glmSTARMA (version 1.0.0)

glmstarma.sim: Simulate spatial time-series based on generalized linear models

Description

Generates a simulated multivariate time series based on a GLM-like model (see glmstarma for details)

Usage

glmstarma.sim(
  ntime,
  parameters,
  model,
  family = NULL,
  wlist,
  covariates = list(),
  wlist_past_mean = NULL,
  wlist_covariates = NULL,
  n_start = 100L,
  control = list()
)

Value

a named list with the following elements:

• observations (numeric matrix): The simulated time series

• link_values (numeric matrix): The underlying linear predictor resulting from the model and simulation

• model (list): The model used for the simulation

• parameters (list): The true parameters used for the simulation

Arguments

ntime

Number of observation times to be simulated

parameters

a named list specifying the parameters of the model to be simulated, which has the following elements:

• intercept (numeric): Intercept parameter. If an inhomogeneous model is simulated, a value must be specified for each component of the time series.

• past_obs (numeric matrix): Parameter values for the past observations.

• past_mean (numeric matrix): Parameter values for the past means.

• covariates (numeric matrix): Parameter values for the covariates.

model

a named list specifying the model for the linear predictor, which can be of the following elements:

• intercept (character): 'homogenous' (default) for a homogenous model, i.e. the same intercept for all components, 'inhomogenous' for inhomogenous models, i.e. an individual intercept for each component.

• past_obs (integer vector/binary matrix): Maximal spatial orders for the time lags in past_obs_time_lags. A binary matrix can be passed as an alternative, with the entry in row \(i\) and column \(j\) indicating whether the \((i - 1)\)-spatial lag for the \(j\)-th time lag is included in the model. If not specified, no regression on past observations is performed.

• past_obs_time_lags (optional integer vector) indicates the time lags for regression on past observations. Defaults are seq(length(past_obs)) (for vectors) and seq(ncol(past_obs)) (for a matrix)

• past_mean (integer vector/binary matrix): Spatial orders for the regression on the (latent) feedback process. Values can be entered in the same format as in past_obs. If not specified, no regression to the feedback process is performed.

• past_mean_time_lags (optional integer vector) indicates the time lags for regression on past values of the feedback process. Defaults are seq(length(past_mean)) (for vectors) and seq(ncol(past_mean)) (for a matrix)

• covariates (integer vector/binary matrix) spatial orders for the covariate processes passed in the argument covariates. The values can be passed as in past_obs and past_means, where the jth entry or column represents the jth covariable. If no values are specified but covariates are included, the spatial order 0 is used by default, which corresponds to the first matrix in argument wlist_covariates.

family

An object of class stfamily that specifies the marginal distributions and the type of model fitted.

wlist

A list of quadratic matrices, with the same dimension as the time series, which describe the spatial dependencies. Row-normalized matrices are recommended.

covariates

List of covariates, containing matrices or returns of the covariate functions of this package (see also TimeConstant, SpatialConstant). The matrices must have the same dimension as ts

wlist_past_mean

(Optional) List of matrices, which describes spatial dependencies for the past mean. If this is NULL, the matrices from wlist are used.

wlist_covariates

(Optional) List of matrices, which describes spatial dependencies for the covariates. If this is NULL, the matrices from wlist are used.

n_start

Number of observations to be used for the burn-in period

control

A list of parameters for controlling the fitting process. This list is passed to glmstarma.control.

Examples

set.seed(42)
n_obs <- 200L
W <- generateW("rectangle", 100, 2, 10)
model_orders <- list(intercept = "homogeneous", past_obs = 2, past_mean = 1)
parameter <- list(intercept = 0.5, past_obs = matrix(c(0.3, 0.2, 0.05), nrow = 3), 
                  past_mean = matrix(c(0.1, 0.05), nrow = 2),
                  covariates = c(0.75, 0.5))
covariates <- list(season = SpatialConstant(sin(2* pi / 12 * seq(n_obs))),
                   location = TimeConstant(rnorm(100, sd = 0.81)))
# Simulation using marginal poisson distribution
glmstarma.sim(n_obs, parameter, model_orders, W, covariates, family = vpoisson("log"))
# Simulation using negative binomial marginals
glmstarma.sim(n_obs, parameter, model_orders, W, covariates, 
              family = vnegative.binomial(dispersion = 3))