R_s)
delta_fs = mvtnorm::rmvnorm(n_c, sigma=R_ss )

# Simulate loadings for two factors
L_cf = matrix( rnorm(n_c^2), nrow=n_c )
L_cf[,seq(from=n_f+1, to=n_c)] = 0
L_cf = L_cf + resid_sd * diag(n_c)

# Simulate correlated densities
d_cs = L_cf %*% delta_fs

# Shape into longform data-frame and add error
Data = data.frame( expand.grid(species=1:n_c, x=1:n_x, y=1:n_y),
                   "var"="logn", "z"=exp(as.vector(d_cs)) )
Data$n = rnorm( n=nrow(Data), mean=Data$z, sd=1 )

# make mesh
mesh = fmesher::fm_mesh_2d( Data[,c('x','y')] )

# Specify factor model with two factors and additional independent variance with shared SD
sem = "
  # Loadings matrix
  f1 -> 1, l1
  f1 -> 2, l2
  f1 -> 3, l3

  # Factor variance = 1
  f1 <-> f1, NA, 1

  # Shared residual variance
  1 <-> 1, sd, 1
  2 <-> 2, sd, 1
  3 <-> 3, sd, 1
"

# fit model
out = tinyVAST( space_term = sem,
           data = Data,
           formula = n ~ 0 + factor(species),
           spatial_domain = mesh,
           variables = c( "f1", "f2", 1:n_c ),
           space_columns = c("x","y"),
           variable_column = "species",
           time_column = "time",
           distribution_column = "dist" )

# Extract covariance among species and factors, where
# estimated covariance is obtained by ignoring factors
V = term_covariance( out, what = "space_term", pred = "one" )

Fit vector autoregressive spatio-temporal model

Description

Fits a vector autoregressive spatio-temporal (VAST) model using a minimal feature-set and a widely used interface.

Usage

tinyVAST(
  formula,
  data,
  time_term = NULL,
  space_term = NULL,
  spacetime_term = NULL,
  family = gaussian(),
  space_columns = c("x", "y"),
  spatial_domain = NULL,
  time_column = "time",
  times = NULL,
  variable_column = "var",
  variables = NULL,
  distribution_column = "dist",
  delta_options = list(formula = ~1),
  spatial_varying = NULL,
  weights = NULL,
  control = tinyVASTcontrol()
)

Arguments

Details

tinyVAST includes several basic inputs that specify the model structure:

• formula specifies covariates and splines in a Generalized Additive Model;

• time_term specifies interactions among variables and over time that are constant across space, constructing the time-variable interaction.

• space_term specifies interactions among variables and over time that occur based on the variable values at each location, constructing the space-variable interaction.

• spacetime_term specifies interactions among variables and over time, constructing the space-time-variable interaction.

These inputs require defining the domain of the model. This includes:

• spatial_domain specifies spatial domain, with determines spatial correlations

• times specifies the temporal domain, i.e., sequence of time-steps

• variables specifies the set of variables, i.e., the variables that will be modeled

The default spacetime_term=NULL and space_term=NULL turns off all multivariate and temporal indexing, such that spatial_domain is then ignored, and the model collapses to a generalized additive model using gam. To specify a univariate spatial model, the user must specify spatial_domain and either space_term="" or spacetime_term="", where the latter two are then parsed to include a single exogenous variance for the single variable

Model building notes

• ⁠binomial familes⁠: A binomial family can be specified in only one way: the response is the observed proportion (proportion = successes / trials), and the 'weights' argument is used to specify the Binomial size (trials, N) parameter (⁠proportion ~ ..., weights = N⁠).

• ⁠factor models⁠: If a factor model is desired, the factor(s) must be named and included in the variables. The factor is then modeled for space_term, time_term, and spacetime_term and it's variance must be fixed a priori for any term where it is not being used.

Value

An object (list) of class tinyVAST. Elements include:

data

Data-frame supplied during model fitting

spatial_domain

the spatial domain supplied during fitting

formula

the formula specified during model fitting

obj

The TMB object from MakeADFun

opt

The output from nlminb

opt

The report from obj$report()

sdrep

The output from sdreport

tmb_inputs

The list of inputs passed to MakeADFun

call

A record of the function call

run_time

Total time to run model

interal

Objects useful for package function, i.e., all arguments passed during the call

deviance_explained

output from deviance_explained

See Also

Details section of make_dsem_ram() for a summary of the math involved with constructing the DSEM, and doi:10.1111/2041-210X.14289 for more background on math and inference

doi:10.48550/arXiv.2401.10193 for more details on how GAM, SEM, and DSEM components are combined from a statistical and software-user perspective

summary.tinyVAST() to visualize parameter estimates related to SEM and DSEM model components

Examples

# Simulate a seperable two-dimensional AR1 spatial process
n_x = n_y = 25
n_w = 10
R_xx = exp(-0.4 * abs(outer(1:n_x, 1:n_x, FUN="-")) )
R_yy = exp(-0.4 * abs(outer(1:n_y, 1:n_y, FUN="-")) )
z = mvtnorm::rmvnorm(1, sigma=kronecker(R_xx,R_yy) )

# Simulate nuissance parameter z from oscillatory (day-night) process
w = sample(1:n_w, replace=TRUE, size=length(z))
Data = data.frame( expand.grid(x=1:n_x, y=1:n_y), w=w, z=as.vector(z) + cos(w/n_w*2*pi))
Data$n = Data$z + rnorm(nrow(Data), sd=1)

# Add columns for multivariate and/or temporal dimensions
Data$var = "n"

# make SPDE mesh for spatial term
mesh = fmesher::fm_mesh_2d( Data[,c('x','y')], n=100 )

# fit model with cyclic confounder as GAM term
out = tinyVAST( data = Data,
                formula = n ~ s(w),
                spatial_domain = mesh,
                space_term = "n <-> n, sd_n" )

# Run crossvalidation (too slow for CRAN)

CV = cv::cv( out, k = 4 )
CV

Control parameters for tinyVAST

Description

Control parameters for tinyVAST

Usage

tinyVASTcontrol(
  nlminb_loops = 1,
  newton_loops = 0,
  eval.max = 1000,
  iter.max = 1000,
  getsd = TRUE,
  silent = getOption("tinyVAST.silent", TRUE),
  trace = getOption("tinyVAST.trace", 0),
  verbose = getOption("tinyVAST.verbose", FALSE),
  profile = c(),
  tmb_par = NULL,
  tmb_map = NULL,
  gmrf_parameterization = c("separable", "projection"),
  reml = FALSE,
  getJointPrecision = FALSE,
  calculate_deviance_explained = TRUE,
  run_model = TRUE,
  suppress_nlminb_warnings = TRUE,
  suppress_user_warnings = FALSE,
  get_rsr = FALSE,
  extra_reporting = FALSE,
  use_anisotropy = FALSE,
  sar_adjacency = "queen"
)

Arguments

Value

An object (list) of class tinyVASTcontrol, containing either default or updated values supplied by the user for model settings

Extract Variance-Covariance Matrix

Description

extract the covariance of fixed effects, or both fixed and random effects.

Usage

## S3 method for class 'tinyVAST'
vcov(object, which = c("fixed", "random", "both"), ...)

Arguments

Value

A square matrix containing the estimated covariances among the parameter estimates in the model. The dimensions dependend upon the argument which, to determine whether fixed, random effects, or both are outputted.