Fit a Bayesian multivariate dynamic linear model with Stan that optionally includes covariates to estimate effects, extremes (Student-t distribution), etc.
The model formula for the fixed effects; at least this formula or time_varying needs to have the response included
The model formula for the time-varying effects; at least this formula or formula needs to have the response included
String describing the name of the variable corresponding to time, defaults to "year"
Whether or not to estimate deviations of B as Student - t with estimated degrees of freedom, defaults to FALSE
The name of the family used for the response; can be one of "normal","binomial","possion","nbinom2","gamma","lognormal"
Whether to estimate time-varying parameters as correlated random walk, defaults to TRUE
The data frame including response and covariates for all model components
Number of mcmc chains, defaults to 3
Number of mcmc iterations, defaults to 2000
Number iterations for mcmc warmup, defaults to 1/2 of the iterations
Any other arguments to pass to rstan::sampling().
A list containing the fitted model and arguments and data used
to fit the model. These include model (the fitted model object of class stanfit),
# \donttest{
set.seed(123)
N = 20
data = data.frame("y" = runif(N),
"cov1" = rnorm(N),
"cov2" = rnorm(N),
"year" = 1:N,
"season" = sample(c("A","B"), size=N, replace=TRUE))
b_1 = cumsum(rnorm(N))
b_2 = cumsum(rnorm(N))
data$y = data$cov1*b_1 + data$cov2*b_2
time_varying = y ~ cov1 + cov2
formula = NULL
# fit a model with a time varying component
fit <- fit_dlm(formula = formula,
time_varying = time_varying,
time = "year",
est_df = FALSE,
family = c("normal"),
data=data, chains = 1, iter = 20)
#>
#> SAMPLING FOR MODEL 'dlm' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.001949 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 19.49 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: WARNING: No variance estimation is
#> Chain 1: performed for num_warmup < 20
#> Chain 1:
#> Chain 1: Iteration: 1 / 20 [ 5%] (Warmup)
#> Chain 1: Iteration: 2 / 20 [ 10%] (Warmup)
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#> Chain 1:
#> Chain 1: Elapsed Time: 1.353 seconds (Warm-up)
#> Chain 1: 1.388 seconds (Sampling)
#> Chain 1: 2.741 seconds (Total)
#> Chain 1:
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
# fit a model with a time varying and fixed component (here, fixed intercept)
fit <- fit_dlm(formula = y ~ 1,
time_varying = y ~ -1 + cov1 + cov2,
time = "year",
est_df = FALSE,
family = c("normal"),
data=data, chains = 1, iter = 20)
#>
#> SAMPLING FOR MODEL 'dlm' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.002437 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 24.37 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: WARNING: No variance estimation is
#> Chain 1: performed for num_warmup < 20
#> Chain 1:
#> Chain 1: Iteration: 1 / 20 [ 5%] (Warmup)
#> Chain 1: Iteration: 2 / 20 [ 10%] (Warmup)
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#> Chain 1: Iteration: 20 / 20 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.742 seconds (Warm-up)
#> Chain 1: 1.185 seconds (Sampling)
#> Chain 1: 1.927 seconds (Total)
#> Chain 1:
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
#' # fit a model with deviations modeled with a multivariate Student-t
fit <- fit_dlm(formula = y ~ 1,
time_varying = y ~ -1 + cov1 + cov2,
time = "year",
est_df = TRUE,
family = c("normal"),
data=data, chains = 1, iter = 20)
#>
#> SAMPLING FOR MODEL 'dlm' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.001717 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 17.17 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: WARNING: No variance estimation is
#> Chain 1: performed for num_warmup < 20
#> Chain 1:
#> Chain 1: Iteration: 1 / 20 [ 5%] (Warmup)
#> Chain 1: Iteration: 2 / 20 [ 10%] (Warmup)
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#> Chain 1: Iteration: 20 / 20 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.522 seconds (Warm-up)
#> Chain 1: 1.387 seconds (Sampling)
#> Chain 1: 1.909 seconds (Total)
#> Chain 1:
#> Warning: There were 2 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
#' #' # fit a model with deviations modeled with a multivariate Student-t
fit <- fit_dlm(formula = y ~ 1,
time_varying = y ~ -1 + cov1 + cov2,
time = "year",
est_df = TRUE,
family = c("normal"),
data=data, chains = 1, iter = 20)
#>
#> SAMPLING FOR MODEL 'dlm' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.001618 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 16.18 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: WARNING: No variance estimation is
#> Chain 1: performed for num_warmup < 20
#> Chain 1:
#> Chain 1: Iteration: 1 / 20 [ 5%] (Warmup)
#> Chain 1: Iteration: 2 / 20 [ 10%] (Warmup)
#> Chain 1: Iteration: 4 / 20 [ 20%] (Warmup)
#> Chain 1: Iteration: 6 / 20 [ 30%] (Warmup)
#> Chain 1: Iteration: 8 / 20 [ 40%] (Warmup)
#> Chain 1: Iteration: 10 / 20 [ 50%] (Warmup)
#> Chain 1: Iteration: 11 / 20 [ 55%] (Sampling)
#> Chain 1: Iteration: 12 / 20 [ 60%] (Sampling)
#> Chain 1: Iteration: 14 / 20 [ 70%] (Sampling)
#> Chain 1: Iteration: 16 / 20 [ 80%] (Sampling)
#> Chain 1: Iteration: 18 / 20 [ 90%] (Sampling)
#> Chain 1: Iteration: 20 / 20 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 4.432 seconds (Warm-up)
#> Chain 1: 2.939 seconds (Sampling)
#> Chain 1: 7.371 seconds (Total)
#> Chain 1:
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
# }